[{"data":1,"prerenderedAt":27930},["ShallowReactive",2],{"navigation_docs":3,"learnalog_locale_counterpart__en_microeconomics_02-comparative-statics":1782,"-zh-microeconomics-02-comparative-statics":1783,"-zh-microeconomics-02-comparative-statics-surround":27925},[4,1038],{"title":5,"path":6,"stem":7,"children":8},"En","\u002Fen","en",[9,12,58,250,406,477,534,715,798,824,943],{"title":10,"path":6,"stem":11},"","en\u002Findex",{"title":13,"path":14,"stem":15,"children":16},"Research Skills and Academic Writing","\u002Fen\u002Facademic-writing","en\u002Facademic-writing\u002Findex",[17,18,22,26,30,34,38,42,46,50,54],{"title":13,"path":14,"stem":15},{"title":19,"path":20,"stem":21},"1. Research Questions, Scope, and Feasibility","\u002Fen\u002Facademic-writing\u002F01-research-questions-and-planning","en\u002Facademic-writing\u002F01-research-questions-and-planning",{"title":23,"path":24,"stem":25},"2. Search, Evaluate, and Read Evidence","\u002Fen\u002Facademic-writing\u002F02-reading-and-literature-matrix","en\u002Facademic-writing\u002F02-reading-and-literature-matrix",{"title":27,"path":28,"stem":29},"3. From Sources to Synthesis and Argument","\u002Fen\u002Facademic-writing\u002F03-arguments-outlines-and-paragraphs","en\u002Facademic-writing\u002F03-arguments-outlines-and-paragraphs",{"title":31,"path":32,"stem":33},"4. Literature Review and a Defensible Gap","\u002Fen\u002Facademic-writing\u002F04-writing-the-literature-review","en\u002Facademic-writing\u002F04-writing-the-literature-review",{"title":35,"path":36,"stem":37},"5. Research Design, Evidence, and Core Sections","\u002Fen\u002Facademic-writing\u002F05-core-sections-and-evidence","en\u002Facademic-writing\u002F05-core-sections-and-evidence",{"title":39,"path":40,"stem":41},"6. Citation, Paraphrasing, Integrity, and AI","\u002Fen\u002Facademic-writing\u002F06-citation-paraphrasing-and-integrity","en\u002Facademic-writing\u002F06-citation-paraphrasing-and-integrity",{"title":43,"path":44,"stem":45},"7. Revision, Review, and Submission","\u002Fen\u002Facademic-writing\u002F07-revision-style-and-submission","en\u002Facademic-writing\u002F07-revision-style-and-submission",{"title":47,"path":48,"stem":49},"8. Research Workbook","\u002Fen\u002Facademic-writing\u002F08-literature-review-checklist-and-template","en\u002Facademic-writing\u002F08-literature-review-checklist-and-template",{"title":51,"path":52,"stem":53},"9. Research Workflow and Tools","\u002Fen\u002Facademic-writing\u002F09-tools-for-academic-writing-and-literature-management","en\u002Facademic-writing\u002F09-tools-for-academic-writing-and-literature-management",{"title":55,"path":56,"stem":57},"10. Worked Project — From Question to Defensible Conclusion","\u002Fen\u002Facademic-writing\u002F10-worked-example-from-block-structure-to-question-chain","en\u002Facademic-writing\u002F10-worked-example-from-block-structure-to-question-chain",{"title":59,"path":60,"stem":61,"children":62,"page":249},"Accounting","\u002Fen\u002Faccounting","en\u002Faccounting",[63,69,87,93,193],{"title":64,"path":65,"stem":66,"children":67},"Accounting — From Evidence to Decisions","\u002Fen\u002Faccounting\u002F00-index","en\u002Faccounting\u002F00-index",[68],{"title":64,"path":65,"stem":66},{"title":70,"path":71,"stem":72,"children":73},"Accounting Appendix","\u002Fen\u002Faccounting\u002Fappendix","en\u002Faccounting\u002Fappendix\u002Findex",[74,75,79,83],{"title":70,"path":71,"stem":72},{"title":76,"path":77,"stem":78},"Worked Examples and Error Diagnosis","\u002Fen\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls","en\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls",{"title":80,"path":81,"stem":82},"Accounting Glossary","\u002Fen\u002Faccounting\u002Fappendix\u002F26-glossary","en\u002Faccounting\u002Fappendix\u002F26-glossary",{"title":84,"path":85,"stem":86},"Reading and Evidence Map","\u002Fen\u002Faccounting\u002Fappendix\u002F27-reading-map","en\u002Faccounting\u002Fappendix\u002F27-reading-map",{"title":88,"path":89,"stem":90,"children":91},"Northstar Record-to-Decision Capstone","\u002Fen\u002Faccounting\u002Fcapstone","en\u002Faccounting\u002Fcapstone\u002Findex",[92],{"title":88,"path":89,"stem":90},{"title":94,"path":95,"stem":96,"children":97},"Financial Accounting","\u002Fen\u002Faccounting\u002Ffinancial-accounting","en\u002Faccounting\u002Ffinancial-accounting\u002Findex",[98,99,117,131,165,179],{"title":94,"path":95,"stem":96},{"title":100,"path":101,"stem":102,"children":103},"1. Foundations","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002Findex",[104,105,109,113],{"title":100,"path":101,"stem":102},{"title":106,"path":107,"stem":108},"Objectives and Qualitative Characteristics","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics",{"title":110,"path":111,"stem":112},"Equation and Elements","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements",{"title":114,"path":115,"stem":116},"Accrual Basis, Estimates and Periods","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles",{"title":118,"path":119,"stem":120,"children":121},"2. Recording Transactions","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002Findex",[122,123,127],{"title":118,"path":119,"stem":120},{"title":124,"path":125,"stem":126},"Double-Entry and Debit\u002FCredit","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr",{"title":128,"path":129,"stem":130},"Accounting Cycle","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle",{"title":132,"path":133,"stem":134,"children":135},"3. Measurement and Adjustments","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002Findex",[136,137,141,145,149,153,157,161],{"title":132,"path":133,"stem":134},{"title":138,"path":139,"stem":140},"Revenue Recognition","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition",{"title":142,"path":143,"stem":144},"Inventory","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory",{"title":146,"path":147,"stem":148},"Receivables and Expected Credit Losses","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables",{"title":150,"path":151,"stem":152},"Property, Plant and Equipment","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe",{"title":154,"path":155,"stem":156},"Intangible Assets","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles",{"title":158,"path":159,"stem":160},"Leases","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases",{"title":162,"path":163,"stem":164},"Current and Deferred Income Tax","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax",{"title":166,"path":167,"stem":168,"children":169},"4. Reporting and Cash","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002Findex",[170,171,175],{"title":166,"path":167,"stem":168},{"title":172,"path":173,"stem":174},"Linked Financial Statements","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements",{"title":176,"path":177,"stem":178},"Cash, Reconciliation and Internal Control","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control",{"title":180,"path":181,"stem":182,"children":183},"5. Analysis and Comparison","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002Findex",[184,185,189],{"title":180,"path":181,"stem":182},{"title":186,"path":187,"stem":188},"Ratio Analysis","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis",{"title":190,"path":191,"stem":192},"IFRS versus US GAAP","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap",{"title":194,"path":195,"stem":196,"children":197},"Management Accounting","\u002Fen\u002Faccounting\u002Fmanagement-accounting","en\u002Faccounting\u002Fmanagement-accounting\u002Findex",[198,199,217,235],{"title":194,"path":195,"stem":196},{"title":200,"path":201,"stem":202,"children":203},"1. Cost Foundations","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002Findex",[204,205,209,213],{"title":200,"path":201,"stem":202},{"title":206,"path":207,"stem":208},"Cost Concepts and Behaviour","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts",{"title":210,"path":211,"stem":212},"Costing Systems","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems",{"title":214,"path":215,"stem":216},"Variable and Absorption Costing","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption",{"title":218,"path":219,"stem":220,"children":221},"2. Planning and Control","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002Findex",[222,223,227,231],{"title":218,"path":219,"stem":220},{"title":224,"path":225,"stem":226},"Cost–Volume–Profit Analysis","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis",{"title":228,"path":229,"stem":230},"Budgeting and Variance Analysis","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances",{"title":232,"path":233,"stem":234},"Performance Measurement","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement",{"title":236,"path":237,"stem":238,"children":239},"3. Decisions and Investment","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002Findex",[240,241,245],{"title":236,"path":237,"stem":238},{"title":242,"path":243,"stem":244},"Short-Term Decisions","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions",{"title":246,"path":247,"stem":248},"Capital Budgeting","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting",false,{"title":251,"path":252,"stem":253,"children":254,"page":249},"Business Analytics","\u002Fen\u002Fbusiness-analytics","en\u002Fbusiness-analytics",[255,261,279,305,335,365,383,400],{"title":256,"path":257,"stem":258,"children":259},"Business Analytics — From Data to Defensible Action","\u002Fen\u002Fbusiness-analytics\u002F00-index","en\u002Fbusiness-analytics\u002F00-index",[260],{"title":256,"path":257,"stem":258},{"title":262,"path":263,"stem":264,"children":265},"0. Decision and Data Foundations","\u002Fen\u002Fbusiness-analytics\u002F00-intro","en\u002Fbusiness-analytics\u002F00-intro\u002Findex",[266,267,271,275],{"title":262,"path":263,"stem":264},{"title":268,"path":269,"stem":270},"Decision Framing","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F01-decision-framing","en\u002Fbusiness-analytics\u002F00-intro\u002F01-decision-framing",{"title":272,"path":273,"stem":274},"Data Contracts","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F02-data-contracts","en\u002Fbusiness-analytics\u002F00-intro\u002F02-data-contracts",{"title":276,"path":277,"stem":278},"Reproducible Analytics Workflow","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F03-reproducible-workflow","en\u002Fbusiness-analytics\u002F00-intro\u002F03-reproducible-workflow",{"title":280,"path":281,"stem":282,"children":283},"1. Descriptive Analytics","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive","en\u002Fbusiness-analytics\u002F01-descriptive\u002Findex",[284,285,289,293,297,301],{"title":280,"path":281,"stem":282},{"title":286,"path":287,"stem":288},"Distributions and Exploratory Data Analysis","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F04-distributions-eda","en\u002Fbusiness-analytics\u002F01-descriptive\u002F04-distributions-eda",{"title":290,"path":291,"stem":292},"KPIs and Denominators","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F05-kpis-denominators","en\u002Fbusiness-analytics\u002F01-descriptive\u002F05-kpis-denominators",{"title":294,"path":295,"stem":296},"Segments, Cohorts and Funnels","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F06-segmentation-cohorts-funnels","en\u002Fbusiness-analytics\u002F01-descriptive\u002F06-segmentation-cohorts-funnels",{"title":298,"path":299,"stem":300},"Visual Evidence and Data Stories","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F07-visualisation-story","en\u002Fbusiness-analytics\u002F01-descriptive\u002F07-visualisation-story",{"title":302,"path":303,"stem":304},"Experiments and Causal Boundaries","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F08-experiments-causal-boundary","en\u002Fbusiness-analytics\u002F01-descriptive\u002F08-experiments-causal-boundary",{"title":306,"path":307,"stem":308,"children":309},"2. Predictive Analytics","\u002Fen\u002Fbusiness-analytics\u002F02-predictive","en\u002Fbusiness-analytics\u002F02-predictive\u002Findex",[310,311,315,319,323,327,331],{"title":306,"path":307,"stem":308},{"title":312,"path":313,"stem":314},"Validation, Baselines and Leakage","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F09-validation-leakage","en\u002Fbusiness-analytics\u002F02-predictive\u002F09-validation-leakage",{"title":316,"path":317,"stem":318},"Regression and Forecasting","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F10-regression-forecasting","en\u002Fbusiness-analytics\u002F02-predictive\u002F10-regression-forecasting",{"title":320,"path":321,"stem":322},"Classification and Calibration","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F11-classification-calibration","en\u002Fbusiness-analytics\u002F02-predictive\u002F11-classification-calibration",{"title":324,"path":325,"stem":326},"Trees and Ensembles","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F12-trees-ensembles","en\u002Fbusiness-analytics\u002F02-predictive\u002F12-trees-ensembles",{"title":328,"path":329,"stem":330},"Decision Metrics and Thresholds","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F13-decision-metrics-thresholds","en\u002Fbusiness-analytics\u002F02-predictive\u002F13-decision-metrics-thresholds",{"title":332,"path":333,"stem":334},"Explainability, Monitoring and Drift","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F14-explainability-drift","en\u002Fbusiness-analytics\u002F02-predictive\u002F14-explainability-drift",{"title":336,"path":337,"stem":338,"children":339},"3. Prescriptive Analytics","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive","en\u002Fbusiness-analytics\u002F03-prescriptive\u002Findex",[340,341,345,349,353,357,361],{"title":336,"path":337,"stem":338},{"title":342,"path":343,"stem":344},"Decision-Making under Uncertainty","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F15-decision-uncertainty","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F15-decision-uncertainty",{"title":346,"path":347,"stem":348},"Linear Optimisation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F16-linear-optimization","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F16-linear-optimization",{"title":350,"path":351,"stem":352},"Inventory and Allocation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F17-inventory-allocation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F17-inventory-allocation",{"title":354,"path":355,"stem":356},"Queueing and Simulation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F18-queueing-simulation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F18-queueing-simulation",{"title":358,"path":359,"stem":360},"Pricing and Revenue Management","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F19-pricing-experimentation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F19-pricing-experimentation",{"title":362,"path":363,"stem":364},"Causal Targeting and Policy Learning","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F20-causal-targeting","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F20-causal-targeting",{"title":366,"path":367,"stem":368,"children":369},"4. Deployment and Governance","\u002Fen\u002Fbusiness-analytics\u002F04-deployment","en\u002Fbusiness-analytics\u002F04-deployment\u002Findex",[370,371,375,379],{"title":366,"path":367,"stem":368},{"title":372,"path":373,"stem":374},"Data Products and Monitoring","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F21-data-products-monitoring","en\u002Fbusiness-analytics\u002F04-deployment\u002F21-data-products-monitoring",{"title":376,"path":377,"stem":378},"Governance, Fairness and Privacy","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F22-governance-fairness-privacy","en\u002Fbusiness-analytics\u002F04-deployment\u002F22-governance-fairness-privacy",{"title":380,"path":381,"stem":382},"Adoption and Business Value","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F23-adoption-value","en\u002Fbusiness-analytics\u002F04-deployment\u002F23-adoption-value",{"title":384,"path":385,"stem":386,"children":387},"Appendix and Revision Tools","\u002Fen\u002Fbusiness-analytics\u002Fappendix","en\u002Fbusiness-analytics\u002Fappendix\u002Findex",[388,389,393,397],{"title":384,"path":385,"stem":386},{"title":390,"path":391,"stem":392},"Formula and Decision Map","\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F24-formula-map","en\u002Fbusiness-analytics\u002Fappendix\u002F24-formula-map",{"title":394,"path":395,"stem":396},"Worked Examples and Pitfalls","\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F25-worked-examples-pitfalls","en\u002Fbusiness-analytics\u002Fappendix\u002F25-worked-examples-pitfalls",{"title":84,"path":398,"stem":399},"\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F26-reading-map","en\u002Fbusiness-analytics\u002Fappendix\u002F26-reading-map",{"title":401,"path":402,"stem":403,"children":404},"Capstone — The Evening Delivery Promise","\u002Fen\u002Fbusiness-analytics\u002Fcapstone","en\u002Fbusiness-analytics\u002Fcapstone\u002Findex",[405],{"title":401,"path":402,"stem":403},{"title":407,"path":408,"stem":409,"children":410,"page":249},"Financial Economic Time Series","\u002Fen\u002Ffinancial-economic-time-series","en\u002Ffinancial-economic-time-series",[411,417,423,429,435,441,447,453,459,465,471],{"title":412,"path":413,"stem":414,"children":415},"Financial and Economic Time Series — Course Guide","\u002Fen\u002Ffinancial-economic-time-series\u002F00-intro","en\u002Ffinancial-economic-time-series\u002F00-intro\u002Findex",[416],{"title":412,"path":413,"stem":414},{"title":418,"path":419,"stem":420,"children":421},"Three Versions of Time Series","\u002Fen\u002Ffinancial-economic-time-series\u002F01-bridge","en\u002Ffinancial-economic-time-series\u002F01-bridge\u002Findex",[422],{"title":418,"path":419,"stem":420},{"title":424,"path":425,"stem":426,"children":427},"Data, Clocks, and Transformations","\u002Fen\u002Ffinancial-economic-time-series\u002F02-data-transformations","en\u002Ffinancial-economic-time-series\u002F02-data-transformations\u002Findex",[428],{"title":424,"path":425,"stem":426},{"title":430,"path":431,"stem":432,"children":433},"Predictive Regressions and Persistent Predictors","\u002Fen\u002Ffinancial-economic-time-series\u002F03-predictive-regressions","en\u002Ffinancial-economic-time-series\u002F03-predictive-regressions\u002Findex",[434],{"title":430,"path":431,"stem":432},{"title":436,"path":437,"stem":438,"children":439},"Volatility, Tails, and Financial Risk","\u002Fen\u002Ffinancial-economic-time-series\u002F04-volatility-risk","en\u002Ffinancial-economic-time-series\u002F04-volatility-risk\u002Findex",[440],{"title":436,"path":437,"stem":438},{"title":442,"path":443,"stem":444,"children":445},"Unit Roots, Cointegration, and Error Correction","\u002Fen\u002Ffinancial-economic-time-series\u002F05-unit-roots-cointegration","en\u002Ffinancial-economic-time-series\u002F05-unit-roots-cointegration\u002Findex",[446],{"title":442,"path":443,"stem":444},{"title":448,"path":449,"stem":450,"children":451},"VAR, Structural Identification, and Local Projections","\u002Fen\u002Ffinancial-economic-time-series\u002F06-var-identification","en\u002Ffinancial-economic-time-series\u002F06-var-identification\u002Findex",[452],{"title":448,"path":449,"stem":450},{"title":454,"path":455,"stem":456,"children":457},"State Space, Mixed Frequency, and Nowcasting","\u002Fen\u002Ffinancial-economic-time-series\u002F07-state-space-nowcasting","en\u002Ffinancial-economic-time-series\u002F07-state-space-nowcasting\u002Findex",[458],{"title":454,"path":455,"stem":456},{"title":460,"path":461,"stem":462,"children":463},"Forecast Evaluation for Decisions","\u002Fen\u002Ffinancial-economic-time-series\u002F08-forecast-evaluation","en\u002Ffinancial-economic-time-series\u002F08-forecast-evaluation\u002Findex",[464],{"title":460,"path":461,"stem":462},{"title":466,"path":467,"stem":468,"children":469},"Integrated R Laboratory","\u002Fen\u002Ffinancial-economic-time-series\u002F09-r-laboratory","en\u002Ffinancial-economic-time-series\u002F09-r-laboratory\u002Findex",[470],{"title":466,"path":467,"stem":468},{"title":472,"path":473,"stem":474,"children":475},"Capstones, Data, and Reading Ladder","\u002Fen\u002Ffinancial-economic-time-series\u002F10-capstone-readings","en\u002Ffinancial-economic-time-series\u002F10-capstone-readings\u002Findex",[476],{"title":472,"path":473,"stem":474},{"title":478,"path":479,"stem":480,"children":481,"page":249},"Intro To Economics","\u002Fen\u002Fintro-to-economics","en\u002Fintro-to-economics",[482,486,490,494,498,502,506,510,514,518,522,526,530],{"title":483,"path":484,"stem":485},"Introduction to Economics — Decisions, Markets, and the Macroeconomy","\u002Fen\u002Fintro-to-economics\u002F00-intro","en\u002Fintro-to-economics\u002F00-intro",{"title":487,"path":488,"stem":489},"Chapter 1 — Choice, Opportunity Cost, and Trade","\u002Fen\u002Fintro-to-economics\u002F01-foundations","en\u002Fintro-to-economics\u002F01-foundations",{"title":491,"path":492,"stem":493},"Chapter 2 — Demand, Supply, Equilibrium, and Welfare","\u002Fen\u002Fintro-to-economics\u002F02-demand-and-supply","en\u002Fintro-to-economics\u002F02-demand-and-supply",{"title":495,"path":496,"stem":497},"Chapter 3 — Elasticity, Revenue, and Tax Incidence","\u002Fen\u002Fintro-to-economics\u002F03-elasticity","en\u002Fintro-to-economics\u002F03-elasticity",{"title":499,"path":500,"stem":501},"Chapter 4 — Firms, Market Power, and Market Failure","\u002Fen\u002Fintro-to-economics\u002F04-market-structures","en\u002Fintro-to-economics\u002F04-market-structures",{"title":503,"path":504,"stem":505},"Chapter 5 — GDP, Income, Wealth, and Welfare","\u002Fen\u002Fintro-to-economics\u002F05-gdp-and-wealth","en\u002Fintro-to-economics\u002F05-gdp-and-wealth",{"title":507,"path":508,"stem":509},"Chapter 6 — Inflation, Purchasing Power, and Labour Markets","\u002Fen\u002Fintro-to-economics\u002F06-inflation-and-unemployment","en\u002Fintro-to-economics\u002F06-inflation-and-unemployment",{"title":511,"path":512,"stem":513},"Chapter 7 — Productivity, Technology, and Economic Growth","\u002Fen\u002Fintro-to-economics\u002F07-economic-growth","en\u002Fintro-to-economics\u002F07-economic-growth",{"title":515,"path":516,"stem":517},"Chapter 8 — Money, Credit, and Banking","\u002Fen\u002Fintro-to-economics\u002F08-money-and-banking","en\u002Fintro-to-economics\u002F08-money-and-banking",{"title":519,"path":520,"stem":521},"Chapter 9 — Business Cycles, AD–AS, and Monetary Policy","\u002Fen\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as","en\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as",{"title":523,"path":524,"stem":525},"Chapter 10 — Fiscal Policy, Distribution, and Public Debt","\u002Fen\u002Fintro-to-economics\u002F10-fiscal-policy","en\u002Fintro-to-economics\u002F10-fiscal-policy",{"title":527,"path":528,"stem":529},"Chapter 11 — Trade, Capital Flows, and Exchange Rates","\u002Fen\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates","en\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates",{"title":531,"path":532,"stem":533},"Chapter 12 — Integrated Economic Analysis Studio","\u002Fen\u002Fintro-to-economics\u002F12-review-and-case-studies","en\u002Fintro-to-economics\u002F12-review-and-case-studies",{"title":535,"path":536,"stem":537,"children":538,"page":249},"Microeconometrics","\u002Fen\u002Fmicroeconometrics","en\u002Fmicroeconometrics",[539,557,563,581,603,629,651,673,691,709],{"title":540,"path":541,"stem":542,"children":543},"0. Causal Questions and Designs","\u002Fen\u002Fmicroeconometrics\u002F00-foundations","en\u002Fmicroeconometrics\u002F00-foundations\u002Findex",[544,545,549,553],{"title":540,"path":541,"stem":542},{"title":546,"path":547,"stem":548},"Causal Questions and Estimands","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F01-causal-question-estimands","en\u002Fmicroeconometrics\u002F00-foundations\u002F01-causal-question-estimands",{"title":550,"path":551,"stem":552},"Potential Outcomes and Experiments","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F02-potential-outcomes-experiments","en\u002Fmicroeconometrics\u002F00-foundations\u002F02-potential-outcomes-experiments",{"title":554,"path":555,"stem":556},"Causal Diagrams and Controls","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F03-dags-controls","en\u002Fmicroeconometrics\u002F00-foundations\u002F03-dags-controls",{"title":558,"path":559,"stem":560,"children":561},"Microeconometrics — Designing Credible Counterfactuals","\u002Fen\u002Fmicroeconometrics\u002F00-index","en\u002Fmicroeconometrics\u002F00-index",[562],{"title":558,"path":559,"stem":560},{"title":564,"path":565,"stem":566,"children":567},"1. Regression and Inference","\u002Fen\u002Fmicroeconometrics\u002F01-regression","en\u002Fmicroeconometrics\u002F01-regression\u002Findex",[568,569,573,577],{"title":564,"path":565,"stem":566},{"title":570,"path":571,"stem":572},"OLS as a Projection","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F04-ols-projection","en\u002Fmicroeconometrics\u002F01-regression\u002F04-ols-projection",{"title":574,"path":575,"stem":576},"FWL, Selection and Controls","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F05-fwl-selection-controls","en\u002Fmicroeconometrics\u002F01-regression\u002F05-fwl-selection-controls",{"title":578,"path":579,"stem":580},"Inference and Clustering","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F06-inference-clustering","en\u002Fmicroeconometrics\u002F01-regression\u002F06-inference-clustering",{"title":582,"path":583,"stem":584,"children":585},"2. Instruments and Panel Data","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel","en\u002Fmicroeconometrics\u002F02-iv-panel\u002Findex",[586,587,591,595,599],{"title":582,"path":583,"stem":584},{"title":588,"path":589,"stem":590},"Instrumental Variables","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F07-iv-identification","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F07-iv-identification",{"title":592,"path":593,"stem":594},"Weak Instruments and LATE","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F08-weak-iv-late","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F08-weak-iv-late",{"title":596,"path":597,"stem":598},"Panel Fixed Effects","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F09-panel-fixed-effects","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F09-panel-fixed-effects",{"title":600,"path":601,"stem":602},"Dynamic Panels and Limits","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F10-dynamic-panel","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F10-dynamic-panel",{"title":604,"path":605,"stem":606,"children":607},"3. Policy Evaluation Designs","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs","en\u002Fmicroeconometrics\u002F03-policy-designs\u002Findex",[608,609,613,617,621,625],{"title":604,"path":605,"stem":606},{"title":610,"path":611,"stem":612},"Difference-in-Differences","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F11-did-core","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F11-did-core",{"title":614,"path":615,"stem":616},"Staggered DID and Event Studies","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F12-staggered-event-studies","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F12-staggered-event-studies",{"title":618,"path":619,"stem":620},"Regression Discontinuity","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F13-rdd","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F13-rdd",{"title":622,"path":623,"stem":624},"Matching, Weighting and Overlap","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F14-matching-weighting","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F14-matching-weighting",{"title":626,"path":627,"stem":628},"Synthetic Control","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F15-synthetic-control","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F15-synthetic-control",{"title":630,"path":631,"stem":632,"children":633},"Module 4 — Choice and Limited Outcomes","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002Findex",[634,635,639,643,647],{"title":630,"path":631,"stem":632},{"title":636,"path":637,"stem":638},"Binary Choice","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F16-binary-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F16-binary-choice",{"title":640,"path":641,"stem":642},"Multinomial and Ordered Choice","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F17-multinomial-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F17-multinomial-choice",{"title":644,"path":645,"stem":646},"Count Outcomes","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F18-count-outcomes","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F18-count-outcomes",{"title":648,"path":649,"stem":650},"Censoring, Truncation and Selection","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F19-censoring-selection","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F19-censoring-selection",{"title":652,"path":653,"stem":654,"children":655},"Module 5 — Modern Causal Analysis","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal","en\u002Fmicroeconometrics\u002F05-modern-causal\u002Findex",[656,657,661,665,669],{"title":652,"path":653,"stem":654},{"title":658,"path":659,"stem":660},"Double Machine Learning","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F20-dml","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F20-dml",{"title":662,"path":663,"stem":664},"Heterogeneity and Policy Learning","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F21-heterogeneity-policy","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F21-heterogeneity-policy",{"title":666,"path":667,"stem":668},"Sensitivity and Partial Identification","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F22-sensitivity-partial-id","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F22-sensitivity-partial-id",{"title":670,"path":671,"stem":672},"External Validity and Transport","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F23-external-validity","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F23-external-validity",{"title":674,"path":675,"stem":676,"children":677},"Module 6 — From Data to Auditable Evidence","\u002Fen\u002Fmicroeconometrics\u002F06-workflow","en\u002Fmicroeconometrics\u002F06-workflow\u002Findex",[678,679,683,687],{"title":674,"path":675,"stem":676},{"title":680,"path":681,"stem":682},"Data Provenance","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F24-data-provenance","en\u002Fmicroeconometrics\u002F06-workflow\u002F24-data-provenance",{"title":684,"path":685,"stem":686},"Reproducibility and Reporting","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F25-reproducibility-reporting","en\u002Fmicroeconometrics\u002F06-workflow\u002F25-reproducibility-reporting",{"title":688,"path":689,"stem":690},"Paper and Evidence Audit","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F26-paper-audit","en\u002Fmicroeconometrics\u002F06-workflow\u002F26-paper-audit",{"title":692,"path":693,"stem":694,"children":695},"Appendix — Revision and Evidence Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix","en\u002Fmicroeconometrics\u002Fappendix\u002Findex",[696,697,701,705],{"title":692,"path":693,"stem":694},{"title":698,"path":699,"stem":700},"Formula and Design Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F27-formula-design-map","en\u002Fmicroeconometrics\u002Fappendix\u002F27-formula-design-map",{"title":702,"path":703,"stem":704},"Ten Worked Microeconometric Pitfalls","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F28-worked-pitfalls","en\u002Fmicroeconometrics\u002Fappendix\u002F28-worked-pitfalls",{"title":706,"path":707,"stem":708},"Reading and Software Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F29-reading-software-map","en\u002Fmicroeconometrics\u002Fappendix\u002F29-reading-software-map",{"title":710,"path":711,"stem":712,"children":713},"Capstone — Should Northbridge Expand Pathways?","\u002Fen\u002Fmicroeconometrics\u002Fcapstone","en\u002Fmicroeconometrics\u002Fcapstone\u002Findex",[714],{"title":710,"path":711,"stem":712},{"title":716,"path":717,"stem":718,"children":719,"page":249},"Microeconomics","\u002Fen\u002Fmicroeconomics","en\u002Fmicroeconomics",[720,726,732,738,744,750,756,762,768,774,780,786,792],{"title":721,"path":722,"stem":723,"children":724},"Advanced Microeconomics — Course Guide","\u002Fen\u002Fmicroeconomics\u002F00-intro","en\u002Fmicroeconomics\u002F00-intro\u002Findex",[725],{"title":721,"path":722,"stem":723},{"title":727,"path":728,"stem":729,"children":730},"Module 1 — Choice, Duality, and Revealed Preference","\u002Fen\u002Fmicroeconomics\u002F01-fundations","en\u002Fmicroeconomics\u002F01-fundations\u002Findex",[731],{"title":727,"path":728,"stem":729},{"title":733,"path":734,"stem":735,"children":736},"Module 2 — Comparative Statics and Welfare Measurement","\u002Fen\u002Fmicroeconomics\u002F02-comparative-statics","en\u002Fmicroeconomics\u002F02-comparative-statics\u002Findex",[737],{"title":733,"path":734,"stem":735},{"title":739,"path":740,"stem":741,"children":742},"Module 3 — Choice under Risk and Insurance","\u002Fen\u002Fmicroeconomics\u002F03-uncertainty","en\u002Fmicroeconomics\u002F03-uncertainty\u002Findex",[743],{"title":739,"path":740,"stem":741},{"title":745,"path":746,"stem":747,"children":748},"Module 4 — General Equilibrium and Welfare","\u002Fen\u002Fmicroeconomics\u002F04-general-equilibrium","en\u002Fmicroeconomics\u002F04-general-equilibrium\u002Findex",[749],{"title":745,"path":746,"stem":747},{"title":751,"path":752,"stem":753,"children":754},"Module 5 — Static, Dynamic, and Repeated Games","\u002Fen\u002Fmicroeconomics\u002F05-game-theory","en\u002Fmicroeconomics\u002F05-game-theory\u002Findex",[755],{"title":751,"path":752,"stem":753},{"title":757,"path":758,"stem":759,"children":760},"Module 6 — Oligopoly, Entry, and Algorithmic Pricing","\u002Fen\u002Fmicroeconomics\u002F06-oligopoly","en\u002Fmicroeconomics\u002F06-oligopoly\u002Findex",[761],{"title":757,"path":758,"stem":759},{"title":763,"path":764,"stem":765,"children":766},"Module 7 — Information Economics and Contracts","\u002Fen\u002Fmicroeconomics\u002F07-information-economics","en\u002Fmicroeconomics\u002F07-information-economics\u002Findex",[767],{"title":763,"path":764,"stem":765},{"title":769,"path":770,"stem":771,"children":772},"Module 8 — Mechanism Design and Auctions","\u002Fen\u002Fmicroeconomics\u002F08-mechanism-design","en\u002Fmicroeconomics\u002F08-mechanism-design\u002Findex",[773],{"title":769,"path":770,"stem":771},{"title":775,"path":776,"stem":777,"children":778},"Module 9 — Behavioural and Experimental Microeconomics","\u002Fen\u002Fmicroeconomics\u002F09-behavioural-economics","en\u002Fmicroeconomics\u002F09-behavioural-economics\u002Findex",[779],{"title":775,"path":776,"stem":777},{"title":781,"path":782,"stem":783,"children":784},"Module 10 — Externalities, Public Goods, and Collective Action","\u002Fen\u002Fmicroeconomics\u002F10-externalities-public-goods","en\u002Fmicroeconomics\u002F10-externalities-public-goods\u002Findex",[785],{"title":781,"path":782,"stem":783},{"title":787,"path":788,"stem":789,"children":790},"Module 11 — Matching and Market Design","\u002Fen\u002Fmicroeconomics\u002F11-market-design","en\u002Fmicroeconomics\u002F11-market-design\u002Findex",[791],{"title":787,"path":788,"stem":789},{"title":793,"path":794,"stem":795,"children":796},"Module 12 — Integrated Microeconomic Design Studio","\u002Fen\u002Fmicroeconomics\u002F12-review","en\u002Fmicroeconomics\u002F12-review\u002Findex",[797],{"title":793,"path":794,"stem":795},{"title":799,"path":800,"stem":801,"children":802},"Playground","\u002Fen\u002Fplayground","en\u002Fplayground\u002Findex",[803,804,808,812,816,820],{"title":799,"path":800,"stem":801},{"title":805,"path":806,"stem":807},"Typst Plugin Playground","\u002Fen\u002Fplayground\u002F01-typstex","en\u002Fplayground\u002F01-typstex",{"title":809,"path":810,"stem":811},"Citation Plugin Test","\u002Fen\u002Fplayground\u002F02-citation","en\u002Fplayground\u002F02-citation",{"title":813,"path":814,"stem":815},"Pyodide Playground","\u002Fen\u002Fplayground\u002F03-pyodide","en\u002Fplayground\u002F03-pyodide",{"title":817,"path":818,"stem":819},"WebR Playground","\u002Fen\u002Fplayground\u002F04-webr","en\u002Fplayground\u002F04-webr",{"title":821,"path":822,"stem":823},"Chart.js Visualizations","\u002Fen\u002Fplayground\u002F05-chartjs","en\u002Fplayground\u002F05-chartjs",{"title":825,"path":826,"stem":827,"children":828,"page":249},"Statistics For Insurance","\u002Fen\u002Fstatistics-for-insurance","en\u002Fstatistics-for-insurance",[829,835,857,883,905,927,937],{"title":830,"path":831,"stem":832,"children":833},"Statistics for General Insurance","\u002Fen\u002Fstatistics-for-insurance\u002F01-intro","en\u002Fstatistics-for-insurance\u002F01-intro\u002Findex",[834],{"title":830,"path":831,"stem":832},{"title":836,"path":837,"stem":838,"children":839},"Claims Development and Reserving","\u002Fen\u002Fstatistics-for-insurance\u002F02-chain-ladder","en\u002Fstatistics-for-insurance\u002F02-chain-ladder\u002Findex",[840,841,845,849,853],{"title":836,"path":837,"stem":838},{"title":842,"path":843,"stem":844},"Basic Chain Ladder","\u002Fen\u002Fstatistics-for-insurance\u002F02-chain-ladder\u002F01-basic-chain","en\u002Fstatistics-for-insurance\u002F02-chain-ladder\u002F01-basic-chain",{"title":846,"path":847,"stem":848},"Frequency–Severity Reserving","\u002Fen\u002Fstatistics-for-insurance\u002F02-chain-ladder\u002F02-average-per-claim","en\u002Fstatistics-for-insurance\u002F02-chain-ladder\u002F02-average-per-claim",{"title":850,"path":851,"stem":852},"Bornhuetter–Ferguson Method","\u002Fen\u002Fstatistics-for-insurance\u002F02-chain-ladder\u002F03-b-f-method","en\u002Fstatistics-for-insurance\u002F02-chain-ladder\u002F03-b-f-method",{"title":854,"path":855,"stem":856},"Uncertainty and Diagnostics","\u002Fen\u002Fstatistics-for-insurance\u002F02-chain-ladder\u002F04-uncertainty-diagnostics","en\u002Fstatistics-for-insurance\u002F02-chain-ladder\u002F04-uncertainty-diagnostics",{"title":858,"path":859,"stem":860,"children":861},"Frequency and Severity Models","\u002Fen\u002Fstatistics-for-insurance\u002F03-common-dist","en\u002Fstatistics-for-insurance\u002F03-common-dist\u002Findex",[862,863,867,871,875,879],{"title":858,"path":859,"stem":860},{"title":864,"path":865,"stem":866},"Core Severity Models","\u002Fen\u002Fstatistics-for-insurance\u002F03-common-dist\u002F01-loss-dist","en\u002Fstatistics-for-insurance\u002F03-common-dist\u002F01-loss-dist",{"title":868,"path":869,"stem":870},"Tail Models and Extreme Values","\u002Fen\u002Fstatistics-for-insurance\u002F03-common-dist\u002F02-more-dist","en\u002Fstatistics-for-insurance\u002F03-common-dist\u002F02-more-dist",{"title":872,"path":873,"stem":874},"Claim Count Models","\u002Fen\u002Fstatistics-for-insurance\u002F03-common-dist\u002F03-case-dist","en\u002Fstatistics-for-insurance\u002F03-common-dist\u002F03-case-dist",{"title":876,"path":877,"stem":878},"Fitting and Validating Loss Models","\u002Fen\u002Fstatistics-for-insurance\u002F03-common-dist\u002F04-fit-dist","en\u002Fstatistics-for-insurance\u002F03-common-dist\u002F04-fit-dist",{"title":880,"path":881,"stem":882},"Mixtures and Heterogeneity","\u002Fen\u002Fstatistics-for-insurance\u002F03-common-dist\u002F05-mix-dist","en\u002Fstatistics-for-insurance\u002F03-common-dist\u002F05-mix-dist",{"title":884,"path":885,"stem":886,"children":887},"Reinsurance as a Loss Transformation","\u002Fen\u002Fstatistics-for-insurance\u002F04-reinsurance","en\u002Fstatistics-for-insurance\u002F04-reinsurance\u002Findex",[888,889,893,897,901],{"title":884,"path":885,"stem":886},{"title":890,"path":891,"stem":892},"Proportional Reinsurance","\u002Fen\u002Fstatistics-for-insurance\u002F04-reinsurance\u002F01-proportional","en\u002Fstatistics-for-insurance\u002F04-reinsurance\u002F01-proportional",{"title":894,"path":895,"stem":896},"Excess-of-Loss Reinsurance","\u002Fen\u002Fstatistics-for-insurance\u002F04-reinsurance\u002F02-excess","en\u002Fstatistics-for-insurance\u002F04-reinsurance\u002F02-excess",{"title":898,"path":899,"stem":900},"Inflation and Layer Erosion","\u002Fen\u002Fstatistics-for-insurance\u002F04-reinsurance\u002F03-inflation","en\u002Fstatistics-for-insurance\u002F04-reinsurance\u002F03-inflation",{"title":902,"path":903,"stem":904},"Reinsurance Decision Lab","\u002Fen\u002Fstatistics-for-insurance\u002F04-reinsurance\u002F04-examples","en\u002Fstatistics-for-insurance\u002F04-reinsurance\u002F04-examples",{"title":906,"path":907,"stem":908,"children":909},"Aggregate Risk and Capital","\u002Fen\u002Fstatistics-for-insurance\u002F05-risk-theory","en\u002Fstatistics-for-insurance\u002F05-risk-theory\u002Findex",[910,911,915,919,923],{"title":906,"path":907,"stem":908},{"title":912,"path":913,"stem":914},"Collective Risk Model","\u002Fen\u002Fstatistics-for-insurance\u002F05-risk-theory\u002F01-collective","en\u002Fstatistics-for-insurance\u002F05-risk-theory\u002F01-collective",{"title":916,"path":917,"stem":918},"Individual Risk Model","\u002Fen\u002Fstatistics-for-insurance\u002F05-risk-theory\u002F02-individual","en\u002Fstatistics-for-insurance\u002F05-risk-theory\u002F02-individual",{"title":920,"path":921,"stem":922},"Aggregate Risk Computation Lab","\u002Fen\u002Fstatistics-for-insurance\u002F05-risk-theory\u002F03-examples","en\u002Fstatistics-for-insurance\u002F05-risk-theory\u002F03-examples",{"title":924,"path":925,"stem":926},"Tail Risk, Dependence, and Capital","\u002Fen\u002Fstatistics-for-insurance\u002F05-risk-theory\u002F04-tail-capital","en\u002Fstatistics-for-insurance\u002F05-risk-theory\u002F04-tail-capital",{"title":928,"path":929,"stem":930,"children":931},"Surplus and Ruin Theory","\u002Fen\u002Fstatistics-for-insurance\u002F06-ruin-theory","en\u002Fstatistics-for-insurance\u002F06-ruin-theory\u002Findex",[932,933],{"title":928,"path":929,"stem":930},{"title":934,"path":935,"stem":936},"Finite-Time Ruin Simulation","\u002Fen\u002Fstatistics-for-insurance\u002F06-ruin-theory\u002F01-finite-time-simulation","en\u002Fstatistics-for-insurance\u002F06-ruin-theory\u002F01-finite-time-simulation",{"title":938,"path":939,"stem":940,"children":941},"Portfolio Risk Capstone","\u002Fen\u002Fstatistics-for-insurance\u002F07-capstone","en\u002Fstatistics-for-insurance\u002F07-capstone\u002Findex",[942],{"title":938,"path":939,"stem":940},{"title":944,"path":945,"stem":946,"children":947,"page":249},"Time Series","\u002Fen\u002Ftime-series","en\u002Ftime-series",[948,958,964,970,976,982,988,994,1016],{"title":949,"path":950,"stem":951,"children":952},"Classical Time Series — Course Guide","\u002Fen\u002Ftime-series\u002F00-intro","en\u002Ftime-series\u002F00-intro\u002Findex",[953,954],{"title":949,"path":950,"stem":951},{"title":955,"path":956,"stem":957},"Preparation — Stationarity in 30 Minutes","\u002Fen\u002Ftime-series\u002F00-intro\u002F01-stationary","en\u002Ftime-series\u002F00-intro\u002F01-stationary",{"title":959,"path":960,"stem":961,"children":962},"Module 1 — Processes, Dependence, and Stationarity","\u002Fen\u002Ftime-series\u002F01-stochastic-process","en\u002Ftime-series\u002F01-stochastic-process\u002Findex",[963],{"title":959,"path":960,"stem":961},{"title":965,"path":966,"stem":967,"children":968},"Module 2 — ARMA, ARIMA, and Model Identification","\u002Fen\u002Ftime-series\u002F02-arma","en\u002Ftime-series\u002F02-arma\u002Findex",[969],{"title":965,"path":966,"stem":967},{"title":971,"path":972,"stem":973,"children":974},"Module 3 — Linear Prediction and State-Space Recursions","\u002Fen\u002Ftime-series\u002F03-prediction","en\u002Ftime-series\u002F03-prediction\u002Findex",[975],{"title":971,"path":972,"stem":973},{"title":977,"path":978,"stem":979,"children":980},"Module 4 — Estimation, Likelihood, and Inference","\u002Fen\u002Ftime-series\u002F04-estimation","en\u002Ftime-series\u002F04-estimation\u002Findex",[981],{"title":977,"path":978,"stem":979},{"title":983,"path":984,"stem":985,"children":986},"Module 5 — Systems, Seasonality, and Cointegration","\u002Fen\u002Ftime-series\u002F05-multi-ar","en\u002Ftime-series\u002F05-multi-ar\u002Findex",[987],{"title":983,"path":984,"stem":985},{"title":989,"path":990,"stem":991,"children":992},"Module 6 — Spectral Analysis, Cycles, and Filters","\u002Fen\u002Ftime-series\u002F06-spectral-analysis","en\u002Ftime-series\u002F06-spectral-analysis\u002Findex",[993],{"title":989,"path":990,"stem":991},{"title":995,"path":996,"stem":997,"children":998},"R Matrix Laboratory","\u002Fen\u002Ftime-series\u002F07-r-implementation","en\u002Ftime-series\u002F07-r-implementation\u002Findex",[999,1000,1004,1008,1012],{"title":995,"path":996,"stem":997},{"title":1001,"path":1002,"stem":1003},"R Matrix Lab 1 — Covariance Geometry","\u002Fen\u002Ftime-series\u002F07-r-implementation\u002F01-covariance-matrices","en\u002Ftime-series\u002F07-r-implementation\u002F01-covariance-matrices",{"title":1005,"path":1006,"stem":1007},"R Matrix Lab 2 — AR Recursions and Yule–Walker Equations","\u002Fen\u002Ftime-series\u002F07-r-implementation\u002F02-ar-recursions","en\u002Ftime-series\u002F07-r-implementation\u002F02-ar-recursions",{"title":1009,"path":1010,"stem":1011},"R Matrix Lab 3 — Prediction and Gaussian Likelihood","\u002Fen\u002Ftime-series\u002F07-r-implementation\u002F03-prediction-likelihood","en\u002Ftime-series\u002F07-r-implementation\u002F03-prediction-likelihood",{"title":1013,"path":1014,"stem":1015},"R Matrix Lab 4 — State Space and Kalman Filtering","\u002Fen\u002Ftime-series\u002F07-r-implementation\u002F04-state-space","en\u002Ftime-series\u002F07-r-implementation\u002F04-state-space",{"title":1017,"path":1018,"stem":1019,"children":1020},"Optional Python Appendix — Empirical Forecasting","\u002Fen\u002Ftime-series\u002F08-python-implementation","en\u002Ftime-series\u002F08-python-implementation\u002Findex",[1021,1022,1026,1030,1034],{"title":1017,"path":1018,"stem":1019},{"title":1023,"path":1024,"stem":1025},"Optional Python Lab 1 — Explore Before Modeling","\u002Fen\u002Ftime-series\u002F08-python-implementation\u002F01-exploration","en\u002Ftime-series\u002F08-python-implementation\u002F01-exploration",{"title":1027,"path":1028,"stem":1029},"Optional Python Lab 2 — Diagnose Stationarity","\u002Fen\u002Ftime-series\u002F08-python-implementation\u002F02-stationarity","en\u002Ftime-series\u002F08-python-implementation\u002F02-stationarity",{"title":1031,"path":1032,"stem":1033},"Optional Python Lab 3 — Fit and Audit ARMA Errors","\u002Fen\u002Ftime-series\u002F08-python-implementation\u002F03-arma-fitting","en\u002Ftime-series\u002F08-python-implementation\u002F03-arma-fitting",{"title":1035,"path":1036,"stem":1037},"Optional Python Lab 4 — Forecast, Backtest, and Monitor","\u002Fen\u002Ftime-series\u002F08-python-implementation\u002F04-forecasting","en\u002Ftime-series\u002F08-python-implementation\u002F04-forecasting",{"title":1039,"path":1040,"stem":1041,"children":1042},"Zh","\u002Fzh","zh",[1043,1045,1063,1247,1323,1365,1421,1467,1543,1625,1633,1731],{"title":10,"path":1040,"stem":1044},"zh\u002Findex",{"title":1046,"path":1047,"stem":1048,"children":1049},"学术写作与文献综述","\u002Fzh\u002Facademic-writing","zh\u002Facademic-writing\u002Findex",[1050,1051,1055,1059],{"title":1046,"path":1047,"stem":1048},{"title":1052,"path":1053,"stem":1054},"4. 文献综述的构建与写作","\u002Fzh\u002Facademic-writing\u002F04-writing-the-literature-review","zh\u002Facademic-writing\u002F04-writing-the-literature-review",{"title":1056,"path":1057,"stem":1058},"8. 文献综述清单与模板","\u002Fzh\u002Facademic-writing\u002F08-literature-review-checklist-and-template","zh\u002Facademic-writing\u002F08-literature-review-checklist-and-template",{"title":1060,"path":1061,"stem":1062},"10. 从分块结构到问题链：文献综述示例","\u002Fzh\u002Facademic-writing\u002F10-从分块结构到问题链-文献综述示例","zh\u002Facademic-writing\u002F10-从分块结构到问题链-文献综述示例",{"title":59,"path":1064,"stem":1065,"children":1066,"page":249},"\u002Fzh\u002Faccounting","zh\u002Faccounting",[1067,1073,1087,1191],{"title":1068,"path":1069,"stem":1070,"children":1071},"会计学学习路线图","\u002Fzh\u002Faccounting\u002F00-index","zh\u002Faccounting\u002F00-index",[1072],{"title":1068,"path":1069,"stem":1070},{"title":1074,"path":1075,"stem":1076,"children":1077},"附录","\u002Fzh\u002Faccounting\u002Fappendix","zh\u002Faccounting\u002Fappendix\u002Findex",[1078,1079,1083],{"title":1074,"path":1075,"stem":1076},{"title":1080,"path":1081,"stem":1082},"综合示例与常见陷阱","\u002Fzh\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls","zh\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls",{"title":1084,"path":1085,"stem":1086},"会计术语速查表","\u002Fzh\u002Faccounting\u002Fappendix\u002F26-glossary","zh\u002Faccounting\u002Fappendix\u002F26-glossary",{"title":1088,"path":1089,"stem":1090,"children":1091},"金融会计","\u002Fzh\u002Faccounting\u002Ffinancial-accounting","zh\u002Faccounting\u002Ffinancial-accounting\u002Findex",[1092,1093,1111,1125,1159,1173],{"title":1088,"path":1089,"stem":1090},{"title":1094,"path":1095,"stem":1096,"children":1097},"1. 基础","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations","zh\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002Findex",[1098,1099,1103,1107],{"title":1094,"path":1095,"stem":1096},{"title":1100,"path":1101,"stem":1102},"会计信息目标与质量特征","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics","zh\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics",{"title":1104,"path":1105,"stem":1106},"会计等式与要素","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements","zh\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements",{"title":1108,"path":1109,"stem":1110},"记账基础与原则","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles","zh\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles",{"title":1112,"path":1113,"stem":1114,"children":1115},"2. 交易记录","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions","zh\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002Findex",[1116,1117,1121],{"title":1112,"path":1113,"stem":1114},{"title":1118,"path":1119,"stem":1120},"复式记账与借贷规则","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr","zh\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr",{"title":1122,"path":1123,"stem":1124},"会计循环","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle","zh\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle",{"title":1126,"path":1127,"stem":1128,"children":1129},"3. 计量与调整","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments","zh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002Findex",[1130,1131,1135,1139,1143,1147,1151,1155],{"title":1126,"path":1127,"stem":1128},{"title":1132,"path":1133,"stem":1134},"收入确认","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition","zh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition",{"title":1136,"path":1137,"stem":1138},"存货","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory","zh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory",{"title":1140,"path":1141,"stem":1142},"应收账款","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables","zh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables",{"title":1144,"path":1145,"stem":1146},"固定资产","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe","zh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe",{"title":1148,"path":1149,"stem":1150},"无形资产","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles","zh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles",{"title":1152,"path":1153,"stem":1154},"租赁","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases","zh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases",{"title":1156,"path":1157,"stem":1158},"所得税","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax","zh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax",{"title":1160,"path":1161,"stem":1162,"children":1163},"4. 报表与现金","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash","zh\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002Findex",[1164,1165,1169],{"title":1160,"path":1161,"stem":1162},{"title":1166,"path":1167,"stem":1168},"财务报表","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements","zh\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements",{"title":1170,"path":1171,"stem":1172},"现金控制","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control","zh\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control",{"title":1174,"path":1175,"stem":1176,"children":1177},"5. 分析与比较","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison","zh\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002Findex",[1178,1179,1183,1187],{"title":1174,"path":1175,"stem":1176},{"title":1180,"path":1181,"stem":1182},"财务比率分析","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis","zh\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis",{"title":1184,"path":1185,"stem":1186},"IFRS 与 US GAAP 对比","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap","zh\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap",{"title":1188,"path":1189,"stem":1190},"2026 准则更新与报告案例","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F27-current-standards-2026","zh\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F27-current-standards-2026",{"title":1192,"path":1193,"stem":1194,"children":1195},"管理会计","\u002Fzh\u002Faccounting\u002Fmanagement-accounting","zh\u002Faccounting\u002Fmanagement-accounting\u002Findex",[1196,1197,1215,1233],{"title":1192,"path":1193,"stem":1194},{"title":1198,"path":1199,"stem":1200,"children":1201},"1. 成本基础","\u002Fzh\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations","zh\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002Findex",[1202,1203,1207,1211],{"title":1198,"path":1199,"stem":1200},{"title":1204,"path":1205,"stem":1206},"成本概念","\u002Fzh\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts","zh\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts",{"title":1208,"path":1209,"stem":1210},"成本核算系统","\u002Fzh\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems","zh\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems",{"title":1212,"path":1213,"stem":1214},"变动成本法 vs. 吸收成本法","\u002Fzh\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption","zh\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption",{"title":1216,"path":1217,"stem":1218,"children":1219},"2. 计划与控制","\u002Fzh\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control","zh\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002Findex",[1220,1221,1225,1229],{"title":1216,"path":1217,"stem":1218},{"title":1222,"path":1223,"stem":1224},"本量利分析","\u002Fzh\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis","zh\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis",{"title":1226,"path":1227,"stem":1228},"预算与差异分析","\u002Fzh\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances","zh\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances",{"title":1230,"path":1231,"stem":1232},"绩效评价","\u002Fzh\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement","zh\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement",{"title":1234,"path":1235,"stem":1236,"children":1237},"3. 决策与投资","\u002Fzh\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment","zh\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002Findex",[1238,1239,1243],{"title":1234,"path":1235,"stem":1236},{"title":1240,"path":1241,"stem":1242},"短期决策","\u002Fzh\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions","zh\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions",{"title":1244,"path":1245,"stem":1246},"资本预算","\u002Fzh\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting","zh\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting",{"title":1248,"path":1249,"stem":1250,"children":1251},"资产定价理论","\u002Fzh\u002Fasset-pricing","zh\u002Fasset-pricing\u002Findex",[1252,1253,1259,1265,1271,1277,1283,1289,1295,1301,1307,1313,1319],{"title":1248,"path":1249,"stem":1250},{"title":1254,"path":1255,"stem":1256,"children":1257},"第一章：引言与基础","\u002Fzh\u002Fasset-pricing\u002F01-intro","zh\u002Fasset-pricing\u002F01-intro\u002Findex",[1258],{"title":1254,"path":1255,"stem":1256},{"title":1260,"path":1261,"stem":1262,"children":1263},"第二章：效用理论与风险偏好","\u002Fzh\u002Fasset-pricing\u002F02-utility","zh\u002Fasset-pricing\u002F02-utility\u002Findex",[1264],{"title":1260,"path":1261,"stem":1262},{"title":1266,"path":1267,"stem":1268,"children":1269},"第三章：均值-方差分析","\u002Fzh\u002Fasset-pricing\u002F03-mean-variance","zh\u002Fasset-pricing\u002F03-mean-variance\u002Findex",[1270],{"title":1266,"path":1267,"stem":1268},{"title":1272,"path":1273,"stem":1274,"children":1275},"第四章：资本资产定价模型(CAPM)","\u002Fzh\u002Fasset-pricing\u002F04-capm","zh\u002Fasset-pricing\u002F04-capm\u002Findex",[1276],{"title":1272,"path":1273,"stem":1274},{"title":1278,"path":1279,"stem":1280,"children":1281},"第五章：因子模型","\u002Fzh\u002Fasset-pricing\u002F05-factor-models","zh\u002Fasset-pricing\u002F05-factor-models\u002Findex",[1282],{"title":1278,"path":1279,"stem":1280},{"title":1284,"path":1285,"stem":1286,"children":1287},"第六章：跨期资产定价","\u002Fzh\u002Fasset-pricing\u002F06-intertemporal","zh\u002Fasset-pricing\u002F06-intertemporal\u002Findex",[1288],{"title":1284,"path":1285,"stem":1286},{"title":1290,"path":1291,"stem":1292,"children":1293},"第七章：期权定价理论","\u002Fzh\u002Fasset-pricing\u002F07-options","zh\u002Fasset-pricing\u002F07-options\u002Findex",[1294],{"title":1290,"path":1291,"stem":1292},{"title":1296,"path":1297,"stem":1298,"children":1299},"第八章：固定收益证券","\u002Fzh\u002Fasset-pricing\u002F08-fixed-income","zh\u002Fasset-pricing\u002F08-fixed-income\u002Findex",[1300],{"title":1296,"path":1297,"stem":1298},{"title":1302,"path":1303,"stem":1304,"children":1305},"第九章：市场有效性与异象","\u002Fzh\u002Fasset-pricing\u002F09-efficiency","zh\u002Fasset-pricing\u002F09-efficiency\u002Findex",[1306],{"title":1302,"path":1303,"stem":1304},{"title":1308,"path":1309,"stem":1310,"children":1311},"第十章：数值方法与实证应用","\u002Fzh\u002Fasset-pricing\u002F10-empirical","zh\u002Fasset-pricing\u002F10-empirical\u002Findex",[1312],{"title":1308,"path":1309,"stem":1310},{"title":1314,"path":1315,"stem":1316,"children":1317},"第十一章：资产定价浏览器交互实验","\u002Fzh\u002Fasset-pricing\u002F11-interactive-labs","zh\u002Fasset-pricing\u002F11-interactive-labs\u002Findex",[1318],{"title":1314,"path":1315,"stem":1316},{"title":1320,"path":1321,"stem":1322},"第十二章：前沿文献与现代资产定价案例（2023—2026）","\u002Fzh\u002Fasset-pricing\u002F12-frontier-literature-2026","zh\u002Fasset-pricing\u002F12-frontier-literature-2026",{"title":1324,"path":1325,"stem":1326,"children":1327},"计量经济学","\u002Fzh\u002Feconometrics","zh\u002Feconometrics\u002Findex",[1328,1329,1333,1337,1341,1345,1349,1353,1357,1361],{"title":1324,"path":1325,"stem":1326},{"title":1330,"path":1331,"stem":1332},"第一章：数据、概率与回归对象","\u002Fzh\u002Feconometrics\u002F01-data-and-regression","zh\u002Feconometrics\u002F01-data-and-regression",{"title":1334,"path":1335,"stem":1336},"第二章：OLS、矩阵与几何解释","\u002Fzh\u002Feconometrics\u002F02-ols-and-geometry","zh\u002Feconometrics\u002F02-ols-and-geometry",{"title":1338,"path":1339,"stem":1340},"第三章：统计推断与稳健标准误","\u002Fzh\u002Feconometrics\u002F03-inference-and-robustness","zh\u002Feconometrics\u002F03-inference-and-robustness",{"title":1342,"path":1343,"stem":1344},"第四章：内生性、工具变量与两阶段最小二乘","\u002Fzh\u002Feconometrics\u002F04-endogeneity-and-iv","zh\u002Feconometrics\u002F04-endogeneity-and-iv",{"title":1346,"path":1347,"stem":1348},"第五章：面板数据与时间序列","\u002Fzh\u002Feconometrics\u002F05-panel-and-time-series","zh\u002Feconometrics\u002F05-panel-and-time-series",{"title":1350,"path":1351,"stem":1352},"第六章：估计方法与因果设计的共同基础","\u002Fzh\u002Feconometrics\u002F06-estimation-and-causal-design","zh\u002Feconometrics\u002F06-estimation-and-causal-design",{"title":1354,"path":1355,"stem":1356},"第七章：可重复计量实证项目","\u002Fzh\u002Feconometrics\u002F07-reproducible-project","zh\u002Feconometrics\u002F07-reproducible-project",{"title":1358,"path":1359,"stem":1360},"第八章：计量经济学浏览器回归实验","\u002Fzh\u002Feconometrics\u002F08-interactive-regression-labs","zh\u002Feconometrics\u002F08-interactive-regression-labs",{"title":1362,"path":1363,"stem":1364},"第九章：前沿文献与现代计量案例（2023—2026）","\u002Fzh\u002Feconometrics\u002F09-frontier-literature-2026","zh\u002Feconometrics\u002F09-frontier-literature-2026",{"title":478,"path":1366,"stem":1367,"children":1368,"page":249},"\u002Fzh\u002Fintro-to-economics","zh\u002Fintro-to-economics",[1369,1373,1377,1381,1385,1389,1393,1397,1401,1405,1409,1413,1417],{"title":1370,"path":1371,"stem":1372},"经济学导论 (微观与宏观)","\u002Fzh\u002Fintro-to-economics\u002F00-intro","zh\u002Fintro-to-economics\u002F00-intro",{"title":1374,"path":1375,"stem":1376},"第1章：经济学基础原理","\u002Fzh\u002Fintro-to-economics\u002F01-foundations","zh\u002Fintro-to-economics\u002F01-foundations",{"title":1378,"path":1379,"stem":1380},"第2章：需求与供给","\u002Fzh\u002Fintro-to-economics\u002F02-demand-and-supply","zh\u002Fintro-to-economics\u002F02-demand-and-supply",{"title":1382,"path":1383,"stem":1384},"第3章：弹性","\u002Fzh\u002Fintro-to-economics\u002F03-elasticity","zh\u002Fintro-to-economics\u002F03-elasticity",{"title":1386,"path":1387,"stem":1388},"第4章：市场结构","\u002Fzh\u002Fintro-to-economics\u002F04-market-structures","zh\u002Fintro-to-economics\u002F04-market-structures",{"title":1390,"path":1391,"stem":1392},"第5章：GDP 与财富","\u002Fzh\u002Fintro-to-economics\u002F05-gdp-and-wealth","zh\u002Fintro-to-economics\u002F05-gdp-and-wealth",{"title":1394,"path":1395,"stem":1396},"第6章：通货膨胀与失业","\u002Fzh\u002Fintro-to-economics\u002F06-inflation-and-unemployment","zh\u002Fintro-to-economics\u002F06-inflation-and-unemployment",{"title":1398,"path":1399,"stem":1400},"第7章：经济增长","\u002Fzh\u002Fintro-to-economics\u002F07-economic-growth","zh\u002Fintro-to-economics\u002F07-economic-growth",{"title":1402,"path":1403,"stem":1404},"第8章：货币与银行","\u002Fzh\u002Fintro-to-economics\u002F08-money-and-banking","zh\u002Fintro-to-economics\u002F08-money-and-banking",{"title":1406,"path":1407,"stem":1408},"第9章：货币政策与 AD-AS 模型","\u002Fzh\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as","zh\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as",{"title":1410,"path":1411,"stem":1412},"第10章：财政政策","\u002Fzh\u002Fintro-to-economics\u002F10-fiscal-policy","zh\u002Fintro-to-economics\u002F10-fiscal-policy",{"title":1414,"path":1415,"stem":1416},"第11章：开放经济与汇率","\u002Fzh\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates","zh\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates",{"title":1418,"path":1419,"stem":1420},"第12章：综合复习与案例分析","\u002Fzh\u002Fintro-to-economics\u002F12-review-and-case-studies","zh\u002Fintro-to-economics\u002F12-review-and-case-studies",{"title":1422,"path":1423,"stem":1424,"children":1425},"宏观经济学","\u002Fzh\u002Fmacroeconomics","zh\u002Fmacroeconomics\u002Findex",[1426,1427,1431,1435,1439,1443,1447,1451,1455,1459,1463],{"title":1422,"path":1423,"stem":1424},{"title":1428,"path":1429,"stem":1430},"第一章：国民账户与宏观指标","\u002Fzh\u002Fmacroeconomics\u002F01-national-accounts","zh\u002Fmacroeconomics\u002F01-national-accounts",{"title":1432,"path":1433,"stem":1434},"第二章：消费、投资与凯恩斯交叉","\u002Fzh\u002Fmacroeconomics\u002F02-consumption-investment","zh\u002Fmacroeconomics\u002F02-consumption-investment",{"title":1436,"path":1437,"stem":1438},"第三章：货币、银行与货币政策","\u002Fzh\u002Fmacroeconomics\u002F03-money-and-monetary-policy","zh\u002Fmacroeconomics\u002F03-money-and-monetary-policy",{"title":1440,"path":1441,"stem":1442},"第四章：AD–AS、通货膨胀与失业","\u002Fzh\u002Fmacroeconomics\u002F04-ad-as-inflation-unemployment","zh\u002Fmacroeconomics\u002F04-ad-as-inflation-unemployment",{"title":1444,"path":1445,"stem":1446},"第五章：财政政策、债务与稳定化","\u002Fzh\u002Fmacroeconomics\u002F05-fiscal-policy-and-debt","zh\u002Fmacroeconomics\u002F05-fiscal-policy-and-debt",{"title":1448,"path":1449,"stem":1450},"第六章：经济增长、生产率与发展","\u002Fzh\u002Fmacroeconomics\u002F06-growth-productivity","zh\u002Fmacroeconomics\u002F06-growth-productivity",{"title":1452,"path":1453,"stem":1454},"第七章：开放经济、汇率与国际收支","\u002Fzh\u002Fmacroeconomics\u002F07-open-economy","zh\u002Fmacroeconomics\u002F07-open-economy",{"title":1456,"path":1457,"stem":1458},"第八章：宏观研究项目与政策分析","\u002Fzh\u002Fmacroeconomics\u002F08-macro-research-project","zh\u002Fmacroeconomics\u002F08-macro-research-project",{"title":1460,"path":1461,"stem":1462},"第九章：宏观经济学浏览器交互实验","\u002Fzh\u002Fmacroeconomics\u002F09-interactive-policy-labs","zh\u002Fmacroeconomics\u002F09-interactive-policy-labs",{"title":1464,"path":1465,"stem":1466},"第十章：前沿文献与当代宏观案例（2023—2026）","\u002Fzh\u002Fmacroeconomics\u002F10-frontier-literature-2026","zh\u002Fmacroeconomics\u002F10-frontier-literature-2026",{"title":1468,"path":1469,"stem":1470,"children":1471},"微观计量经济学","\u002Fzh\u002Fmicroeconometrics","zh\u002Fmicroeconometrics\u002Findex",[1472,1473,1479,1485,1491,1497,1503,1509,1515,1521,1527,1533,1539],{"title":1468,"path":1469,"stem":1470},{"title":1474,"path":1475,"stem":1476,"children":1477},"第一章：微观计量与因果推断导论","\u002Fzh\u002Fmicroeconometrics\u002F01-intro","zh\u002Fmicroeconometrics\u002F01-intro\u002Findex",[1478],{"title":1474,"path":1475,"stem":1476},{"title":1480,"path":1481,"stem":1482,"children":1483},"第二章：线性回归与 OLS","\u002Fzh\u002Fmicroeconometrics\u002F02-ols","zh\u002Fmicroeconometrics\u002F02-ols\u002Findex",[1484],{"title":1480,"path":1481,"stem":1482},{"title":1486,"path":1487,"stem":1488,"children":1489},"第三章：工具变量法","\u002Fzh\u002Fmicroeconometrics\u002F03-iv","zh\u002Fmicroeconometrics\u002F03-iv\u002Findex",[1490],{"title":1486,"path":1487,"stem":1488},{"title":1492,"path":1493,"stem":1494,"children":1495},"第四章：面板数据方法","\u002Fzh\u002Fmicroeconometrics\u002F04-panel","zh\u002Fmicroeconometrics\u002F04-panel\u002Findex",[1496],{"title":1492,"path":1493,"stem":1494},{"title":1498,"path":1499,"stem":1500,"children":1501},"第五章：双重差分法","\u002Fzh\u002Fmicroeconometrics\u002F05-did","zh\u002Fmicroeconometrics\u002F05-did\u002Findex",[1502],{"title":1498,"path":1499,"stem":1500},{"title":1504,"path":1505,"stem":1506,"children":1507},"第六章：断点回归设计","\u002Fzh\u002Fmicroeconometrics\u002F06-rdd","zh\u002Fmicroeconometrics\u002F06-rdd\u002Findex",[1508],{"title":1504,"path":1505,"stem":1506},{"title":1510,"path":1511,"stem":1512,"children":1513},"第七章：匹配、倾向得分与加权","\u002Fzh\u002Fmicroeconometrics\u002F07-matching","zh\u002Fmicroeconometrics\u002F07-matching\u002Findex",[1514],{"title":1510,"path":1511,"stem":1512},{"title":1516,"path":1517,"stem":1518,"children":1519},"第八章：离散选择模型","\u002Fzh\u002Fmicroeconometrics\u002F08-discrete-choice","zh\u002Fmicroeconometrics\u002F08-discrete-choice\u002Findex",[1520],{"title":1516,"path":1517,"stem":1518},{"title":1522,"path":1523,"stem":1524,"children":1525},"第九章：计数数据与受限因变量","\u002Fzh\u002Fmicroeconometrics\u002F09-count-limited","zh\u002Fmicroeconometrics\u002F09-count-limited\u002Findex",[1526],{"title":1522,"path":1523,"stem":1524},{"title":1528,"path":1529,"stem":1530,"children":1531},"第十章：合成控制法","\u002Fzh\u002Fmicroeconometrics\u002F10-synthetic-control","zh\u002Fmicroeconometrics\u002F10-synthetic-control\u002Findex",[1532],{"title":1528,"path":1529,"stem":1530},{"title":1534,"path":1535,"stem":1536,"children":1537},"第十一章：机器学习与因果推断","\u002Fzh\u002Fmicroeconometrics\u002F11-ml-causal","zh\u002Fmicroeconometrics\u002F11-ml-causal\u002Findex",[1538],{"title":1534,"path":1535,"stem":1536},{"title":1540,"path":1541,"stem":1542},"第十二章：前沿文献与现代微观案例（2024—2026）","\u002Fzh\u002Fmicroeconometrics\u002F12-frontier-literature-2026","zh\u002Fmicroeconometrics\u002F12-frontier-literature-2026",{"title":716,"path":1544,"stem":1545,"children":1546,"page":249},"\u002Fzh\u002Fmicroeconomics","zh\u002Fmicroeconomics",[1547,1553,1559,1565,1571,1577,1583,1589,1595,1601,1607,1613,1619],{"title":1548,"path":1549,"stem":1550,"children":1551},"微观经济学 III","\u002Fzh\u002Fmicroeconomics\u002F00-intro","zh\u002Fmicroeconomics\u002F00-intro\u002Findex",[1552],{"title":1548,"path":1549,"stem":1550},{"title":1554,"path":1555,"stem":1556,"children":1557},"消费者理论与分析基础","\u002Fzh\u002Fmicroeconomics\u002F01-fundations","zh\u002Fmicroeconomics\u002F01-fundations\u002Findex",[1558],{"title":1554,"path":1555,"stem":1556},{"title":1560,"path":1561,"stem":1562,"children":1563},"比较静态分析与福利测度","\u002Fzh\u002Fmicroeconomics\u002F02-comparative-statics","zh\u002Fmicroeconomics\u002F02-comparative-statics\u002Findex",[1564],{"title":1560,"path":1561,"stem":1562},{"title":1566,"path":1567,"stem":1568,"children":1569},"不确定性下的决策","\u002Fzh\u002Fmicroeconomics\u002F03-uncertainty","zh\u002Fmicroeconomics\u002F03-uncertainty\u002Findex",[1570],{"title":1566,"path":1567,"stem":1568},{"title":1572,"path":1573,"stem":1574,"children":1575},"一般均衡与福利经济学","\u002Fzh\u002Fmicroeconomics\u002F04-general-equilibrium","zh\u002Fmicroeconomics\u002F04-general-equilibrium\u002Findex",[1576],{"title":1572,"path":1573,"stem":1574},{"title":1578,"path":1579,"stem":1580,"children":1581},"博弈论：静态与动态博弈","\u002Fzh\u002Fmicroeconomics\u002F05-game-theory","zh\u002Fmicroeconomics\u002F05-game-theory\u002Findex",[1582],{"title":1578,"path":1579,"stem":1580},{"title":1584,"path":1585,"stem":1586,"children":1587},"寡头垄断与策略性市场行为","\u002Fzh\u002Fmicroeconomics\u002F06-oligopoly","zh\u002Fmicroeconomics\u002F06-oligopoly\u002Findex",[1588],{"title":1584,"path":1585,"stem":1586},{"title":1590,"path":1591,"stem":1592,"children":1593},"信息经济学：逆向选择与道德风险","\u002Fzh\u002Fmicroeconomics\u002F07-information-economics","zh\u002Fmicroeconomics\u002F07-information-economics\u002Findex",[1594],{"title":1590,"path":1591,"stem":1592},{"title":1596,"path":1597,"stem":1598,"children":1599},"机制设计与拍卖理论","\u002Fzh\u002Fmicroeconomics\u002F08-mechanism-design","zh\u002Fmicroeconomics\u002F08-mechanism-design\u002Findex",[1600],{"title":1596,"path":1597,"stem":1598},{"title":1602,"path":1603,"stem":1604,"children":1605},"行为与实验微观经济学","\u002Fzh\u002Fmicroeconomics\u002F09-behavioural-economics","zh\u002Fmicroeconomics\u002F09-behavioural-economics\u002Findex",[1606],{"title":1602,"path":1603,"stem":1604},{"title":1608,"path":1609,"stem":1610,"children":1611},"外部性、公共物品与机制","\u002Fzh\u002Fmicroeconomics\u002F10-externalities-public-goods","zh\u002Fmicroeconomics\u002F10-externalities-public-goods\u002Findex",[1612],{"title":1608,"path":1609,"stem":1610},{"title":1614,"path":1615,"stem":1616,"children":1617},"市场设计与匹配理论","\u002Fzh\u002Fmicroeconomics\u002F11-market-design","zh\u002Fmicroeconomics\u002F11-market-design\u002Findex",[1618],{"title":1614,"path":1615,"stem":1616},{"title":1620,"path":1621,"stem":1622,"children":1623},"第十二章：微观经济学：回顾与前沿应用","\u002Fzh\u002Fmicroeconomics\u002F12-review","zh\u002Fmicroeconomics\u002F12-review\u002Findex",[1624],{"title":1620,"path":1621,"stem":1622},{"title":799,"path":1626,"stem":1627,"children":1628,"page":249},"\u002Fzh\u002Fplayground","zh\u002Fplayground",[1629],{"title":1630,"path":1631,"stem":1632},"Chart.js 可视化","\u002Fzh\u002Fplayground\u002F05-chartjs","zh\u002Fplayground\u002F05-chartjs",{"title":1634,"path":1635,"stem":1636,"children":1637},"概率论与数理统计","\u002Fzh\u002Fprob-and-stats","zh\u002Fprob-and-stats\u002Findex",[1638,1639,1645,1680,1727],{"title":1634,"path":1635,"stem":1636},{"title":1640,"path":1641,"stem":1642,"children":1643},"第零章：概率统计的对象与学习方法","\u002Fzh\u002Fprob-and-stats\u002F00-intro","zh\u002Fprob-and-stats\u002F00-intro\u002Findex",[1644],{"title":1640,"path":1641,"stem":1642},{"title":1646,"path":1647,"stem":1648,"children":1649,"page":249},"01 Probability","\u002Fzh\u002Fprob-and-stats\u002F01-probability","zh\u002Fprob-and-stats\u002F01-probability",[1650,1656,1662,1668,1674],{"title":1651,"path":1652,"stem":1653,"children":1654},"第一章：概率论基础","\u002Fzh\u002Fprob-and-stats\u002F01-probability\u002F01-prob-theory","zh\u002Fprob-and-stats\u002F01-probability\u002F01-prob-theory\u002Findex",[1655],{"title":1651,"path":1652,"stem":1653},{"title":1657,"path":1658,"stem":1659,"children":1660},"第二章：随机变量与分布","\u002Fzh\u002Fprob-and-stats\u002F01-probability\u002F02-random-variables","zh\u002Fprob-and-stats\u002F01-probability\u002F02-random-variables\u002Findex",[1661],{"title":1657,"path":1658,"stem":1659},{"title":1663,"path":1664,"stem":1665,"children":1666},"第三章：期望、方差与条件矩","\u002Fzh\u002Fprob-and-stats\u002F01-probability\u002F03-moment","zh\u002Fprob-and-stats\u002F01-probability\u002F03-moment\u002Findex",[1667],{"title":1663,"path":1664,"stem":1665},{"title":1669,"path":1670,"stem":1671,"children":1672},"第四章：常见分布族与建模机制","\u002Fzh\u002Fprob-and-stats\u002F01-probability\u002F04-families","zh\u002Fprob-and-stats\u002F01-probability\u002F04-families\u002Findex",[1673],{"title":1669,"path":1670,"stem":1671},{"title":1675,"path":1676,"stem":1677,"children":1678},"第五章：收敛与渐近理论","\u002Fzh\u002Fprob-and-stats\u002F01-probability\u002F05-asymptotics","zh\u002Fprob-and-stats\u002F01-probability\u002F05-asymptotics\u002Findex",[1679],{"title":1675,"path":1676,"stem":1677},{"title":1681,"path":1682,"stem":1683,"children":1684,"page":249},"02 Statistics","\u002Fzh\u002Fprob-and-stats\u002F02-statistics","zh\u002Fprob-and-stats\u002F02-statistics",[1685,1691,1697,1703,1709,1715,1721],{"title":1686,"path":1687,"stem":1688,"children":1689},"第六章：抽样分布","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F01-sampling","zh\u002Fprob-and-stats\u002F02-statistics\u002F01-sampling\u002Findex",[1690],{"title":1686,"path":1687,"stem":1688},{"title":1692,"path":1693,"stem":1694,"children":1695},"第七章：区间估计","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F02-interval-estimation","zh\u002Fprob-and-stats\u002F02-statistics\u002F02-interval-estimation\u002Findex",[1696],{"title":1692,"path":1693,"stem":1694},{"title":1698,"path":1699,"stem":1700,"children":1701},"第八章：点估计理论","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F03-point-estimation","zh\u002Fprob-and-stats\u002F02-statistics\u002F03-point-estimation\u002Findex",[1702],{"title":1698,"path":1699,"stem":1700},{"title":1704,"path":1705,"stem":1706,"children":1707},"第九章：点估计方法","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F04-pe-method","zh\u002Fprob-and-stats\u002F02-statistics\u002F04-pe-method\u002Findex",[1708],{"title":1704,"path":1705,"stem":1706},{"title":1710,"path":1711,"stem":1712,"children":1713},"第十章：假设检验原理","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F05-hypothesis","zh\u002Fprob-and-stats\u002F02-statistics\u002F05-hypothesis\u002Findex",[1714],{"title":1710,"path":1711,"stem":1712},{"title":1716,"path":1717,"stem":1718,"children":1719},"第十一章：常用检验方法与选择","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F06-hypothesis-method","zh\u002Fprob-and-stats\u002F02-statistics\u002F06-hypothesis-method\u002Findex",[1720],{"title":1716,"path":1717,"stem":1718},{"title":1722,"path":1723,"stem":1724,"children":1725},"第十二章：Bootstrap 与重抽样","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F07-bootstrap","zh\u002Fprob-and-stats\u002F02-statistics\u002F07-bootstrap\u002Findex",[1726],{"title":1722,"path":1723,"stem":1724},{"title":1728,"path":1729,"stem":1730},"第十三章：前沿文献与现代统计案例（2023—2026）","\u002Fzh\u002Fprob-and-stats\u002F03-frontier-literature-2026","zh\u002Fprob-and-stats\u002F03-frontier-literature-2026",{"title":1732,"path":1733,"stem":1734,"children":1735,"page":249},"Quant","\u002Fzh\u002Fquant","zh\u002Fquant",[1736,1742,1746,1750,1754,1758,1762,1766,1770,1774,1778],{"title":1737,"path":1738,"stem":1739,"children":1740},"量化投资——从可检验信号到可执行组合","\u002Fzh\u002Fquant\u002F00-index","zh\u002Fquant\u002F00-index",[1741],{"title":1737,"path":1738,"stem":1739},{"title":1743,"path":1744,"stem":1745},"数据获取与预处理","\u002Fzh\u002Fquant\u002F01-research-data","zh\u002Fquant\u002F01-research-data",{"title":1747,"path":1748,"stem":1749},"因子与交易信号","\u002Fzh\u002Fquant\u002F02-factor-and-signals","zh\u002Fquant\u002F02-factor-and-signals",{"title":1751,"path":1752,"stem":1753},"策略建模与回测","\u002Fzh\u002Fquant\u002F03-modeling-and-backtest","zh\u002Fquant\u002F03-modeling-and-backtest",{"title":1755,"path":1756,"stem":1757},"组合构建与风险建模（资产定价视角）","\u002Fzh\u002Fquant\u002F04-portfolio-and-risk","zh\u002Fquant\u002F04-portfolio-and-risk",{"title":1759,"path":1760,"stem":1761},"执行策略与市场微结构概览","\u002Fzh\u002Fquant\u002F05-execution-and-microstructure","zh\u002Fquant\u002F05-execution-and-microstructure",{"title":1763,"path":1764,"stem":1765},"策略上线、监控与迭代","\u002Fzh\u002Fquant\u002F06-production-and-monitoring","zh\u002Fquant\u002F06-production-and-monitoring",{"title":1767,"path":1768,"stem":1769},"量化工程与工具链概览","\u002Fzh\u002Fquant\u002F07-engineering-stack","zh\u002Fquant\u002F07-engineering-stack",{"title":1771,"path":1772,"stem":1773},"计量方法与实证检验","\u002Fzh\u002Fquant\u002F08-econometric-methods","zh\u002Fquant\u002F08-econometric-methods",{"title":1775,"path":1776,"stem":1777},"案例研究：多因子股票 Alpha 策略全流程","\u002Fzh\u002Fquant\u002F09-case-study","zh\u002Fquant\u002F09-case-study",{"title":1779,"path":1780,"stem":1781},"量化投资文献与软件图谱","\u002Fzh\u002Fquant\u002F10-reading-software-map","zh\u002Fquant\u002F10-reading-software-map",{"path":734},{"id":1784,"title":1560,"body":1785,"description":27918,"extension":27919,"features":27920,"hero":27920,"layout":27920,"locale":27920,"meta":27921,"navigation":27920,"path":1561,"published":27922,"seo":27923,"stem":1562,"__hash__":27924},"docs\u002Fzh\u002Fmicroeconomics\u002F02-comparative-statics\u002Findex.md",{"type":1786,"value":1787,"toc":27870},"minimark",[1788,1793,1797,1801,1804,1820,1823,1842,1846,1849,1853,1858,1861,1864,2761,3045,3052,3056,3207,3402,3405,3420,3423,3427,3431,3434,4155,4158,4910,4916,4919,5428,5503,6227,6230,6454,6457,6816,6819,6823,6857,7194,7259,7620,7624,7627,7632,7643,7648,7659,7663,7667,7670,7674,7677,8286,8292,8505,8508,8510,8514,8518,8694,8700,8704,8714,8717,9139,9360,9363,9610,9615,9898,9902,9911,9913,10327,10547,10550,10798,10801,10805,11103,11108,11265,11269,11272,11282,11284,11288,11292,11295,11367,11648,11651,11655,11776,12012,12015,12237,12242,12339,12342,12636,12640,12643,12663,12668,12676,12678,12682,12686,13478,13483,13488,13491,13918,13921,14347,14403,14870,14873,15321,15324,15857,15862,16765,16770,16773,17185,17343,17509,17512,18111,18114,18787,18792,19386,19389,19639,19706,19749,20092,21056,21059,21858,21975,21979,22429,22433,22781,23108,23111,23313,23375,23785,23788,24058,24505,24607,24613,24621,24623,24627,24631,24761,24935,24941,24945,24950,25015,25020,25028,25031,25035,25038,25257,25260,25442,25444,25678,25684,25686,25690,25694,25697,25991,25997,26001,26036,26047,26053,26055,26059,26064,26082,26087,26098,26100,26104,27110,27123,27126,27132,27138,27696,27817,27820,27834,27837,27854,27857,27860],[1789,1790,1792],"h1",{"id":1791},"第-2-讲比较静态分析与福利测度","第 2 讲：比较静态分析与福利测度",[1794,1795,1796],"h2",{"id":1796},"本章导学",[1798,1799,1800],"p",{},"第 1 章解决了“给定价格和收入时消费者如何选择”的问题。本章进一步追问：当价格、收入或政策参数发生变化时，选择会怎样变，福利又该怎样度量？比较静态不是机械地求偏导，而是把行为变化拆成可以解释的经济效应。",[1798,1802,1803],{},"学完本章后，你应当能够：",[1805,1806,1807,1811,1814,1817],"ul",{},[1808,1809,1810],"li",{},"用斯勒茨基方程分解价格变化的替代效应和收入效应。",[1808,1812,1813],{},"区分马歇尔需求与希克斯需求在福利分析中的角色。",[1808,1815,1816],{},"计算并解释补偿变差（CV）、等价变差（EV）和消费者剩余。",[1808,1818,1819],{},"判断不同税收、补贴或价格政策对消费者福利和效率的影响。",[1798,1821,1822],{},"常见考查重点是“推导 + 解释”：先从需求或支出函数算出福利变化，再说明为什么 CV、EV 和消费者剩余可能不同。作业中尤其要注意价格上升和下降时符号的处理，不要把“补偿多少”与“损失多少”混在一起。",[1798,1824,1825,1826,1831,1832,1836,1837,1841],{},"本章向前连接",[1827,1828,1830],"a",{"href":1829},"..\u002F01-fundations\u002F","第 1 章","的对偶理论，向后连接",[1827,1833,1835],{"href":1834},"..\u002F03-uncertainty\u002F","第 3 章","的不确定性决策和",[1827,1838,1840],{"href":1839},"..\u002F04-general-equilibrium\u002F","第 4 章","的一般均衡福利判断。可以把它看作整门课的政策评估入口。",[1794,1843,1845],{"id":1844},"经济动机-economic-motivation","经济动机 (Economic Motivation)",[1798,1847,1848],{},"当市场价格或消费者收入发生变化时，他们的购买行为会如何改变？我们如何衡量这些变化对消费者福利的影响？这些是政策制定者（例如，在考虑征收消费税时）和企业（例如，在调整产品价格时）必须回答的关键问题。",[1794,1850,1852],{"id":1851},"_1-比较静态分析基础","1. 比较静态分析基础",[1854,1855,1857],"h3",{"id":1856},"_11-隐函数定理的应用","1.1 隐函数定理的应用",[1798,1859,1860],{},"比较静态分析研究外生参数（如价格、收入）的微小变化如何影响内生变量（如需求量）。",[1798,1862,1863],{},"考虑效用最大化的一阶条件：",[1865,1866,1869],"span",{"className":1867},[1868],"katex-display",[1865,1870,1873,2064],{"className":1871},[1872],"katex",[1865,1874,1877],{"className":1875},[1876],"katex-mathml",[1878,1879,1882],"math",{"xmlns":1880,"display":1881},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML","block",[1883,1884,1885,2059],"semantics",{},[1886,1887,1891,1958,2007],"mtable",{"rowspacing":1888,"columnalign":1889,"columnspacing":1890},"0.25em","right left","0em",[1892,1893,1894,1945],"mtr",{},[1895,1896,1897],"mtd",{},[1898,1899,1902],"mstyle",{"scriptlevel":1900,"displaystyle":1901},"0","true",[1903,1904,1905,1932,1936,1939],"mrow",{},[1906,1907,1908,1918],"mfrac",{},[1903,1909,1910,1915],{},[1911,1912,1914],"mi",{"mathvariant":1913},"normal","∂",[1911,1916,1917],{},"U",[1903,1919,1920,1922],{},[1911,1921,1914],{"mathvariant":1913},[1923,1924,1925,1928],"msub",{},[1911,1926,1927],{},"x",[1929,1930,1931],"mn",{},"1",[1933,1934,1935],"mo",{},"−",[1911,1937,1938],{},"λ",[1923,1940,1941,1943],{},[1911,1942,1798],{},[1929,1944,1931],{},[1895,1946,1947],{},[1898,1948,1949],{"scriptlevel":1900,"displaystyle":1901},[1903,1950,1951,1953,1956],{},[1903,1952],{},[1933,1954,1955],{},"=",[1929,1957,1900],{},[1892,1959,1960,1995],{},[1895,1961,1962],{},[1898,1963,1964],{"scriptlevel":1900,"displaystyle":1901},[1903,1965,1966,1985,1987,1989],{},[1906,1967,1968,1974],{},[1903,1969,1970,1972],{},[1911,1971,1914],{"mathvariant":1913},[1911,1973,1917],{},[1903,1975,1976,1978],{},[1911,1977,1914],{"mathvariant":1913},[1923,1979,1980,1982],{},[1911,1981,1927],{},[1929,1983,1984],{},"2",[1933,1986,1935],{},[1911,1988,1938],{},[1923,1990,1991,1993],{},[1911,1992,1798],{},[1929,1994,1984],{},[1895,1996,1997],{},[1898,1998,1999],{"scriptlevel":1900,"displaystyle":1901},[1903,2000,2001,2003,2005],{},[1903,2002],{},[1933,2004,1955],{},[1929,2006,1900],{},[1892,2008,2009,2047],{},[1895,2010,2011],{},[1898,2012,2013],{"scriptlevel":1900,"displaystyle":1901},[1903,2014,2015,2021,2027,2030,2036,2042,2044],{},[1923,2016,2017,2019],{},[1911,2018,1798],{},[1929,2020,1931],{},[1923,2022,2023,2025],{},[1911,2024,1927],{},[1929,2026,1931],{},[1933,2028,2029],{},"+",[1923,2031,2032,2034],{},[1911,2033,1798],{},[1929,2035,1984],{},[1923,2037,2038,2040],{},[1911,2039,1927],{},[1929,2041,1984],{},[1933,2043,1935],{},[1911,2045,2046],{},"m",[1895,2048,2049],{},[1898,2050,2051],{"scriptlevel":1900,"displaystyle":1901},[1903,2052,2053,2055,2057],{},[1903,2054],{},[1933,2056,1955],{},[1929,2058,1900],{},[2060,2061,2063],"annotation",{"encoding":2062},"application\u002Fx-tex","\\begin{align*}\n\\frac{\\partial U}{\\partial x_1} - \\lambda p_1 &= 0 \\\\\n\\frac{\\partial U}{\\partial x_2} - \\lambda p_2 &= 0 \\\\\np_1 x_1 + p_2 x_2 - m &= 0\n\\end{align*}",[1865,2065,2068],{"className":2066,"ariaHidden":1901},[2067],"katex-html",[1865,2069,2072,2077],{"className":2070},[2071],"base",[1865,2073],{"className":2074,"style":2076},[2075],"strut","height:6.2149em;vertical-align:-2.8574em;",[1865,2078,2081],{"className":2079},[2080],"mord",[1865,2082,2084,2666],{"className":2083},[1886],[1865,2085,2088],{"className":2086},[2087],"col-align-r",[1865,2089,2093,2657],{"className":2090},[2091,2092],"vlist-t","vlist-t2",[1865,2094,2097,2654],{"className":2095},[2096],"vlist-r",[1865,2098,2102,2298,2464],{"className":2099,"style":2101},[2100],"vlist","height:3.3574em;",[1865,2103,2105,2110],{"style":2104},"top:-5.3574em;",[1865,2106],{"className":2107,"style":2109},[2108],"pstrut","height:3.3714em;",[1865,2111,2113,2243,2248,2252,2255,2258],{"className":2112},[2080],[1865,2114,2116,2121,2239],{"className":2115},[2080],[1865,2117],{"className":2118},[2119,2120],"mopen","nulldelimiter",[1865,2122,2124],{"className":2123},[1906],[1865,2125,2127,2230],{"className":2126},[2091,2092],[1865,2128,2130,2227],{"className":2129},[2096],[1865,2131,2134,2200,2211],{"className":2132,"style":2133},[2100],"height:1.3714em;",[1865,2135,2137,2141],{"style":2136},"top:-2.314em;",[1865,2138],{"className":2139,"style":2140},[2108],"height:3em;",[1865,2142,2144,2148],{"className":2143},[2080],[1865,2145,1914],{"className":2146,"style":2147},[2080],"margin-right:0.0556em;",[1865,2149,2151,2155],{"className":2150},[2080],[1865,2152,1927],{"className":2153},[2080,2154],"mathnormal",[1865,2156,2159],{"className":2157},[2158],"msupsub",[1865,2160,2162,2191],{"className":2161},[2091,2092],[1865,2163,2165,2186],{"className":2164},[2096],[1865,2166,2169],{"className":2167,"style":2168},[2100],"height:0.3011em;",[1865,2170,2172,2176],{"style":2171},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1865,2173],{"className":2174,"style":2175},[2108],"height:2.7em;",[1865,2177,2183],{"className":2178},[2179,2180,2181,2182],"sizing","reset-size6","size3","mtight",[1865,2184,1931],{"className":2185},[2080,2182],[1865,2187,2190],{"className":2188},[2189],"vlist-s","​",[1865,2192,2194],{"className":2193},[2096],[1865,2195,2198],{"className":2196,"style":2197},[2100],"height:0.15em;",[1865,2199],{},[1865,2201,2203,2206],{"style":2202},"top:-3.23em;",[1865,2204],{"className":2205,"style":2140},[2108],[1865,2207],{"className":2208,"style":2210},[2209],"frac-line","border-bottom-width:0.04em;",[1865,2212,2214,2217],{"style":2213},"top:-3.677em;",[1865,2215],{"className":2216,"style":2140},[2108],[1865,2218,2220,2223],{"className":2219},[2080],[1865,2221,1914],{"className":2222,"style":2147},[2080],[1865,2224,1917],{"className":2225,"style":2226},[2080,2154],"margin-right:0.109em;",[1865,2228,2190],{"className":2229},[2189],[1865,2231,2233],{"className":2232},[2096],[1865,2234,2237],{"className":2235,"style":2236},[2100],"height:0.836em;",[1865,2238],{},[1865,2240],{"className":2241},[2242,2120],"mclose",[1865,2244],{"className":2245,"style":2247},[2246],"mspace","margin-right:0.2222em;",[1865,2249,1935],{"className":2250},[2251],"mbin",[1865,2253],{"className":2254,"style":2247},[2246],[1865,2256,1938],{"className":2257},[2080,2154],[1865,2259,2261,2264],{"className":2260},[2080],[1865,2262,1798],{"className":2263},[2080,2154],[1865,2265,2267],{"className":2266},[2158],[1865,2268,2270,2290],{"className":2269},[2091,2092],[1865,2271,2273,2287],{"className":2272},[2096],[1865,2274,2276],{"className":2275,"style":2168},[2100],[1865,2277,2278,2281],{"style":2171},[1865,2279],{"className":2280,"style":2175},[2108],[1865,2282,2284],{"className":2283},[2179,2180,2181,2182],[1865,2285,1931],{"className":2286},[2080,2182],[1865,2288,2190],{"className":2289},[2189],[1865,2291,2293],{"className":2292},[2096],[1865,2294,2296],{"className":2295,"style":2197},[2100],[1865,2297],{},[1865,2299,2301,2304],{"style":2300},"top:-2.85em;",[1865,2302],{"className":2303,"style":2109},[2108],[1865,2305,2307,2412,2415,2418,2421,2424],{"className":2306},[2080],[1865,2308,2310,2313,2409],{"className":2309},[2080],[1865,2311],{"className":2312},[2119,2120],[1865,2314,2316],{"className":2315},[1906],[1865,2317,2319,2401],{"className":2318},[2091,2092],[1865,2320,2322,2398],{"className":2321},[2096],[1865,2323,2325,2376,2384],{"className":2324,"style":2133},[2100],[1865,2326,2327,2330],{"style":2136},[1865,2328],{"className":2329,"style":2140},[2108],[1865,2331,2333,2336],{"className":2332},[2080],[1865,2334,1914],{"className":2335,"style":2147},[2080],[1865,2337,2339,2342],{"className":2338},[2080],[1865,2340,1927],{"className":2341},[2080,2154],[1865,2343,2345],{"className":2344},[2158],[1865,2346,2348,2368],{"className":2347},[2091,2092],[1865,2349,2351,2365],{"className":2350},[2096],[1865,2352,2354],{"className":2353,"style":2168},[2100],[1865,2355,2356,2359],{"style":2171},[1865,2357],{"className":2358,"style":2175},[2108],[1865,2360,2362],{"className":2361},[2179,2180,2181,2182],[1865,2363,1984],{"className":2364},[2080,2182],[1865,2366,2190],{"className":2367},[2189],[1865,2369,2371],{"className":2370},[2096],[1865,2372,2374],{"className":2373,"style":2197},[2100],[1865,2375],{},[1865,2377,2378,2381],{"style":2202},[1865,2379],{"className":2380,"style":2140},[2108],[1865,2382],{"className":2383,"style":2210},[2209],[1865,2385,2386,2389],{"style":2213},[1865,2387],{"className":2388,"style":2140},[2108],[1865,2390,2392,2395],{"className":2391},[2080],[1865,2393,1914],{"className":2394,"style":2147},[2080],[1865,2396,1917],{"className":2397,"style":2226},[2080,2154],[1865,2399,2190],{"className":2400},[2189],[1865,2402,2404],{"className":2403},[2096],[1865,2405,2407],{"className":2406,"style":2236},[2100],[1865,2408],{},[1865,2410],{"className":2411},[2242,2120],[1865,2413],{"className":2414,"style":2247},[2246],[1865,2416,1935],{"className":2417},[2251],[1865,2419],{"className":2420,"style":2247},[2246],[1865,2422,1938],{"className":2423},[2080,2154],[1865,2425,2427,2430],{"className":2426},[2080],[1865,2428,1798],{"className":2429},[2080,2154],[1865,2431,2433],{"className":2432},[2158],[1865,2434,2436,2456],{"className":2435},[2091,2092],[1865,2437,2439,2453],{"className":2438},[2096],[1865,2440,2442],{"className":2441,"style":2168},[2100],[1865,2443,2444,2447],{"style":2171},[1865,2445],{"className":2446,"style":2175},[2108],[1865,2448,2450],{"className":2449},[2179,2180,2181,2182],[1865,2451,1984],{"className":2452},[2080,2182],[1865,2454,2190],{"className":2455},[2189],[1865,2457,2459],{"className":2458},[2096],[1865,2460,2462],{"className":2461,"style":2197},[2100],[1865,2463],{},[1865,2465,2467,2470],{"style":2466},"top:-0.874em;",[1865,2468],{"className":2469,"style":2109},[2108],[1865,2471,2473,2513,2553,2556,2559,2562,2602,2642,2645,2648,2651],{"className":2472},[2080],[1865,2474,2476,2479],{"className":2475},[2080],[1865,2477,1798],{"className":2478},[2080,2154],[1865,2480,2482],{"className":2481},[2158],[1865,2483,2485,2505],{"className":2484},[2091,2092],[1865,2486,2488,2502],{"className":2487},[2096],[1865,2489,2491],{"className":2490,"style":2168},[2100],[1865,2492,2493,2496],{"style":2171},[1865,2494],{"className":2495,"style":2175},[2108],[1865,2497,2499],{"className":2498},[2179,2180,2181,2182],[1865,2500,1931],{"className":2501},[2080,2182],[1865,2503,2190],{"className":2504},[2189],[1865,2506,2508],{"className":2507},[2096],[1865,2509,2511],{"className":2510,"style":2197},[2100],[1865,2512],{},[1865,2514,2516,2519],{"className":2515},[2080],[1865,2517,1927],{"className":2518},[2080,2154],[1865,2520,2522],{"className":2521},[2158],[1865,2523,2525,2545],{"className":2524},[2091,2092],[1865,2526,2528,2542],{"className":2527},[2096],[1865,2529,2531],{"className":2530,"style":2168},[2100],[1865,2532,2533,2536],{"style":2171},[1865,2534],{"className":2535,"style":2175},[2108],[1865,2537,2539],{"className":2538},[2179,2180,2181,2182],[1865,2540,1931],{"className":2541},[2080,2182],[1865,2543,2190],{"className":2544},[2189],[1865,2546,2548],{"className":2547},[2096],[1865,2549,2551],{"className":2550,"style":2197},[2100],[1865,2552],{},[1865,2554],{"className":2555,"style":2247},[2246],[1865,2557,2029],{"className":2558},[2251],[1865,2560],{"className":2561,"style":2247},[2246],[1865,2563,2565,2568],{"className":2564},[2080],[1865,2566,1798],{"className":2567},[2080,2154],[1865,2569,2571],{"className":2570},[2158],[1865,2572,2574,2594],{"className":2573},[2091,2092],[1865,2575,2577,2591],{"className":2576},[2096],[1865,2578,2580],{"className":2579,"style":2168},[2100],[1865,2581,2582,2585],{"style":2171},[1865,2583],{"className":2584,"style":2175},[2108],[1865,2586,2588],{"className":2587},[2179,2180,2181,2182],[1865,2589,1984],{"className":2590},[2080,2182],[1865,2592,2190],{"className":2593},[2189],[1865,2595,2597],{"className":2596},[2096],[1865,2598,2600],{"className":2599,"style":2197},[2100],[1865,2601],{},[1865,2603,2605,2608],{"className":2604},[2080],[1865,2606,1927],{"className":2607},[2080,2154],[1865,2609,2611],{"className":2610},[2158],[1865,2612,2614,2634],{"className":2613},[2091,2092],[1865,2615,2617,2631],{"className":2616},[2096],[1865,2618,2620],{"className":2619,"style":2168},[2100],[1865,2621,2622,2625],{"style":2171},[1865,2623],{"className":2624,"style":2175},[2108],[1865,2626,2628],{"className":2627},[2179,2180,2181,2182],[1865,2629,1984],{"className":2630},[2080,2182],[1865,2632,2190],{"className":2633},[2189],[1865,2635,2637],{"className":2636},[2096],[1865,2638,2640],{"className":2639,"style":2197},[2100],[1865,2641],{},[1865,2643],{"className":2644,"style":2247},[2246],[1865,2646,1935],{"className":2647},[2251],[1865,2649],{"className":2650,"style":2247},[2246],[1865,2652,2046],{"className":2653},[2080,2154],[1865,2655,2190],{"className":2656},[2189],[1865,2658,2660],{"className":2659},[2096],[1865,2661,2664],{"className":2662,"style":2663},[2100],"height:2.8574em;",[1865,2665],{},[1865,2667,2670],{"className":2668},[2669],"col-align-l",[1865,2671,2673,2753],{"className":2672},[2091,2092],[1865,2674,2676,2750],{"className":2675},[2096],[1865,2677,2679,2704,2727],{"className":2678,"style":2101},[2100],[1865,2680,2681,2684],{"style":2104},[1865,2682],{"className":2683,"style":2109},[2108],[1865,2685,2687,2690,2694,2698,2701],{"className":2686},[2080],[1865,2688],{"className":2689},[2080],[1865,2691],{"className":2692,"style":2693},[2246],"margin-right:0.2778em;",[1865,2695,1955],{"className":2696},[2697],"mrel",[1865,2699],{"className":2700,"style":2693},[2246],[1865,2702,1900],{"className":2703},[2080],[1865,2705,2706,2709],{"style":2300},[1865,2707],{"className":2708,"style":2109},[2108],[1865,2710,2712,2715,2718,2721,2724],{"className":2711},[2080],[1865,2713],{"className":2714},[2080],[1865,2716],{"className":2717,"style":2693},[2246],[1865,2719,1955],{"className":2720},[2697],[1865,2722],{"className":2723,"style":2693},[2246],[1865,2725,1900],{"className":2726},[2080],[1865,2728,2729,2732],{"style":2466},[1865,2730],{"className":2731,"style":2109},[2108],[1865,2733,2735,2738,2741,2744,2747],{"className":2734},[2080],[1865,2736],{"className":2737},[2080],[1865,2739],{"className":2740,"style":2693},[2246],[1865,2742,1955],{"className":2743},[2697],[1865,2745],{"className":2746,"style":2693},[2246],[1865,2748,1900],{"className":2749},[2080],[1865,2751,2190],{"className":2752},[2189],[1865,2754,2756],{"className":2755},[2096],[1865,2757,2759],{"className":2758,"style":2663},[2100],[1865,2760],{},[1798,2762,2763,2764,2905,2906,3044],{},"这是一个包含3个方程、3个未知数(",[1865,2765,2767,2798],{"className":2766},[1872],[1865,2768,2770],{"className":2769},[1876],[1878,2771,2772],{"xmlns":1880},[1883,2773,2774,2795],{},[1903,2775,2776,2782,2785,2791,2793],{},[1923,2777,2778,2780],{},[1911,2779,1927],{},[1929,2781,1931],{},[1933,2783,2784],{"separator":1901},",",[1923,2786,2787,2789],{},[1911,2788,1927],{},[1929,2790,1984],{},[1933,2792,2784],{"separator":1901},[1911,2794,1938],{},[2060,2796,2797],{"encoding":2062},"x_1, x_2, \\lambda",[1865,2799,2801],{"className":2800,"ariaHidden":1901},[2067],[1865,2802,2804,2808,2848,2852,2856,2896,2899,2902],{"className":2803},[2071],[1865,2805],{"className":2806,"style":2807},[2075],"height:0.8889em;vertical-align:-0.1944em;",[1865,2809,2811,2814],{"className":2810},[2080],[1865,2812,1927],{"className":2813},[2080,2154],[1865,2815,2817],{"className":2816},[2158],[1865,2818,2820,2840],{"className":2819},[2091,2092],[1865,2821,2823,2837],{"className":2822},[2096],[1865,2824,2826],{"className":2825,"style":2168},[2100],[1865,2827,2828,2831],{"style":2171},[1865,2829],{"className":2830,"style":2175},[2108],[1865,2832,2834],{"className":2833},[2179,2180,2181,2182],[1865,2835,1931],{"className":2836},[2080,2182],[1865,2838,2190],{"className":2839},[2189],[1865,2841,2843],{"className":2842},[2096],[1865,2844,2846],{"className":2845,"style":2197},[2100],[1865,2847],{},[1865,2849,2784],{"className":2850},[2851],"mpunct",[1865,2853],{"className":2854,"style":2855},[2246],"margin-right:0.1667em;",[1865,2857,2859,2862],{"className":2858},[2080],[1865,2860,1927],{"className":2861},[2080,2154],[1865,2863,2865],{"className":2864},[2158],[1865,2866,2868,2888],{"className":2867},[2091,2092],[1865,2869,2871,2885],{"className":2870},[2096],[1865,2872,2874],{"className":2873,"style":2168},[2100],[1865,2875,2876,2879],{"style":2171},[1865,2877],{"className":2878,"style":2175},[2108],[1865,2880,2882],{"className":2881},[2179,2180,2181,2182],[1865,2883,1984],{"className":2884},[2080,2182],[1865,2886,2190],{"className":2887},[2189],[1865,2889,2891],{"className":2890},[2096],[1865,2892,2894],{"className":2893,"style":2197},[2100],[1865,2895],{},[1865,2897,2784],{"className":2898},[2851],[1865,2900],{"className":2901,"style":2855},[2246],[1865,2903,1938],{"className":2904},[2080,2154],")和参数(",[1865,2907,2909,2939],{"className":2908},[1872],[1865,2910,2912],{"className":2911},[1876],[1878,2913,2914],{"xmlns":1880},[1883,2915,2916,2936],{},[1903,2917,2918,2924,2926,2932,2934],{},[1923,2919,2920,2922],{},[1911,2921,1798],{},[1929,2923,1931],{},[1933,2925,2784],{"separator":1901},[1923,2927,2928,2930],{},[1911,2929,1798],{},[1929,2931,1984],{},[1933,2933,2784],{"separator":1901},[1911,2935,2046],{},[2060,2937,2938],{"encoding":2062},"p_1, p_2, m",[1865,2940,2942],{"className":2941,"ariaHidden":1901},[2067],[1865,2943,2945,2949,2989,2992,2995,3035,3038,3041],{"className":2944},[2071],[1865,2946],{"className":2947,"style":2948},[2075],"height:0.625em;vertical-align:-0.1944em;",[1865,2950,2952,2955],{"className":2951},[2080],[1865,2953,1798],{"className":2954},[2080,2154],[1865,2956,2958],{"className":2957},[2158],[1865,2959,2961,2981],{"className":2960},[2091,2092],[1865,2962,2964,2978],{"className":2963},[2096],[1865,2965,2967],{"className":2966,"style":2168},[2100],[1865,2968,2969,2972],{"style":2171},[1865,2970],{"className":2971,"style":2175},[2108],[1865,2973,2975],{"className":2974},[2179,2180,2181,2182],[1865,2976,1931],{"className":2977},[2080,2182],[1865,2979,2190],{"className":2980},[2189],[1865,2982,2984],{"className":2983},[2096],[1865,2985,2987],{"className":2986,"style":2197},[2100],[1865,2988],{},[1865,2990,2784],{"className":2991},[2851],[1865,2993],{"className":2994,"style":2855},[2246],[1865,2996,2998,3001],{"className":2997},[2080],[1865,2999,1798],{"className":3000},[2080,2154],[1865,3002,3004],{"className":3003},[2158],[1865,3005,3007,3027],{"className":3006},[2091,2092],[1865,3008,3010,3024],{"className":3009},[2096],[1865,3011,3013],{"className":3012,"style":2168},[2100],[1865,3014,3015,3018],{"style":2171},[1865,3016],{"className":3017,"style":2175},[2108],[1865,3019,3021],{"className":3020},[2179,2180,2181,2182],[1865,3022,1984],{"className":3023},[2080,2182],[1865,3025,2190],{"className":3026},[2189],[1865,3028,3030],{"className":3029},[2096],[1865,3031,3033],{"className":3032,"style":2197},[2100],[1865,3034],{},[1865,3036,2784],{"className":3037},[2851],[1865,3039],{"className":3040,"style":2855},[2246],[1865,3042,2046],{"className":3043},[2080,2154],")的系统。",[1798,3046,3047,3051],{},[3048,3049,3050],"strong",{},"隐函数定理","告诉我们，在满足正则性条件（雅可比矩阵非奇异）的情况下，我们可以将解表示为参数的隐函数，并求出其导数。",[1854,3053,3055],{"id":3054},"_12-价格变化的直接效应","1.2 价格变化的直接效应",[1798,3057,3058,3059,3129,3130,3206],{},"当价格",[1865,3060,3062,3080],{"className":3061},[1872],[1865,3063,3065],{"className":3064},[1876],[1878,3066,3067],{"xmlns":1880},[1883,3068,3069,3077],{},[1903,3070,3071],{},[1923,3072,3073,3075],{},[1911,3074,1798],{},[1929,3076,1931],{},[2060,3078,3079],{"encoding":2062},"p_1",[1865,3081,3083],{"className":3082,"ariaHidden":1901},[2067],[1865,3084,3086,3089],{"className":3085},[2071],[1865,3087],{"className":3088,"style":2948},[2075],[1865,3090,3092,3095],{"className":3091},[2080],[1865,3093,1798],{"className":3094},[2080,2154],[1865,3096,3098],{"className":3097},[2158],[1865,3099,3101,3121],{"className":3100},[2091,2092],[1865,3102,3104,3118],{"className":3103},[2096],[1865,3105,3107],{"className":3106,"style":2168},[2100],[1865,3108,3109,3112],{"style":2171},[1865,3110],{"className":3111,"style":2175},[2108],[1865,3113,3115],{"className":3114},[2179,2180,2181,2182],[1865,3116,1931],{"className":3117},[2080,2182],[1865,3119,2190],{"className":3120},[2189],[1865,3122,3124],{"className":3123},[2096],[1865,3125,3127],{"className":3126,"style":2197},[2100],[1865,3128],{},"发生微小变化",[1865,3131,3133,3154],{"className":3132},[1872],[1865,3134,3136],{"className":3135},[1876],[1878,3137,3138],{"xmlns":1880},[1883,3139,3140,3151],{},[1903,3141,3142,3145],{},[1911,3143,3144],{},"d",[1923,3146,3147,3149],{},[1911,3148,1798],{},[1929,3150,1931],{},[2060,3152,3153],{"encoding":2062},"dp_1",[1865,3155,3157],{"className":3156,"ariaHidden":1901},[2067],[1865,3158,3160,3163,3166],{"className":3159},[2071],[1865,3161],{"className":3162,"style":2807},[2075],[1865,3164,3144],{"className":3165},[2080,2154],[1865,3167,3169,3172],{"className":3168},[2080],[1865,3170,1798],{"className":3171},[2080,2154],[1865,3173,3175],{"className":3174},[2158],[1865,3176,3178,3198],{"className":3177},[2091,2092],[1865,3179,3181,3195],{"className":3180},[2096],[1865,3182,3184],{"className":3183,"style":2168},[2100],[1865,3185,3186,3189],{"style":2171},[1865,3187],{"className":3188,"style":2175},[2108],[1865,3190,3192],{"className":3191},[2179,2180,2181,2182],[1865,3193,1931],{"className":3194},[2080,2182],[1865,3196,2190],{"className":3197},[2189],[1865,3199,3201],{"className":3200},[2096],[1865,3202,3204],{"className":3203,"style":2197},[2100],[1865,3205],{},"时，最优需求的变化为：",[1865,3208,3210],{"className":3209},[1868],[1865,3211,3213,3248],{"className":3212},[1872],[1865,3214,3216],{"className":3215},[1876],[1878,3217,3218],{"xmlns":1880,"display":1881},[1883,3219,3220,3245],{},[1903,3221,3222],{},[1906,3223,3224,3235],{},[1903,3225,3226,3228],{},[1911,3227,1914],{"mathvariant":1913},[1923,3229,3230,3232],{},[1911,3231,1927],{},[1911,3233,3234],{},"i",[1903,3236,3237,3239],{},[1911,3238,1914],{"mathvariant":1913},[1923,3240,3241,3243],{},[1911,3242,1798],{},[1929,3244,1931],{},[2060,3246,3247],{"encoding":2062},"\\frac{\\partial x_i}{\\partial p_1}",[1865,3249,3251],{"className":3250,"ariaHidden":1901},[2067],[1865,3252,3254,3258],{"className":3253},[2071],[1865,3255],{"className":3256,"style":3257},[2075],"height:2.2519em;vertical-align:-0.8804em;",[1865,3259,3261,3264,3399],{"className":3260},[2080],[1865,3262],{"className":3263},[2119,2120],[1865,3265,3267],{"className":3266},[1906],[1865,3268,3270,3390],{"className":3269},[2091,2092],[1865,3271,3273,3387],{"className":3272},[2096],[1865,3274,3276,3327,3335],{"className":3275,"style":2133},[2100],[1865,3277,3278,3281],{"style":2136},[1865,3279],{"className":3280,"style":2140},[2108],[1865,3282,3284,3287],{"className":3283},[2080],[1865,3285,1914],{"className":3286,"style":2147},[2080],[1865,3288,3290,3293],{"className":3289},[2080],[1865,3291,1798],{"className":3292},[2080,2154],[1865,3294,3296],{"className":3295},[2158],[1865,3297,3299,3319],{"className":3298},[2091,2092],[1865,3300,3302,3316],{"className":3301},[2096],[1865,3303,3305],{"className":3304,"style":2168},[2100],[1865,3306,3307,3310],{"style":2171},[1865,3308],{"className":3309,"style":2175},[2108],[1865,3311,3313],{"className":3312},[2179,2180,2181,2182],[1865,3314,1931],{"className":3315},[2080,2182],[1865,3317,2190],{"className":3318},[2189],[1865,3320,3322],{"className":3321},[2096],[1865,3323,3325],{"className":3324,"style":2197},[2100],[1865,3326],{},[1865,3328,3329,3332],{"style":2202},[1865,3330],{"className":3331,"style":2140},[2108],[1865,3333],{"className":3334,"style":2210},[2209],[1865,3336,3337,3340],{"style":2213},[1865,3338],{"className":3339,"style":2140},[2108],[1865,3341,3343,3346],{"className":3342},[2080],[1865,3344,1914],{"className":3345,"style":2147},[2080],[1865,3347,3349,3352],{"className":3348},[2080],[1865,3350,1927],{"className":3351},[2080,2154],[1865,3353,3355],{"className":3354},[2158],[1865,3356,3358,3379],{"className":3357},[2091,2092],[1865,3359,3361,3376],{"className":3360},[2096],[1865,3362,3365],{"className":3363,"style":3364},[2100],"height:0.3117em;",[1865,3366,3367,3370],{"style":2171},[1865,3368],{"className":3369,"style":2175},[2108],[1865,3371,3373],{"className":3372},[2179,2180,2181,2182],[1865,3374,3234],{"className":3375},[2080,2154,2182],[1865,3377,2190],{"className":3378},[2189],[1865,3380,3382],{"className":3381},[2096],[1865,3383,3385],{"className":3384,"style":2197},[2100],[1865,3386],{},[1865,3388,2190],{"className":3389},[2189],[1865,3391,3393],{"className":3392},[2096],[1865,3394,3397],{"className":3395,"style":3396},[2100],"height:0.8804em;",[1865,3398],{},[1865,3400],{"className":3401},[2242,2120],[1798,3403,3404],{},"这个偏导数包含了两种效应的混合：",[3406,3407,3408,3414],"ol",{},[1808,3409,3410,3413],{},[3048,3411,3412],{},"替代效应",": 相对价格变化导致的需求调整（效用保持不变）",[1808,3415,3416,3419],{},[3048,3417,3418],{},"收入效应",": 实际购买力变化导致的需求调整",[3421,3422],"hr",{},[1794,3424,3426],{"id":3425},"_2-斯勒茨基方程-slutsky-equation","2. 斯勒茨基方程 (Slutsky Equation)",[1854,3428,3430],{"id":3429},"_21-方程的推导","2.1 方程的推导",[1798,3432,3433],{},"斯勒茨基方程是消费者理论中最重要的结果之一。它将价格变化对马歇尔需求的影响分解为两个部分：",[1865,3435,3437],{"className":3436},[1868],[1865,3438,3440,3548],{"className":3439},[1872],[1865,3441,3443],{"className":3442},[1876],[1878,3444,3445],{"xmlns":1880,"display":1881},[1883,3446,3447,3545],{},[1903,3448,3449,3472,3474,3497,3519,3521,3527],{},[1906,3450,3451,3461],{},[1903,3452,3453,3455],{},[1911,3454,1914],{"mathvariant":1913},[1923,3456,3457,3459],{},[1911,3458,1927],{},[1911,3460,3234],{},[1903,3462,3463,3465],{},[1911,3464,1914],{"mathvariant":1913},[1923,3466,3467,3469],{},[1911,3468,1798],{},[1911,3470,3471],{},"j",[1933,3473,1955],{},[1906,3475,3476,3487],{},[1903,3477,3478,3480],{},[1911,3479,1914],{"mathvariant":1913},[1923,3481,3482,3485],{},[1911,3483,3484],{},"h",[1911,3486,3234],{},[1903,3488,3489,3491],{},[1911,3490,1914],{"mathvariant":1913},[1923,3492,3493,3495],{},[1911,3494,1798],{},[1911,3496,3471],{},[1923,3498,3499,3504],{},[1933,3500,3503],{"fence":3501,"stretchy":1901,"minsize":3502,"maxsize":3502},"false","2.4em","∣",[1903,3505,3506,3509,3511],{},[1911,3507,3508],{},"u",[1933,3510,1955],{},[3512,3513,3514,3516],"mover",{"accent":1901},[1911,3515,3508],{},[1933,3517,3518],{},"ˉ",[1933,3520,1935],{},[1923,3522,3523,3525],{},[1911,3524,1927],{},[1911,3526,3471],{},[1906,3528,3529,3539],{},[1903,3530,3531,3533],{},[1911,3532,1914],{"mathvariant":1913},[1923,3534,3535,3537],{},[1911,3536,1927],{},[1911,3538,3234],{},[1903,3540,3541,3543],{},[1911,3542,1914],{"mathvariant":1913},[1911,3544,2046],{},[2060,3546,3547],{"encoding":2062},"\\frac{\\partial x_i}{\\partial p_j} = \\frac{\\partial h_i}{\\partial p_j}\\bigg|_{u=\\bar{u}} - x_j \\frac{\\partial x_i}{\\partial m}",[1865,3549,3551,3712,4002],{"className":3550,"ariaHidden":1901},[2067],[1865,3552,3554,3558,3703,3706,3709],{"className":3553},[2071],[1865,3555],{"className":3556,"style":3557},[2075],"height:2.3435em;vertical-align:-0.9721em;",[1865,3559,3561,3564,3700],{"className":3560},[2080],[1865,3562],{"className":3563},[2119,2120],[1865,3565,3567],{"className":3566},[1906],[1865,3568,3570,3691],{"className":3569},[2091,2092],[1865,3571,3573,3688],{"className":3572},[2096],[1865,3574,3576,3629,3637],{"className":3575,"style":2133},[2100],[1865,3577,3578,3581],{"style":2136},[1865,3579],{"className":3580,"style":2140},[2108],[1865,3582,3584,3587],{"className":3583},[2080],[1865,3585,1914],{"className":3586,"style":2147},[2080],[1865,3588,3590,3593],{"className":3589},[2080],[1865,3591,1798],{"className":3592},[2080,2154],[1865,3594,3596],{"className":3595},[2158],[1865,3597,3599,3620],{"className":3598},[2091,2092],[1865,3600,3602,3617],{"className":3601},[2096],[1865,3603,3605],{"className":3604,"style":3364},[2100],[1865,3606,3607,3610],{"style":2171},[1865,3608],{"className":3609,"style":2175},[2108],[1865,3611,3613],{"className":3612},[2179,2180,2181,2182],[1865,3614,3471],{"className":3615,"style":3616},[2080,2154,2182],"margin-right:0.0572em;",[1865,3618,2190],{"className":3619},[2189],[1865,3621,3623],{"className":3622},[2096],[1865,3624,3627],{"className":3625,"style":3626},[2100],"height:0.2861em;",[1865,3628],{},[1865,3630,3631,3634],{"style":2202},[1865,3632],{"className":3633,"style":2140},[2108],[1865,3635],{"className":3636,"style":2210},[2209],[1865,3638,3639,3642],{"style":2213},[1865,3640],{"className":3641,"style":2140},[2108],[1865,3643,3645,3648],{"className":3644},[2080],[1865,3646,1914],{"className":3647,"style":2147},[2080],[1865,3649,3651,3654],{"className":3650},[2080],[1865,3652,1927],{"className":3653},[2080,2154],[1865,3655,3657],{"className":3656},[2158],[1865,3658,3660,3680],{"className":3659},[2091,2092],[1865,3661,3663,3677],{"className":3662},[2096],[1865,3664,3666],{"className":3665,"style":3364},[2100],[1865,3667,3668,3671],{"style":2171},[1865,3669],{"className":3670,"style":2175},[2108],[1865,3672,3674],{"className":3673},[2179,2180,2181,2182],[1865,3675,3234],{"className":3676},[2080,2154,2182],[1865,3678,2190],{"className":3679},[2189],[1865,3681,3683],{"className":3682},[2096],[1865,3684,3686],{"className":3685,"style":2197},[2100],[1865,3687],{},[1865,3689,2190],{"className":3690},[2189],[1865,3692,3694],{"className":3693},[2096],[1865,3695,3698],{"className":3696,"style":3697},[2100],"height:0.9721em;",[1865,3699],{},[1865,3701],{"className":3702},[2242,2120],[1865,3704],{"className":3705,"style":2693},[2246],[1865,3707,1955],{"className":3708},[2697],[1865,3710],{"className":3711,"style":2693},[2246],[1865,3713,3715,3719,3861,3993,3996,3999],{"className":3714},[2071],[1865,3716],{"className":3717,"style":3718},[2075],"height:2.4497em;vertical-align:-0.9997em;",[1865,3720,3722,3725,3858],{"className":3721},[2080],[1865,3723],{"className":3724},[2119,2120],[1865,3726,3728],{"className":3727},[1906],[1865,3729,3731,3850],{"className":3730},[2091,2092],[1865,3732,3734,3847],{"className":3733},[2096],[1865,3735,3737,3788,3796],{"className":3736,"style":2133},[2100],[1865,3738,3739,3742],{"style":2136},[1865,3740],{"className":3741,"style":2140},[2108],[1865,3743,3745,3748],{"className":3744},[2080],[1865,3746,1914],{"className":3747,"style":2147},[2080],[1865,3749,3751,3754],{"className":3750},[2080],[1865,3752,1798],{"className":3753},[2080,2154],[1865,3755,3757],{"className":3756},[2158],[1865,3758,3760,3780],{"className":3759},[2091,2092],[1865,3761,3763,3777],{"className":3762},[2096],[1865,3764,3766],{"className":3765,"style":3364},[2100],[1865,3767,3768,3771],{"style":2171},[1865,3769],{"className":3770,"style":2175},[2108],[1865,3772,3774],{"className":3773},[2179,2180,2181,2182],[1865,3775,3471],{"className":3776,"style":3616},[2080,2154,2182],[1865,3778,2190],{"className":3779},[2189],[1865,3781,3783],{"className":3782},[2096],[1865,3784,3786],{"className":3785,"style":3626},[2100],[1865,3787],{},[1865,3789,3790,3793],{"style":2202},[1865,3791],{"className":3792,"style":2140},[2108],[1865,3794],{"className":3795,"style":2210},[2209],[1865,3797,3798,3801],{"style":2213},[1865,3799],{"className":3800,"style":2140},[2108],[1865,3802,3804,3807],{"className":3803},[2080],[1865,3805,1914],{"className":3806,"style":2147},[2080],[1865,3808,3810,3813],{"className":3809},[2080],[1865,3811,3484],{"className":3812},[2080,2154],[1865,3814,3816],{"className":3815},[2158],[1865,3817,3819,3839],{"className":3818},[2091,2092],[1865,3820,3822,3836],{"className":3821},[2096],[1865,3823,3825],{"className":3824,"style":3364},[2100],[1865,3826,3827,3830],{"style":2171},[1865,3828],{"className":3829,"style":2175},[2108],[1865,3831,3833],{"className":3832},[2179,2180,2181,2182],[1865,3834,3234],{"className":3835},[2080,2154,2182],[1865,3837,2190],{"className":3838},[2189],[1865,3840,3842],{"className":3841},[2096],[1865,3843,3845],{"className":3844,"style":2197},[2100],[1865,3846],{},[1865,3848,2190],{"className":3849},[2189],[1865,3851,3853],{"className":3852},[2096],[1865,3854,3856],{"className":3855,"style":3697},[2100],[1865,3857],{},[1865,3859],{"className":3860},[2242,2120],[1865,3862,3864,3914],{"className":3863},[2080],[1865,3865,3867],{"className":3866},[2080],[1865,3868,3872],{"className":3869},[3870,3871],"delimsizing","mult",[1865,3873,3875,3905],{"className":3874},[2091,2092],[1865,3876,3878,3902],{"className":3877},[2096],[1865,3879,3882],{"className":3880,"style":3881},[2100],"height:1.45em;",[1865,3883,3885,3889],{"style":3884},"top:-3.45em;",[1865,3886],{"className":3887,"style":3888},[2108],"height:4.4em;",[1865,3890,3892],{"style":3891},"width:0.333em;height:2.4em;",[3893,3894,3898],"svg",{"xmlns":3895,"width":3896,"height":3502,"viewBox":3897},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","0.333em","0 0 333 2400",[3899,3900],"path",{"d":3901},"M145 15 v585 v1200 v585 c2.667,10,9.667,15,21,15\nc10,0,16.667,-5,20,-15 v-585 v-1200 v-585 c-2.667,-10,-9.667,-15,-21,-15\nc-10,0,-16.667,5,-20,15z M188 15 H145 v585 v1200 v585 h43z",[1865,3903,2190],{"className":3904},[2189],[1865,3906,3908],{"className":3907},[2096],[1865,3909,3912],{"className":3910,"style":3911},[2100],"height:0.95em;",[1865,3913],{},[1865,3915,3917],{"className":3916},[2158],[1865,3918,3920,3984],{"className":3919},[2091,2092],[1865,3921,3923,3981],{"className":3922},[2096],[1865,3924,3927],{"className":3925,"style":3926},[2100],"height:-0.6023em;",[1865,3928,3930,3933],{"style":3929},"top:-1.7003em;margin-right:0.05em;",[1865,3931],{"className":3932,"style":2175},[2108],[1865,3934,3936],{"className":3935},[2179,2180,2181,2182],[1865,3937,3939,3942,3945],{"className":3938},[2080,2182],[1865,3940,3508],{"className":3941},[2080,2154,2182],[1865,3943,1955],{"className":3944},[2697,2182],[1865,3946,3949],{"className":3947},[2080,3948,2182],"accent",[1865,3950,3952],{"className":3951},[2091],[1865,3953,3955],{"className":3954},[2096],[1865,3956,3959,3968],{"className":3957,"style":3958},[2100],"height:0.5678em;",[1865,3960,3962,3965],{"style":3961},"top:-2.7em;",[1865,3963],{"className":3964,"style":2175},[2108],[1865,3966,3508],{"className":3967},[2080,2154,2182],[1865,3969,3970,3973],{"style":3961},[1865,3971],{"className":3972,"style":2175},[2108],[1865,3974,3978],{"className":3975,"style":3977},[3976],"accent-body","left:-0.2222em;",[1865,3979,3518],{"className":3980},[2080,2182],[1865,3982,2190],{"className":3983},[2189],[1865,3985,3987],{"className":3986},[2096],[1865,3988,3991],{"className":3989,"style":3990},[2100],"height:0.9997em;",[1865,3992],{},[1865,3994],{"className":3995,"style":2247},[2246],[1865,3997,1935],{"className":3998},[2251],[1865,4000],{"className":4001,"style":2247},[2246],[1865,4003,4005,4009,4049],{"className":4004},[2071],[1865,4006],{"className":4007,"style":4008},[2075],"height:2.0574em;vertical-align:-0.686em;",[1865,4010,4012,4015],{"className":4011},[2080],[1865,4013,1927],{"className":4014},[2080,2154],[1865,4016,4018],{"className":4017},[2158],[1865,4019,4021,4041],{"className":4020},[2091,2092],[1865,4022,4024,4038],{"className":4023},[2096],[1865,4025,4027],{"className":4026,"style":3364},[2100],[1865,4028,4029,4032],{"style":2171},[1865,4030],{"className":4031,"style":2175},[2108],[1865,4033,4035],{"className":4034},[2179,2180,2181,2182],[1865,4036,3471],{"className":4037,"style":3616},[2080,2154,2182],[1865,4039,2190],{"className":4040},[2189],[1865,4042,4044],{"className":4043},[2096],[1865,4045,4047],{"className":4046,"style":3626},[2100],[1865,4048],{},[1865,4050,4052,4055,4152],{"className":4051},[2080],[1865,4053],{"className":4054},[2119,2120],[1865,4056,4058],{"className":4057},[1906],[1865,4059,4061,4143],{"className":4060},[2091,2092],[1865,4062,4064,4140],{"className":4063},[2096],[1865,4065,4067,4081,4089],{"className":4066,"style":2133},[2100],[1865,4068,4069,4072],{"style":2136},[1865,4070],{"className":4071,"style":2140},[2108],[1865,4073,4075,4078],{"className":4074},[2080],[1865,4076,1914],{"className":4077,"style":2147},[2080],[1865,4079,2046],{"className":4080},[2080,2154],[1865,4082,4083,4086],{"style":2202},[1865,4084],{"className":4085,"style":2140},[2108],[1865,4087],{"className":4088,"style":2210},[2209],[1865,4090,4091,4094],{"style":2213},[1865,4092],{"className":4093,"style":2140},[2108],[1865,4095,4097,4100],{"className":4096},[2080],[1865,4098,1914],{"className":4099,"style":2147},[2080],[1865,4101,4103,4106],{"className":4102},[2080],[1865,4104,1927],{"className":4105},[2080,2154],[1865,4107,4109],{"className":4108},[2158],[1865,4110,4112,4132],{"className":4111},[2091,2092],[1865,4113,4115,4129],{"className":4114},[2096],[1865,4116,4118],{"className":4117,"style":3364},[2100],[1865,4119,4120,4123],{"style":2171},[1865,4121],{"className":4122,"style":2175},[2108],[1865,4124,4126],{"className":4125},[2179,2180,2181,2182],[1865,4127,3234],{"className":4128},[2080,2154,2182],[1865,4130,2190],{"className":4131},[2189],[1865,4133,4135],{"className":4134},[2096],[1865,4136,4138],{"className":4137,"style":2197},[2100],[1865,4139],{},[1865,4141,2190],{"className":4142},[2189],[1865,4144,4146],{"className":4145},[2096],[1865,4147,4150],{"className":4148,"style":4149},[2100],"height:0.686em;",[1865,4151],{},[1865,4153],{"className":4154},[2242,2120],[1798,4156,4157],{},"其中：",[1805,4159,4160,4373,4699],{},[1808,4161,4162,4368,4369,4372],{},[1865,4163,4165,4199],{"className":4164},[1872],[1865,4166,4168],{"className":4167},[1876],[1878,4169,4170],{"xmlns":1880},[1883,4171,4172,4196],{},[1903,4173,4174],{},[1906,4175,4176,4186],{},[1903,4177,4178,4180],{},[1911,4179,1914],{"mathvariant":1913},[1923,4181,4182,4184],{},[1911,4183,1927],{},[1911,4185,3234],{},[1903,4187,4188,4190],{},[1911,4189,1914],{"mathvariant":1913},[1923,4191,4192,4194],{},[1911,4193,1798],{},[1911,4195,3471],{},[2060,4197,4198],{"encoding":2062},"\\frac{\\partial x_i}{\\partial p_j}",[1865,4200,4202],{"className":4201,"ariaHidden":1901},[2067],[1865,4203,4205,4209],{"className":4204},[2071],[1865,4206],{"className":4207,"style":4208},[2075],"height:1.4385em;vertical-align:-0.5423em;",[1865,4210,4212,4215,4365],{"className":4211},[2080],[1865,4213],{"className":4214},[2119,2120],[1865,4216,4218],{"className":4217},[1906],[1865,4219,4221,4356],{"className":4220},[2091,2092],[1865,4222,4224,4353],{"className":4223},[2096],[1865,4225,4228,4289,4297],{"className":4226,"style":4227},[2100],"height:0.8962em;",[1865,4229,4231,4234],{"style":4230},"top:-2.655em;",[1865,4232],{"className":4233,"style":2140},[2108],[1865,4235,4237],{"className":4236},[2179,2180,2181,2182],[1865,4238,4240,4243],{"className":4239},[2080,2182],[1865,4241,1914],{"className":4242,"style":2147},[2080,2182],[1865,4244,4246,4249],{"className":4245},[2080,2182],[1865,4247,1798],{"className":4248},[2080,2154,2182],[1865,4250,4252],{"className":4251},[2158],[1865,4253,4255,4280],{"className":4254},[2091,2092],[1865,4256,4258,4277],{"className":4257},[2096],[1865,4259,4262],{"className":4260,"style":4261},[2100],"height:0.3281em;",[1865,4263,4265,4269],{"style":4264},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[1865,4266],{"className":4267,"style":4268},[2108],"height:2.5em;",[1865,4270,4274],{"className":4271},[2179,4272,4273,2182],"reset-size3","size1",[1865,4275,3471],{"className":4276,"style":3616},[2080,2154,2182],[1865,4278,2190],{"className":4279},[2189],[1865,4281,4283],{"className":4282},[2096],[1865,4284,4287],{"className":4285,"style":4286},[2100],"height:0.2819em;",[1865,4288],{},[1865,4290,4291,4294],{"style":2202},[1865,4292],{"className":4293,"style":2140},[2108],[1865,4295],{"className":4296,"style":2210},[2209],[1865,4298,4300,4303],{"style":4299},"top:-3.4101em;",[1865,4301],{"className":4302,"style":2140},[2108],[1865,4304,4306],{"className":4305},[2179,2180,2181,2182],[1865,4307,4309,4312],{"className":4308},[2080,2182],[1865,4310,1914],{"className":4311,"style":2147},[2080,2182],[1865,4313,4315,4318],{"className":4314},[2080,2182],[1865,4316,1927],{"className":4317},[2080,2154,2182],[1865,4319,4321],{"className":4320},[2158],[1865,4322,4324,4344],{"className":4323},[2091,2092],[1865,4325,4327,4341],{"className":4326},[2096],[1865,4328,4330],{"className":4329,"style":4261},[2100],[1865,4331,4332,4335],{"style":4264},[1865,4333],{"className":4334,"style":4268},[2108],[1865,4336,4338],{"className":4337},[2179,4272,4273,2182],[1865,4339,3234],{"className":4340},[2080,2154,2182],[1865,4342,2190],{"className":4343},[2189],[1865,4345,4347],{"className":4346},[2096],[1865,4348,4351],{"className":4349,"style":4350},[2100],"height:0.143em;",[1865,4352],{},[1865,4354,2190],{"className":4355},[2189],[1865,4357,4359],{"className":4358},[2096],[1865,4360,4363],{"className":4361,"style":4362},[2100],"height:0.5423em;",[1865,4364],{},[1865,4366],{"className":4367},[2242,2120]," 是",[3048,4370,4371],{},"总效应"," (Total Effect)",[1808,4374,4375,4368,4696,4698],{},[1865,4376,4378,4428],{"className":4377},[1872],[1865,4379,4381],{"className":4380},[1876],[1878,4382,4383],{"xmlns":1880},[1883,4384,4385,4425],{},[1903,4386,4387,4409],{},[1906,4388,4389,4399],{},[1903,4390,4391,4393],{},[1911,4392,1914],{"mathvariant":1913},[1923,4394,4395,4397],{},[1911,4396,3484],{},[1911,4398,3234],{},[1903,4400,4401,4403],{},[1911,4402,1914],{"mathvariant":1913},[1923,4404,4405,4407],{},[1911,4406,1798],{},[1911,4408,3471],{},[1923,4410,4411,4413],{},[1933,4412,3503],{"fence":3501,"stretchy":1901,"minsize":3502,"maxsize":3502},[1903,4414,4415,4417,4419],{},[1911,4416,3508],{},[1933,4418,1955],{},[3512,4420,4421,4423],{"accent":1901},[1911,4422,3508],{},[1933,4424,3518],{},[2060,4426,4427],{"encoding":2062},"\\frac{\\partial h_i}{\\partial p_j}\\bigg|_{u=\\bar{u}}",[1865,4429,4431],{"className":4430,"ariaHidden":1901},[2067],[1865,4432,4434,4437,4585],{"className":4433},[2071],[1865,4435],{"className":4436,"style":3718},[2075],[1865,4438,4440,4443,4582],{"className":4439},[2080],[1865,4441],{"className":4442},[2119,2120],[1865,4444,4446],{"className":4445},[1906],[1865,4447,4449,4574],{"className":4448},[2091,2092],[1865,4450,4452,4571],{"className":4451},[2096],[1865,4453,4455,4509,4517],{"className":4454,"style":4227},[2100],[1865,4456,4457,4460],{"style":4230},[1865,4458],{"className":4459,"style":2140},[2108],[1865,4461,4463],{"className":4462},[2179,2180,2181,2182],[1865,4464,4466,4469],{"className":4465},[2080,2182],[1865,4467,1914],{"className":4468,"style":2147},[2080,2182],[1865,4470,4472,4475],{"className":4471},[2080,2182],[1865,4473,1798],{"className":4474},[2080,2154,2182],[1865,4476,4478],{"className":4477},[2158],[1865,4479,4481,4501],{"className":4480},[2091,2092],[1865,4482,4484,4498],{"className":4483},[2096],[1865,4485,4487],{"className":4486,"style":4261},[2100],[1865,4488,4489,4492],{"style":4264},[1865,4490],{"className":4491,"style":4268},[2108],[1865,4493,4495],{"className":4494},[2179,4272,4273,2182],[1865,4496,3471],{"className":4497,"style":3616},[2080,2154,2182],[1865,4499,2190],{"className":4500},[2189],[1865,4502,4504],{"className":4503},[2096],[1865,4505,4507],{"className":4506,"style":4286},[2100],[1865,4508],{},[1865,4510,4511,4514],{"style":2202},[1865,4512],{"className":4513,"style":2140},[2108],[1865,4515],{"className":4516,"style":2210},[2209],[1865,4518,4519,4522],{"style":4299},[1865,4520],{"className":4521,"style":2140},[2108],[1865,4523,4525],{"className":4524},[2179,2180,2181,2182],[1865,4526,4528,4531],{"className":4527},[2080,2182],[1865,4529,1914],{"className":4530,"style":2147},[2080,2182],[1865,4532,4534,4537],{"className":4533},[2080,2182],[1865,4535,3484],{"className":4536},[2080,2154,2182],[1865,4538,4540],{"className":4539},[2158],[1865,4541,4543,4563],{"className":4542},[2091,2092],[1865,4544,4546,4560],{"className":4545},[2096],[1865,4547,4549],{"className":4548,"style":4261},[2100],[1865,4550,4551,4554],{"style":4264},[1865,4552],{"className":4553,"style":4268},[2108],[1865,4555,4557],{"className":4556},[2179,4272,4273,2182],[1865,4558,3234],{"className":4559},[2080,2154,2182],[1865,4561,2190],{"className":4562},[2189],[1865,4564,4566],{"className":4565},[2096],[1865,4567,4569],{"className":4568,"style":4350},[2100],[1865,4570],{},[1865,4572,2190],{"className":4573},[2189],[1865,4575,4577],{"className":4576},[2096],[1865,4578,4580],{"className":4579,"style":4362},[2100],[1865,4581],{},[1865,4583],{"className":4584},[2242,2120],[1865,4586,4588,4625],{"className":4587},[2080],[1865,4589,4591],{"className":4590},[2080],[1865,4592,4594],{"className":4593},[3870,3871],[1865,4595,4597,4617],{"className":4596},[2091,2092],[1865,4598,4600,4614],{"className":4599},[2096],[1865,4601,4603],{"className":4602,"style":3881},[2100],[1865,4604,4605,4608],{"style":3884},[1865,4606],{"className":4607,"style":3888},[2108],[1865,4609,4610],{"style":3891},[3893,4611,4612],{"xmlns":3895,"width":3896,"height":3502,"viewBox":3897},[3899,4613],{"d":3901},[1865,4615,2190],{"className":4616},[2189],[1865,4618,4620],{"className":4619},[2096],[1865,4621,4623],{"className":4622,"style":3911},[2100],[1865,4624],{},[1865,4626,4628],{"className":4627},[2158],[1865,4629,4631,4688],{"className":4630},[2091,2092],[1865,4632,4634,4685],{"className":4633},[2096],[1865,4635,4637],{"className":4636,"style":3926},[2100],[1865,4638,4639,4642],{"style":3929},[1865,4640],{"className":4641,"style":2175},[2108],[1865,4643,4645],{"className":4644},[2179,2180,2181,2182],[1865,4646,4648,4651,4654],{"className":4647},[2080,2182],[1865,4649,3508],{"className":4650},[2080,2154,2182],[1865,4652,1955],{"className":4653},[2697,2182],[1865,4655,4657],{"className":4656},[2080,3948,2182],[1865,4658,4660],{"className":4659},[2091],[1865,4661,4663],{"className":4662},[2096],[1865,4664,4666,4674],{"className":4665,"style":3958},[2100],[1865,4667,4668,4671],{"style":3961},[1865,4669],{"className":4670,"style":2175},[2108],[1865,4672,3508],{"className":4673},[2080,2154,2182],[1865,4675,4676,4679],{"style":3961},[1865,4677],{"className":4678,"style":2175},[2108],[1865,4680,4682],{"className":4681,"style":3977},[3976],[1865,4683,3518],{"className":4684},[2080,2182],[1865,4686,2190],{"className":4687},[2189],[1865,4689,4691],{"className":4690},[2096],[1865,4692,4694],{"className":4693,"style":3990},[2100],[1865,4695],{},[3048,4697,3412],{}," (Substitution Effect)，在效用不变时的需求变化",[1808,4700,4701,4368,4907,4909],{},[1865,4702,4704,4742],{"className":4703},[1872],[1865,4705,4707],{"className":4706},[1876],[1878,4708,4709],{"xmlns":1880},[1883,4710,4711,4739],{},[1903,4712,4713,4715,4721],{},[1933,4714,1935],{},[1923,4716,4717,4719],{},[1911,4718,1927],{},[1911,4720,3471],{},[1906,4722,4723,4733],{},[1903,4724,4725,4727],{},[1911,4726,1914],{"mathvariant":1913},[1923,4728,4729,4731],{},[1911,4730,1927],{},[1911,4732,3234],{},[1903,4734,4735,4737],{},[1911,4736,1914],{"mathvariant":1913},[1911,4738,2046],{},[2060,4740,4741],{"encoding":2062},"-x_j \\frac{\\partial x_i}{\\partial m}",[1865,4743,4745],{"className":4744,"ariaHidden":1901},[2067],[1865,4746,4748,4752,4755,4795],{"className":4747},[2071],[1865,4749],{"className":4750,"style":4751},[2075],"height:1.2412em;vertical-align:-0.345em;",[1865,4753,1935],{"className":4754},[2080],[1865,4756,4758,4761],{"className":4757},[2080],[1865,4759,1927],{"className":4760},[2080,2154],[1865,4762,4764],{"className":4763},[2158],[1865,4765,4767,4787],{"className":4766},[2091,2092],[1865,4768,4770,4784],{"className":4769},[2096],[1865,4771,4773],{"className":4772,"style":3364},[2100],[1865,4774,4775,4778],{"style":2171},[1865,4776],{"className":4777,"style":2175},[2108],[1865,4779,4781],{"className":4780},[2179,2180,2181,2182],[1865,4782,3471],{"className":4783,"style":3616},[2080,2154,2182],[1865,4785,2190],{"className":4786},[2189],[1865,4788,4790],{"className":4789},[2096],[1865,4791,4793],{"className":4792,"style":3626},[2100],[1865,4794],{},[1865,4796,4798,4801,4904],{"className":4797},[2080],[1865,4799],{"className":4800},[2119,2120],[1865,4802,4804],{"className":4803},[1906],[1865,4805,4807,4895],{"className":4806},[2091,2092],[1865,4808,4810,4892],{"className":4809},[2096],[1865,4811,4813,4830,4838],{"className":4812,"style":4227},[2100],[1865,4814,4815,4818],{"style":4230},[1865,4816],{"className":4817,"style":2140},[2108],[1865,4819,4821],{"className":4820},[2179,2180,2181,2182],[1865,4822,4824,4827],{"className":4823},[2080,2182],[1865,4825,1914],{"className":4826,"style":2147},[2080,2182],[1865,4828,2046],{"className":4829},[2080,2154,2182],[1865,4831,4832,4835],{"style":2202},[1865,4833],{"className":4834,"style":2140},[2108],[1865,4836],{"className":4837,"style":2210},[2209],[1865,4839,4840,4843],{"style":4299},[1865,4841],{"className":4842,"style":2140},[2108],[1865,4844,4846],{"className":4845},[2179,2180,2181,2182],[1865,4847,4849,4852],{"className":4848},[2080,2182],[1865,4850,1914],{"className":4851,"style":2147},[2080,2182],[1865,4853,4855,4858],{"className":4854},[2080,2182],[1865,4856,1927],{"className":4857},[2080,2154,2182],[1865,4859,4861],{"className":4860},[2158],[1865,4862,4864,4884],{"className":4863},[2091,2092],[1865,4865,4867,4881],{"className":4866},[2096],[1865,4868,4870],{"className":4869,"style":4261},[2100],[1865,4871,4872,4875],{"style":4264},[1865,4873],{"className":4874,"style":4268},[2108],[1865,4876,4878],{"className":4877},[2179,4272,4273,2182],[1865,4879,3234],{"className":4880},[2080,2154,2182],[1865,4882,2190],{"className":4883},[2189],[1865,4885,4887],{"className":4886},[2096],[1865,4888,4890],{"className":4889,"style":4350},[2100],[1865,4891],{},[1865,4893,2190],{"className":4894},[2189],[1865,4896,4898],{"className":4897},[2096],[1865,4899,4902],{"className":4900,"style":4901},[2100],"height:0.345em;",[1865,4903],{},[1865,4905],{"className":4906},[2242,2120],[3048,4908,3418],{}," (Income Effect)，因实际收入变化导致的需求变化",[1798,4911,4912,4915],{},[3048,4913,4914],{},"详细推导",":",[1798,4917,4918],{},"从恒等式出发：",[1865,4920,4922],{"className":4921},[1868],[1865,4923,4925,5021],{"className":4924},[1872],[1865,4926,4928],{"className":4927},[1876],[1878,4929,4930],{"xmlns":1880,"display":1881},[1883,4931,4932,5018],{},[1903,4933,4934,4940,4943,4949,4951,4957,4959,4961,4964,4967,4973,4975,4981,4983,4989,4991,4994,4996,5002,5004,5010,5012,5014,5016],{},[1923,4935,4936,4938],{},[1911,4937,1927],{},[1911,4939,3234],{},[1933,4941,4942],{"stretchy":3501},"(",[1923,4944,4945,4947],{},[1911,4946,1798],{},[1929,4948,1931],{},[1933,4950,2784],{"separator":1901},[1923,4952,4953,4955],{},[1911,4954,1798],{},[1929,4956,1984],{},[1933,4958,2784],{"separator":1901},[1911,4960,2046],{},[1933,4962,4963],{"stretchy":3501},")",[1933,4965,4966],{},"≡",[1923,4968,4969,4971],{},[1911,4970,3484],{},[1911,4972,3234],{},[1933,4974,4942],{"stretchy":3501},[1923,4976,4977,4979],{},[1911,4978,1798],{},[1929,4980,1931],{},[1933,4982,2784],{"separator":1901},[1923,4984,4985,4987],{},[1911,4986,1798],{},[1929,4988,1984],{},[1933,4990,2784],{"separator":1901},[1911,4992,4993],{},"v",[1933,4995,4942],{"stretchy":3501},[1923,4997,4998,5000],{},[1911,4999,1798],{},[1929,5001,1931],{},[1933,5003,2784],{"separator":1901},[1923,5005,5006,5008],{},[1911,5007,1798],{},[1929,5009,1984],{},[1933,5011,2784],{"separator":1901},[1911,5013,2046],{},[1933,5015,4963],{"stretchy":3501},[1933,5017,4963],{"stretchy":3501},[2060,5019,5020],{"encoding":2062},"x_i(p_1, p_2, m) \\equiv h_i(p_1, p_2, v(p_1, p_2, m))",[1865,5022,5024,5181],{"className":5023,"ariaHidden":1901},[2067],[1865,5025,5027,5031,5071,5074,5114,5117,5120,5160,5163,5166,5169,5172,5175,5178],{"className":5026},[2071],[1865,5028],{"className":5029,"style":5030},[2075],"height:1em;vertical-align:-0.25em;",[1865,5032,5034,5037],{"className":5033},[2080],[1865,5035,1927],{"className":5036},[2080,2154],[1865,5038,5040],{"className":5039},[2158],[1865,5041,5043,5063],{"className":5042},[2091,2092],[1865,5044,5046,5060],{"className":5045},[2096],[1865,5047,5049],{"className":5048,"style":3364},[2100],[1865,5050,5051,5054],{"style":2171},[1865,5052],{"className":5053,"style":2175},[2108],[1865,5055,5057],{"className":5056},[2179,2180,2181,2182],[1865,5058,3234],{"className":5059},[2080,2154,2182],[1865,5061,2190],{"className":5062},[2189],[1865,5064,5066],{"className":5065},[2096],[1865,5067,5069],{"className":5068,"style":2197},[2100],[1865,5070],{},[1865,5072,4942],{"className":5073},[2119],[1865,5075,5077,5080],{"className":5076},[2080],[1865,5078,1798],{"className":5079},[2080,2154],[1865,5081,5083],{"className":5082},[2158],[1865,5084,5086,5106],{"className":5085},[2091,2092],[1865,5087,5089,5103],{"className":5088},[2096],[1865,5090,5092],{"className":5091,"style":2168},[2100],[1865,5093,5094,5097],{"style":2171},[1865,5095],{"className":5096,"style":2175},[2108],[1865,5098,5100],{"className":5099},[2179,2180,2181,2182],[1865,5101,1931],{"className":5102},[2080,2182],[1865,5104,2190],{"className":5105},[2189],[1865,5107,5109],{"className":5108},[2096],[1865,5110,5112],{"className":5111,"style":2197},[2100],[1865,5113],{},[1865,5115,2784],{"className":5116},[2851],[1865,5118],{"className":5119,"style":2855},[2246],[1865,5121,5123,5126],{"className":5122},[2080],[1865,5124,1798],{"className":5125},[2080,2154],[1865,5127,5129],{"className":5128},[2158],[1865,5130,5132,5152],{"className":5131},[2091,2092],[1865,5133,5135,5149],{"className":5134},[2096],[1865,5136,5138],{"className":5137,"style":2168},[2100],[1865,5139,5140,5143],{"style":2171},[1865,5141],{"className":5142,"style":2175},[2108],[1865,5144,5146],{"className":5145},[2179,2180,2181,2182],[1865,5147,1984],{"className":5148},[2080,2182],[1865,5150,2190],{"className":5151},[2189],[1865,5153,5155],{"className":5154},[2096],[1865,5156,5158],{"className":5157,"style":2197},[2100],[1865,5159],{},[1865,5161,2784],{"className":5162},[2851],[1865,5164],{"className":5165,"style":2855},[2246],[1865,5167,2046],{"className":5168},[2080,2154],[1865,5170,4963],{"className":5171},[2242],[1865,5173],{"className":5174,"style":2693},[2246],[1865,5176,4966],{"className":5177},[2697],[1865,5179],{"className":5180,"style":2693},[2246],[1865,5182,5184,5187,5227,5230,5270,5273,5276,5316,5319,5322,5326,5329,5369,5372,5375,5415,5418,5421,5424],{"className":5183},[2071],[1865,5185],{"className":5186,"style":5030},[2075],[1865,5188,5190,5193],{"className":5189},[2080],[1865,5191,3484],{"className":5192},[2080,2154],[1865,5194,5196],{"className":5195},[2158],[1865,5197,5199,5219],{"className":5198},[2091,2092],[1865,5200,5202,5216],{"className":5201},[2096],[1865,5203,5205],{"className":5204,"style":3364},[2100],[1865,5206,5207,5210],{"style":2171},[1865,5208],{"className":5209,"style":2175},[2108],[1865,5211,5213],{"className":5212},[2179,2180,2181,2182],[1865,5214,3234],{"className":5215},[2080,2154,2182],[1865,5217,2190],{"className":5218},[2189],[1865,5220,5222],{"className":5221},[2096],[1865,5223,5225],{"className":5224,"style":2197},[2100],[1865,5226],{},[1865,5228,4942],{"className":5229},[2119],[1865,5231,5233,5236],{"className":5232},[2080],[1865,5234,1798],{"className":5235},[2080,2154],[1865,5237,5239],{"className":5238},[2158],[1865,5240,5242,5262],{"className":5241},[2091,2092],[1865,5243,5245,5259],{"className":5244},[2096],[1865,5246,5248],{"className":5247,"style":2168},[2100],[1865,5249,5250,5253],{"style":2171},[1865,5251],{"className":5252,"style":2175},[2108],[1865,5254,5256],{"className":5255},[2179,2180,2181,2182],[1865,5257,1931],{"className":5258},[2080,2182],[1865,5260,2190],{"className":5261},[2189],[1865,5263,5265],{"className":5264},[2096],[1865,5266,5268],{"className":5267,"style":2197},[2100],[1865,5269],{},[1865,5271,2784],{"className":5272},[2851],[1865,5274],{"className":5275,"style":2855},[2246],[1865,5277,5279,5282],{"className":5278},[2080],[1865,5280,1798],{"className":5281},[2080,2154],[1865,5283,5285],{"className":5284},[2158],[1865,5286,5288,5308],{"className":5287},[2091,2092],[1865,5289,5291,5305],{"className":5290},[2096],[1865,5292,5294],{"className":5293,"style":2168},[2100],[1865,5295,5296,5299],{"style":2171},[1865,5297],{"className":5298,"style":2175},[2108],[1865,5300,5302],{"className":5301},[2179,2180,2181,2182],[1865,5303,1984],{"className":5304},[2080,2182],[1865,5306,2190],{"className":5307},[2189],[1865,5309,5311],{"className":5310},[2096],[1865,5312,5314],{"className":5313,"style":2197},[2100],[1865,5315],{},[1865,5317,2784],{"className":5318},[2851],[1865,5320],{"className":5321,"style":2855},[2246],[1865,5323,4993],{"className":5324,"style":5325},[2080,2154],"margin-right:0.0359em;",[1865,5327,4942],{"className":5328},[2119],[1865,5330,5332,5335],{"className":5331},[2080],[1865,5333,1798],{"className":5334},[2080,2154],[1865,5336,5338],{"className":5337},[2158],[1865,5339,5341,5361],{"className":5340},[2091,2092],[1865,5342,5344,5358],{"className":5343},[2096],[1865,5345,5347],{"className":5346,"style":2168},[2100],[1865,5348,5349,5352],{"style":2171},[1865,5350],{"className":5351,"style":2175},[2108],[1865,5353,5355],{"className":5354},[2179,2180,2181,2182],[1865,5356,1931],{"className":5357},[2080,2182],[1865,5359,2190],{"className":5360},[2189],[1865,5362,5364],{"className":5363},[2096],[1865,5365,5367],{"className":5366,"style":2197},[2100],[1865,5368],{},[1865,5370,2784],{"className":5371},[2851],[1865,5373],{"className":5374,"style":2855},[2246],[1865,5376,5378,5381],{"className":5377},[2080],[1865,5379,1798],{"className":5380},[2080,2154],[1865,5382,5384],{"className":5383},[2158],[1865,5385,5387,5407],{"className":5386},[2091,2092],[1865,5388,5390,5404],{"className":5389},[2096],[1865,5391,5393],{"className":5392,"style":2168},[2100],[1865,5394,5395,5398],{"style":2171},[1865,5396],{"className":5397,"style":2175},[2108],[1865,5399,5401],{"className":5400},[2179,2180,2181,2182],[1865,5402,1984],{"className":5403},[2080,2182],[1865,5405,2190],{"className":5406},[2189],[1865,5408,5410],{"className":5409},[2096],[1865,5411,5413],{"className":5412,"style":2197},[2100],[1865,5414],{},[1865,5416,2784],{"className":5417},[2851],[1865,5419],{"className":5420,"style":2855},[2246],[1865,5422,2046],{"className":5423},[2080,2154],[1865,5425,5427],{"className":5426},[2242],"))",[1798,5429,5430,5431,5502],{},"对",[1865,5432,5434,5452],{"className":5433},[1872],[1865,5435,5437],{"className":5436},[1876],[1878,5438,5439],{"xmlns":1880},[1883,5440,5441,5449],{},[1903,5442,5443],{},[1923,5444,5445,5447],{},[1911,5446,1798],{},[1911,5448,3471],{},[2060,5450,5451],{"encoding":2062},"p_j",[1865,5453,5455],{"className":5454,"ariaHidden":1901},[2067],[1865,5456,5458,5462],{"className":5457},[2071],[1865,5459],{"className":5460,"style":5461},[2075],"height:0.7167em;vertical-align:-0.2861em;",[1865,5463,5465,5468],{"className":5464},[2080],[1865,5466,1798],{"className":5467},[2080,2154],[1865,5469,5471],{"className":5470},[2158],[1865,5472,5474,5494],{"className":5473},[2091,2092],[1865,5475,5477,5491],{"className":5476},[2096],[1865,5478,5480],{"className":5479,"style":3364},[2100],[1865,5481,5482,5485],{"style":2171},[1865,5483],{"className":5484,"style":2175},[2108],[1865,5486,5488],{"className":5487},[2179,2180,2181,2182],[1865,5489,3471],{"className":5490,"style":3616},[2080,2154,2182],[1865,5492,2190],{"className":5493},[2189],[1865,5495,5497],{"className":5496},[2096],[1865,5498,5500],{"className":5499,"style":3626},[2100],[1865,5501],{},"求全导数：",[1865,5504,5506],{"className":5505},[1868],[1865,5507,5509,5622],{"className":5508},[1872],[1865,5510,5512],{"className":5511},[1876],[1878,5513,5514],{"xmlns":1880,"display":1881},[1883,5515,5516,5619],{},[1886,5517,5518],{"rowspacing":1888,"columnalign":1889,"columnspacing":1890},[1892,5519,5520,5546],{},[1895,5521,5522],{},[1898,5523,5524],{"scriptlevel":1900,"displaystyle":1901},[1906,5525,5526,5536],{},[1903,5527,5528,5530],{},[1911,5529,1914],{"mathvariant":1913},[1923,5531,5532,5534],{},[1911,5533,1927],{},[1911,5535,3234],{},[1903,5537,5538,5540],{},[1911,5539,1914],{"mathvariant":1913},[1923,5541,5542,5544],{},[1911,5543,1798],{},[1911,5545,3471],{},[1895,5547,5548],{},[1898,5549,5550],{"scriptlevel":1900,"displaystyle":1901},[1903,5551,5552,5554,5556,5578,5580,5598,5601],{},[1903,5553],{},[1933,5555,1955],{},[1906,5557,5558,5568],{},[1903,5559,5560,5562],{},[1911,5561,1914],{"mathvariant":1913},[1923,5563,5564,5566],{},[1911,5565,3484],{},[1911,5567,3234],{},[1903,5569,5570,5572],{},[1911,5571,1914],{"mathvariant":1913},[1923,5573,5574,5576],{},[1911,5575,1798],{},[1911,5577,3471],{},[1933,5579,2029],{},[1906,5581,5582,5592],{},[1903,5583,5584,5586],{},[1911,5585,1914],{"mathvariant":1913},[1923,5587,5588,5590],{},[1911,5589,3484],{},[1911,5591,3234],{},[1903,5593,5594,5596],{},[1911,5595,1914],{"mathvariant":1913},[1911,5597,3508],{},[1933,5599,5600],{},"⋅",[1906,5602,5603,5609],{},[1903,5604,5605,5607],{},[1911,5606,1914],{"mathvariant":1913},[1911,5608,4993],{},[1903,5610,5611,5613],{},[1911,5612,1914],{"mathvariant":1913},[1923,5614,5615,5617],{},[1911,5616,1798],{},[1911,5618,3471],{},[2060,5620,5621],{"encoding":2062},"\\begin{align*}\n\\frac{\\partial x_i}{\\partial p_j} &= \\frac{\\partial h_i}{\\partial p_j} + \\frac{\\partial h_i}{\\partial u} \\cdot \\frac{\\partial v}{\\partial p_j}\n\\end{align*}",[1865,5623,5625],{"className":5624,"ariaHidden":1901},[2067],[1865,5626,5628,5632],{"className":5627},[2071],[1865,5629],{"className":5630,"style":5631},[2075],"height:2.3435em;vertical-align:-0.9218em;",[1865,5633,5635],{"className":5634},[2080],[1865,5636,5638,5814],{"className":5637},[1886],[1865,5639,5641],{"className":5640},[2087],[1865,5642,5644,5805],{"className":5643},[2091,2092],[1865,5645,5647,5802],{"className":5646},[2096],[1865,5648,5651],{"className":5649,"style":5650},[2100],"height:1.4218em;",[1865,5652,5654,5657],{"style":5653},"top:-3.4218em;",[1865,5655],{"className":5656,"style":2109},[2108],[1865,5658,5660],{"className":5659},[2080],[1865,5661,5663,5666,5799],{"className":5662},[2080],[1865,5664],{"className":5665},[2119,2120],[1865,5667,5669],{"className":5668},[1906],[1865,5670,5672,5791],{"className":5671},[2091,2092],[1865,5673,5675,5788],{"className":5674},[2096],[1865,5676,5678,5729,5737],{"className":5677,"style":2133},[2100],[1865,5679,5680,5683],{"style":2136},[1865,5681],{"className":5682,"style":2140},[2108],[1865,5684,5686,5689],{"className":5685},[2080],[1865,5687,1914],{"className":5688,"style":2147},[2080],[1865,5690,5692,5695],{"className":5691},[2080],[1865,5693,1798],{"className":5694},[2080,2154],[1865,5696,5698],{"className":5697},[2158],[1865,5699,5701,5721],{"className":5700},[2091,2092],[1865,5702,5704,5718],{"className":5703},[2096],[1865,5705,5707],{"className":5706,"style":3364},[2100],[1865,5708,5709,5712],{"style":2171},[1865,5710],{"className":5711,"style":2175},[2108],[1865,5713,5715],{"className":5714},[2179,2180,2181,2182],[1865,5716,3471],{"className":5717,"style":3616},[2080,2154,2182],[1865,5719,2190],{"className":5720},[2189],[1865,5722,5724],{"className":5723},[2096],[1865,5725,5727],{"className":5726,"style":3626},[2100],[1865,5728],{},[1865,5730,5731,5734],{"style":2202},[1865,5732],{"className":5733,"style":2140},[2108],[1865,5735],{"className":5736,"style":2210},[2209],[1865,5738,5739,5742],{"style":2213},[1865,5740],{"className":5741,"style":2140},[2108],[1865,5743,5745,5748],{"className":5744},[2080],[1865,5746,1914],{"className":5747,"style":2147},[2080],[1865,5749,5751,5754],{"className":5750},[2080],[1865,5752,1927],{"className":5753},[2080,2154],[1865,5755,5757],{"className":5756},[2158],[1865,5758,5760,5780],{"className":5759},[2091,2092],[1865,5761,5763,5777],{"className":5762},[2096],[1865,5764,5766],{"className":5765,"style":3364},[2100],[1865,5767,5768,5771],{"style":2171},[1865,5769],{"className":5770,"style":2175},[2108],[1865,5772,5774],{"className":5773},[2179,2180,2181,2182],[1865,5775,3234],{"className":5776},[2080,2154,2182],[1865,5778,2190],{"className":5779},[2189],[1865,5781,5783],{"className":5782},[2096],[1865,5784,5786],{"className":5785,"style":2197},[2100],[1865,5787],{},[1865,5789,2190],{"className":5790},[2189],[1865,5792,5794],{"className":5793},[2096],[1865,5795,5797],{"className":5796,"style":3697},[2100],[1865,5798],{},[1865,5800],{"className":5801},[2242,2120],[1865,5803,2190],{"className":5804},[2189],[1865,5806,5808],{"className":5807},[2096],[1865,5809,5812],{"className":5810,"style":5811},[2100],"height:0.9218em;",[1865,5813],{},[1865,5815,5817],{"className":5816},[2669],[1865,5818,5820,6219],{"className":5819},[2091,2092],[1865,5821,5823,6216],{"className":5822},[2096],[1865,5824,5826],{"className":5825,"style":5650},[2100],[1865,5827,5828,5831],{"style":5653},[1865,5829],{"className":5830,"style":2109},[2108],[1865,5832,5834,5837,5840,5843,5846,5988,5991,5994,5997,6102,6105,6108,6111],{"className":5833},[2080],[1865,5835],{"className":5836},[2080],[1865,5838],{"className":5839,"style":2693},[2246],[1865,5841,1955],{"className":5842},[2697],[1865,5844],{"className":5845,"style":2693},[2246],[1865,5847,5849,5852,5985],{"className":5848},[2080],[1865,5850],{"className":5851},[2119,2120],[1865,5853,5855],{"className":5854},[1906],[1865,5856,5858,5977],{"className":5857},[2091,2092],[1865,5859,5861,5974],{"className":5860},[2096],[1865,5862,5864,5915,5923],{"className":5863,"style":2133},[2100],[1865,5865,5866,5869],{"style":2136},[1865,5867],{"className":5868,"style":2140},[2108],[1865,5870,5872,5875],{"className":5871},[2080],[1865,5873,1914],{"className":5874,"style":2147},[2080],[1865,5876,5878,5881],{"className":5877},[2080],[1865,5879,1798],{"className":5880},[2080,2154],[1865,5882,5884],{"className":5883},[2158],[1865,5885,5887,5907],{"className":5886},[2091,2092],[1865,5888,5890,5904],{"className":5889},[2096],[1865,5891,5893],{"className":5892,"style":3364},[2100],[1865,5894,5895,5898],{"style":2171},[1865,5896],{"className":5897,"style":2175},[2108],[1865,5899,5901],{"className":5900},[2179,2180,2181,2182],[1865,5902,3471],{"className":5903,"style":3616},[2080,2154,2182],[1865,5905,2190],{"className":5906},[2189],[1865,5908,5910],{"className":5909},[2096],[1865,5911,5913],{"className":5912,"style":3626},[2100],[1865,5914],{},[1865,5916,5917,5920],{"style":2202},[1865,5918],{"className":5919,"style":2140},[2108],[1865,5921],{"className":5922,"style":2210},[2209],[1865,5924,5925,5928],{"style":2213},[1865,5926],{"className":5927,"style":2140},[2108],[1865,5929,5931,5934],{"className":5930},[2080],[1865,5932,1914],{"className":5933,"style":2147},[2080],[1865,5935,5937,5940],{"className":5936},[2080],[1865,5938,3484],{"className":5939},[2080,2154],[1865,5941,5943],{"className":5942},[2158],[1865,5944,5946,5966],{"className":5945},[2091,2092],[1865,5947,5949,5963],{"className":5948},[2096],[1865,5950,5952],{"className":5951,"style":3364},[2100],[1865,5953,5954,5957],{"style":2171},[1865,5955],{"className":5956,"style":2175},[2108],[1865,5958,5960],{"className":5959},[2179,2180,2181,2182],[1865,5961,3234],{"className":5962},[2080,2154,2182],[1865,5964,2190],{"className":5965},[2189],[1865,5967,5969],{"className":5968},[2096],[1865,5970,5972],{"className":5971,"style":2197},[2100],[1865,5973],{},[1865,5975,2190],{"className":5976},[2189],[1865,5978,5980],{"className":5979},[2096],[1865,5981,5983],{"className":5982,"style":3697},[2100],[1865,5984],{},[1865,5986],{"className":5987},[2242,2120],[1865,5989],{"className":5990,"style":2247},[2246],[1865,5992,2029],{"className":5993},[2251],[1865,5995],{"className":5996,"style":2247},[2246],[1865,5998,6000,6003,6099],{"className":5999},[2080],[1865,6001],{"className":6002},[2119,2120],[1865,6004,6006],{"className":6005},[1906],[1865,6007,6009,6091],{"className":6008},[2091,2092],[1865,6010,6012,6088],{"className":6011},[2096],[1865,6013,6015,6029,6037],{"className":6014,"style":2133},[2100],[1865,6016,6017,6020],{"style":2136},[1865,6018],{"className":6019,"style":2140},[2108],[1865,6021,6023,6026],{"className":6022},[2080],[1865,6024,1914],{"className":6025,"style":2147},[2080],[1865,6027,3508],{"className":6028},[2080,2154],[1865,6030,6031,6034],{"style":2202},[1865,6032],{"className":6033,"style":2140},[2108],[1865,6035],{"className":6036,"style":2210},[2209],[1865,6038,6039,6042],{"style":2213},[1865,6040],{"className":6041,"style":2140},[2108],[1865,6043,6045,6048],{"className":6044},[2080],[1865,6046,1914],{"className":6047,"style":2147},[2080],[1865,6049,6051,6054],{"className":6050},[2080],[1865,6052,3484],{"className":6053},[2080,2154],[1865,6055,6057],{"className":6056},[2158],[1865,6058,6060,6080],{"className":6059},[2091,2092],[1865,6061,6063,6077],{"className":6062},[2096],[1865,6064,6066],{"className":6065,"style":3364},[2100],[1865,6067,6068,6071],{"style":2171},[1865,6069],{"className":6070,"style":2175},[2108],[1865,6072,6074],{"className":6073},[2179,2180,2181,2182],[1865,6075,3234],{"className":6076},[2080,2154,2182],[1865,6078,2190],{"className":6079},[2189],[1865,6081,6083],{"className":6082},[2096],[1865,6084,6086],{"className":6085,"style":2197},[2100],[1865,6087],{},[1865,6089,2190],{"className":6090},[2189],[1865,6092,6094],{"className":6093},[2096],[1865,6095,6097],{"className":6096,"style":4149},[2100],[1865,6098],{},[1865,6100],{"className":6101},[2242,2120],[1865,6103],{"className":6104,"style":2247},[2246],[1865,6106,5600],{"className":6107},[2251],[1865,6109],{"className":6110,"style":2247},[2246],[1865,6112,6114,6117,6213],{"className":6113},[2080],[1865,6115],{"className":6116},[2119,2120],[1865,6118,6120],{"className":6119},[1906],[1865,6121,6123,6205],{"className":6122},[2091,2092],[1865,6124,6126,6202],{"className":6125},[2096],[1865,6127,6129,6180,6188],{"className":6128,"style":2133},[2100],[1865,6130,6131,6134],{"style":2136},[1865,6132],{"className":6133,"style":2140},[2108],[1865,6135,6137,6140],{"className":6136},[2080],[1865,6138,1914],{"className":6139,"style":2147},[2080],[1865,6141,6143,6146],{"className":6142},[2080],[1865,6144,1798],{"className":6145},[2080,2154],[1865,6147,6149],{"className":6148},[2158],[1865,6150,6152,6172],{"className":6151},[2091,2092],[1865,6153,6155,6169],{"className":6154},[2096],[1865,6156,6158],{"className":6157,"style":3364},[2100],[1865,6159,6160,6163],{"style":2171},[1865,6161],{"className":6162,"style":2175},[2108],[1865,6164,6166],{"className":6165},[2179,2180,2181,2182],[1865,6167,3471],{"className":6168,"style":3616},[2080,2154,2182],[1865,6170,2190],{"className":6171},[2189],[1865,6173,6175],{"className":6174},[2096],[1865,6176,6178],{"className":6177,"style":3626},[2100],[1865,6179],{},[1865,6181,6182,6185],{"style":2202},[1865,6183],{"className":6184,"style":2140},[2108],[1865,6186],{"className":6187,"style":2210},[2209],[1865,6189,6190,6193],{"style":2213},[1865,6191],{"className":6192,"style":2140},[2108],[1865,6194,6196,6199],{"className":6195},[2080],[1865,6197,1914],{"className":6198,"style":2147},[2080],[1865,6200,4993],{"className":6201,"style":5325},[2080,2154],[1865,6203,2190],{"className":6204},[2189],[1865,6206,6208],{"className":6207},[2096],[1865,6209,6211],{"className":6210,"style":3697},[2100],[1865,6212],{},[1865,6214],{"className":6215},[2242,2120],[1865,6217,2190],{"className":6218},[2189],[1865,6220,6222],{"className":6221},[2096],[1865,6223,6225],{"className":6224,"style":5811},[2100],[1865,6226],{},[1798,6228,6229],{},"由罗伊恒等式：",[1865,6231,6233],{"className":6232},[1868],[1865,6234,6236,6278],{"className":6235},[1872],[1865,6237,6239],{"className":6238},[1876],[1878,6240,6241],{"xmlns":1880,"display":1881},[1883,6242,6243,6275],{},[1903,6244,6245,6263,6265,6267,6269],{},[1906,6246,6247,6253],{},[1903,6248,6249,6251],{},[1911,6250,1914],{"mathvariant":1913},[1911,6252,4993],{},[1903,6254,6255,6257],{},[1911,6256,1914],{"mathvariant":1913},[1923,6258,6259,6261],{},[1911,6260,1798],{},[1911,6262,3471],{},[1933,6264,1955],{},[1933,6266,1935],{},[1911,6268,1938],{},[1923,6270,6271,6273],{},[1911,6272,1927],{},[1911,6274,3471],{},[2060,6276,6277],{"encoding":2062},"\\frac{\\partial v}{\\partial p_j} = -\\lambda x_j",[1865,6279,6281,6401],{"className":6280,"ariaHidden":1901},[2067],[1865,6282,6284,6287,6392,6395,6398],{"className":6283},[2071],[1865,6285],{"className":6286,"style":3557},[2075],[1865,6288,6290,6293,6389],{"className":6289},[2080],[1865,6291],{"className":6292},[2119,2120],[1865,6294,6296],{"className":6295},[1906],[1865,6297,6299,6381],{"className":6298},[2091,2092],[1865,6300,6302,6378],{"className":6301},[2096],[1865,6303,6305,6356,6364],{"className":6304,"style":2133},[2100],[1865,6306,6307,6310],{"style":2136},[1865,6308],{"className":6309,"style":2140},[2108],[1865,6311,6313,6316],{"className":6312},[2080],[1865,6314,1914],{"className":6315,"style":2147},[2080],[1865,6317,6319,6322],{"className":6318},[2080],[1865,6320,1798],{"className":6321},[2080,2154],[1865,6323,6325],{"className":6324},[2158],[1865,6326,6328,6348],{"className":6327},[2091,2092],[1865,6329,6331,6345],{"className":6330},[2096],[1865,6332,6334],{"className":6333,"style":3364},[2100],[1865,6335,6336,6339],{"style":2171},[1865,6337],{"className":6338,"style":2175},[2108],[1865,6340,6342],{"className":6341},[2179,2180,2181,2182],[1865,6343,3471],{"className":6344,"style":3616},[2080,2154,2182],[1865,6346,2190],{"className":6347},[2189],[1865,6349,6351],{"className":6350},[2096],[1865,6352,6354],{"className":6353,"style":3626},[2100],[1865,6355],{},[1865,6357,6358,6361],{"style":2202},[1865,6359],{"className":6360,"style":2140},[2108],[1865,6362],{"className":6363,"style":2210},[2209],[1865,6365,6366,6369],{"style":2213},[1865,6367],{"className":6368,"style":2140},[2108],[1865,6370,6372,6375],{"className":6371},[2080],[1865,6373,1914],{"className":6374,"style":2147},[2080],[1865,6376,4993],{"className":6377,"style":5325},[2080,2154],[1865,6379,2190],{"className":6380},[2189],[1865,6382,6384],{"className":6383},[2096],[1865,6385,6387],{"className":6386,"style":3697},[2100],[1865,6388],{},[1865,6390],{"className":6391},[2242,2120],[1865,6393],{"className":6394,"style":2693},[2246],[1865,6396,1955],{"className":6397},[2697],[1865,6399],{"className":6400,"style":2693},[2246],[1865,6402,6404,6408,6411,6414],{"className":6403},[2071],[1865,6405],{"className":6406,"style":6407},[2075],"height:0.9805em;vertical-align:-0.2861em;",[1865,6409,1935],{"className":6410},[2080],[1865,6412,1938],{"className":6413},[2080,2154],[1865,6415,6417,6420],{"className":6416},[2080],[1865,6418,1927],{"className":6419},[2080,2154],[1865,6421,6423],{"className":6422},[2158],[1865,6424,6426,6446],{"className":6425},[2091,2092],[1865,6427,6429,6443],{"className":6428},[2096],[1865,6430,6432],{"className":6431,"style":3364},[2100],[1865,6433,6434,6437],{"style":2171},[1865,6435],{"className":6436,"style":2175},[2108],[1865,6438,6440],{"className":6439},[2179,2180,2181,2182],[1865,6441,3471],{"className":6442,"style":3616},[2080,2154,2182],[1865,6444,2190],{"className":6445},[2189],[1865,6447,6449],{"className":6448},[2096],[1865,6450,6452],{"className":6451,"style":3626},[2100],[1865,6453],{},[1798,6455,6456],{},"由支出函数的性质：",[1865,6458,6460],{"className":6459},[1868],[1865,6461,6463,6519],{"className":6462},[1872],[1865,6464,6466],{"className":6465},[1876],[1878,6467,6468],{"xmlns":1880,"display":1881},[1883,6469,6470,6516],{},[1903,6471,6472,6490,6492,6498],{},[1906,6473,6474,6484],{},[1903,6475,6476,6478],{},[1911,6477,1914],{"mathvariant":1913},[1923,6479,6480,6482],{},[1911,6481,3484],{},[1911,6483,3234],{},[1903,6485,6486,6488],{},[1911,6487,1914],{"mathvariant":1913},[1911,6489,3508],{},[1933,6491,1955],{},[1906,6493,6494,6496],{},[1929,6495,1931],{},[1911,6497,1938],{},[1906,6499,6500,6510],{},[1903,6501,6502,6504],{},[1911,6503,1914],{"mathvariant":1913},[1923,6505,6506,6508],{},[1911,6507,1927],{},[1911,6509,3234],{},[1903,6511,6512,6514],{},[1911,6513,1914],{"mathvariant":1913},[1911,6515,2046],{},[2060,6517,6518],{"encoding":2062},"\\frac{\\partial h_i}{\\partial u} = \\frac{1}{\\lambda} \\frac{\\partial x_i}{\\partial m}",[1865,6520,6522,6642],{"className":6521,"ariaHidden":1901},[2067],[1865,6523,6525,6528,6633,6636,6639],{"className":6524},[2071],[1865,6526],{"className":6527,"style":4008},[2075],[1865,6529,6531,6534,6630],{"className":6530},[2080],[1865,6532],{"className":6533},[2119,2120],[1865,6535,6537],{"className":6536},[1906],[1865,6538,6540,6622],{"className":6539},[2091,2092],[1865,6541,6543,6619],{"className":6542},[2096],[1865,6544,6546,6560,6568],{"className":6545,"style":2133},[2100],[1865,6547,6548,6551],{"style":2136},[1865,6549],{"className":6550,"style":2140},[2108],[1865,6552,6554,6557],{"className":6553},[2080],[1865,6555,1914],{"className":6556,"style":2147},[2080],[1865,6558,3508],{"className":6559},[2080,2154],[1865,6561,6562,6565],{"style":2202},[1865,6563],{"className":6564,"style":2140},[2108],[1865,6566],{"className":6567,"style":2210},[2209],[1865,6569,6570,6573],{"style":2213},[1865,6571],{"className":6572,"style":2140},[2108],[1865,6574,6576,6579],{"className":6575},[2080],[1865,6577,1914],{"className":6578,"style":2147},[2080],[1865,6580,6582,6585],{"className":6581},[2080],[1865,6583,3484],{"className":6584},[2080,2154],[1865,6586,6588],{"className":6587},[2158],[1865,6589,6591,6611],{"className":6590},[2091,2092],[1865,6592,6594,6608],{"className":6593},[2096],[1865,6595,6597],{"className":6596,"style":3364},[2100],[1865,6598,6599,6602],{"style":2171},[1865,6600],{"className":6601,"style":2175},[2108],[1865,6603,6605],{"className":6604},[2179,2180,2181,2182],[1865,6606,3234],{"className":6607},[2080,2154,2182],[1865,6609,2190],{"className":6610},[2189],[1865,6612,6614],{"className":6613},[2096],[1865,6615,6617],{"className":6616,"style":2197},[2100],[1865,6618],{},[1865,6620,2190],{"className":6621},[2189],[1865,6623,6625],{"className":6624},[2096],[1865,6626,6628],{"className":6627,"style":4149},[2100],[1865,6629],{},[1865,6631],{"className":6632},[2242,2120],[1865,6634],{"className":6635,"style":2693},[2246],[1865,6637,1955],{"className":6638},[2697],[1865,6640],{"className":6641,"style":2693},[2246],[1865,6643,6645,6648,6711],{"className":6644},[2071],[1865,6646],{"className":6647,"style":4008},[2075],[1865,6649,6651,6654,6708],{"className":6650},[2080],[1865,6652],{"className":6653},[2119,2120],[1865,6655,6657],{"className":6656},[1906],[1865,6658,6660,6700],{"className":6659},[2091,2092],[1865,6661,6663,6697],{"className":6662},[2096],[1865,6664,6667,6678,6686],{"className":6665,"style":6666},[2100],"height:1.3214em;",[1865,6668,6669,6672],{"style":2136},[1865,6670],{"className":6671,"style":2140},[2108],[1865,6673,6675],{"className":6674},[2080],[1865,6676,1938],{"className":6677},[2080,2154],[1865,6679,6680,6683],{"style":2202},[1865,6681],{"className":6682,"style":2140},[2108],[1865,6684],{"className":6685,"style":2210},[2209],[1865,6687,6688,6691],{"style":2213},[1865,6689],{"className":6690,"style":2140},[2108],[1865,6692,6694],{"className":6693},[2080],[1865,6695,1931],{"className":6696},[2080],[1865,6698,2190],{"className":6699},[2189],[1865,6701,6703],{"className":6702},[2096],[1865,6704,6706],{"className":6705,"style":4149},[2100],[1865,6707],{},[1865,6709],{"className":6710},[2242,2120],[1865,6712,6714,6717,6813],{"className":6713},[2080],[1865,6715],{"className":6716},[2119,2120],[1865,6718,6720],{"className":6719},[1906],[1865,6721,6723,6805],{"className":6722},[2091,2092],[1865,6724,6726,6802],{"className":6725},[2096],[1865,6727,6729,6743,6751],{"className":6728,"style":2133},[2100],[1865,6730,6731,6734],{"style":2136},[1865,6732],{"className":6733,"style":2140},[2108],[1865,6735,6737,6740],{"className":6736},[2080],[1865,6738,1914],{"className":6739,"style":2147},[2080],[1865,6741,2046],{"className":6742},[2080,2154],[1865,6744,6745,6748],{"style":2202},[1865,6746],{"className":6747,"style":2140},[2108],[1865,6749],{"className":6750,"style":2210},[2209],[1865,6752,6753,6756],{"style":2213},[1865,6754],{"className":6755,"style":2140},[2108],[1865,6757,6759,6762],{"className":6758},[2080],[1865,6760,1914],{"className":6761,"style":2147},[2080],[1865,6763,6765,6768],{"className":6764},[2080],[1865,6766,1927],{"className":6767},[2080,2154],[1865,6769,6771],{"className":6770},[2158],[1865,6772,6774,6794],{"className":6773},[2091,2092],[1865,6775,6777,6791],{"className":6776},[2096],[1865,6778,6780],{"className":6779,"style":3364},[2100],[1865,6781,6782,6785],{"style":2171},[1865,6783],{"className":6784,"style":2175},[2108],[1865,6786,6788],{"className":6787},[2179,2180,2181,2182],[1865,6789,3234],{"className":6790},[2080,2154,2182],[1865,6792,2190],{"className":6793},[2189],[1865,6795,6797],{"className":6796},[2096],[1865,6798,6800],{"className":6799,"style":2197},[2100],[1865,6801],{},[1865,6803,2190],{"className":6804},[2189],[1865,6806,6808],{"className":6807},[2096],[1865,6809,6811],{"className":6810,"style":4149},[2100],[1865,6812],{},[1865,6814],{"className":6815},[2242,2120],[1798,6817,6818],{},"代入并整理得到斯勒茨基方程。",[1854,6820,6822],{"id":6821},"_22-矩阵形式","2.2 矩阵形式",[1798,6824,6825,6826,6856],{},"对于",[1865,6827,6829,6843],{"className":6828},[1872],[1865,6830,6832],{"className":6831},[1876],[1878,6833,6834],{"xmlns":1880},[1883,6835,6836,6841],{},[1903,6837,6838],{},[1911,6839,6840],{},"n",[2060,6842,6840],{"encoding":2062},[1865,6844,6846],{"className":6845,"ariaHidden":1901},[2067],[1865,6847,6849,6853],{"className":6848},[2071],[1865,6850],{"className":6851,"style":6852},[2075],"height:0.4306em;",[1865,6854,6840],{"className":6855},[2080,2154],"种商品，斯勒茨基方程可以写成矩阵形式：",[1865,6858,6860],{"className":6859},[1868],[1865,6861,6863,6932],{"className":6862},[1872],[1865,6864,6866],{"className":6865},[1876],[1878,6867,6868],{"xmlns":1880,"display":1881},[1883,6869,6870,6929],{},[1903,6871,6872,6892,6894,6897,6899,6901,6903,6905,6907,6909,6923],{},[1906,6873,6874,6880],{},[1903,6875,6876,6878],{},[1911,6877,1914],{"mathvariant":1913},[1911,6879,1927],{},[1903,6881,6882,6884],{},[1911,6883,1914],{"mathvariant":1913},[6885,6886,6887,6889],"msup",{},[1911,6888,1798],{},[1933,6890,6891],{"mathvariant":1913,"lspace":1890,"rspace":1890},"′",[1933,6893,1955],{},[1911,6895,6896],{},"S",[1933,6898,4942],{"stretchy":3501},[1911,6900,1798],{},[1933,6902,2784],{"separator":1901},[1911,6904,3508],{},[1933,6906,4963],{"stretchy":3501},[1933,6908,1935],{},[1906,6910,6911,6917],{},[1903,6912,6913,6915],{},[1911,6914,1914],{"mathvariant":1913},[1911,6916,1927],{},[1903,6918,6919,6921],{},[1911,6920,1914],{"mathvariant":1913},[1911,6922,2046],{},[6885,6924,6925,6927],{},[1911,6926,1927],{},[1933,6928,6891],{"mathvariant":1913,"lspace":1890,"rspace":1890},[2060,6930,6931],{"encoding":2062},"\\frac{\\partial x}{\\partial p'} = S(p, u) - \\frac{\\partial x}{\\partial m} x'",[1865,6933,6935,7049,7086],{"className":6934,"ariaHidden":1901},[2067],[1865,6936,6938,6941,7040,7043,7046],{"className":6937},[2071],[1865,6939],{"className":6940,"style":3257},[2075],[1865,6942,6944,6947,7037],{"className":6943},[2080],[1865,6945],{"className":6946},[2119,2120],[1865,6948,6950],{"className":6949},[1906],[1865,6951,6953,7029],{"className":6952},[2091,2092],[1865,6954,6956,7026],{"className":6955},[2096],[1865,6957,6959,7004,7012],{"className":6958,"style":2133},[2100],[1865,6960,6961,6964],{"style":2136},[1865,6962],{"className":6963,"style":2140},[2108],[1865,6965,6967,6970],{"className":6966},[2080],[1865,6968,1914],{"className":6969,"style":2147},[2080],[1865,6971,6973,6976],{"className":6972},[2080],[1865,6974,1798],{"className":6975},[2080,2154],[1865,6977,6979],{"className":6978},[2158],[1865,6980,6982],{"className":6981},[2091],[1865,6983,6985],{"className":6984},[2096],[1865,6986,6989],{"className":6987,"style":6988},[2100],"height:0.6779em;",[1865,6990,6992,6995],{"style":6991},"top:-2.989em;margin-right:0.05em;",[1865,6993],{"className":6994,"style":2175},[2108],[1865,6996,6998],{"className":6997},[2179,2180,2181,2182],[1865,6999,7001],{"className":7000},[2080,2182],[1865,7002,6891],{"className":7003},[2080,2182],[1865,7005,7006,7009],{"style":2202},[1865,7007],{"className":7008,"style":2140},[2108],[1865,7010],{"className":7011,"style":2210},[2209],[1865,7013,7014,7017],{"style":2213},[1865,7015],{"className":7016,"style":2140},[2108],[1865,7018,7020,7023],{"className":7019},[2080],[1865,7021,1914],{"className":7022,"style":2147},[2080],[1865,7024,1927],{"className":7025},[2080,2154],[1865,7027,2190],{"className":7028},[2189],[1865,7030,7032],{"className":7031},[2096],[1865,7033,7035],{"className":7034,"style":3396},[2100],[1865,7036],{},[1865,7038],{"className":7039},[2242,2120],[1865,7041],{"className":7042,"style":2693},[2246],[1865,7044,1955],{"className":7045},[2697],[1865,7047],{"className":7048,"style":2693},[2246],[1865,7050,7052,7055,7059,7062,7065,7068,7071,7074,7077,7080,7083],{"className":7051},[2071],[1865,7053],{"className":7054,"style":5030},[2075],[1865,7056,6896],{"className":7057,"style":7058},[2080,2154],"margin-right:0.0576em;",[1865,7060,4942],{"className":7061},[2119],[1865,7063,1798],{"className":7064},[2080,2154],[1865,7066,2784],{"className":7067},[2851],[1865,7069],{"className":7070,"style":2855},[2246],[1865,7072,3508],{"className":7073},[2080,2154],[1865,7075,4963],{"className":7076},[2242],[1865,7078],{"className":7079,"style":2247},[2246],[1865,7081,1935],{"className":7082},[2251],[1865,7084],{"className":7085,"style":2247},[2246],[1865,7087,7089,7092,7160],{"className":7088},[2071],[1865,7090],{"className":7091,"style":4008},[2075],[1865,7093,7095,7098,7157],{"className":7094},[2080],[1865,7096],{"className":7097},[2119,2120],[1865,7099,7101],{"className":7100},[1906],[1865,7102,7104,7149],{"className":7103},[2091,2092],[1865,7105,7107,7146],{"className":7106},[2096],[1865,7108,7110,7124,7132],{"className":7109,"style":2133},[2100],[1865,7111,7112,7115],{"style":2136},[1865,7113],{"className":7114,"style":2140},[2108],[1865,7116,7118,7121],{"className":7117},[2080],[1865,7119,1914],{"className":7120,"style":2147},[2080],[1865,7122,2046],{"className":7123},[2080,2154],[1865,7125,7126,7129],{"style":2202},[1865,7127],{"className":7128,"style":2140},[2108],[1865,7130],{"className":7131,"style":2210},[2209],[1865,7133,7134,7137],{"style":2213},[1865,7135],{"className":7136,"style":2140},[2108],[1865,7138,7140,7143],{"className":7139},[2080],[1865,7141,1914],{"className":7142,"style":2147},[2080],[1865,7144,1927],{"className":7145},[2080,2154],[1865,7147,2190],{"className":7148},[2189],[1865,7150,7152],{"className":7151},[2096],[1865,7153,7155],{"className":7154,"style":4149},[2100],[1865,7156],{},[1865,7158],{"className":7159},[2242,2120],[1865,7161,7163,7166],{"className":7162},[2080],[1865,7164,1927],{"className":7165},[2080,2154],[1865,7167,7169],{"className":7168},[2158],[1865,7170,7172],{"className":7171},[2091],[1865,7173,7175],{"className":7174},[2096],[1865,7176,7179],{"className":7177,"style":7178},[2100],"height:0.8019em;",[1865,7180,7182,7185],{"style":7181},"top:-3.113em;margin-right:0.05em;",[1865,7183],{"className":7184,"style":2175},[2108],[1865,7186,7188],{"className":7187},[2179,2180,2181,2182],[1865,7189,7191],{"className":7190},[2080,2182],[1865,7192,6891],{"className":7193},[2080,2182],[1798,7195,7196,7197,7254,7255,7258],{},"其中",[1865,7198,7200,7224],{"className":7199},[1872],[1865,7201,7203],{"className":7202},[1876],[1878,7204,7205],{"xmlns":1880},[1883,7206,7207,7221],{},[1903,7208,7209,7211,7213,7215,7217,7219],{},[1911,7210,6896],{},[1933,7212,4942],{"stretchy":3501},[1911,7214,1798],{},[1933,7216,2784],{"separator":1901},[1911,7218,3508],{},[1933,7220,4963],{"stretchy":3501},[2060,7222,7223],{"encoding":2062},"S(p, u)",[1865,7225,7227],{"className":7226,"ariaHidden":1901},[2067],[1865,7228,7230,7233,7236,7239,7242,7245,7248,7251],{"className":7229},[2071],[1865,7231],{"className":7232,"style":5030},[2075],[1865,7234,6896],{"className":7235,"style":7058},[2080,2154],[1865,7237,4942],{"className":7238},[2119],[1865,7240,1798],{"className":7241},[2080,2154],[1865,7243,2784],{"className":7244},[2851],[1865,7246],{"className":7247,"style":2855},[2246],[1865,7249,3508],{"className":7250},[2080,2154],[1865,7252,4963],{"className":7253},[2242],"是",[3048,7256,7257],{},"斯勒茨基替代矩阵","，它具有以下重要性质：",[3406,7260,7261,7421,7557],{},[1808,7262,7263,7266,7267,7420],{},[3048,7264,7265],{},"对称性",": ",[1865,7268,7270,7304],{"className":7269},[1872],[1865,7271,7273],{"className":7272},[1876],[1878,7274,7275],{"xmlns":1880},[1883,7276,7277,7301],{},[1903,7278,7279,7289,7291],{},[1923,7280,7281,7283],{},[1911,7282,6896],{},[1903,7284,7285,7287],{},[1911,7286,3234],{},[1911,7288,3471],{},[1933,7290,1955],{},[1923,7292,7293,7295],{},[1911,7294,6896],{},[1903,7296,7297,7299],{},[1911,7298,3471],{},[1911,7300,3234],{},[2060,7302,7303],{"encoding":2062},"S_{ij} = S_{ji}",[1865,7305,7307,7368],{"className":7306,"ariaHidden":1901},[2067],[1865,7308,7310,7314,7359,7362,7365],{"className":7309},[2071],[1865,7311],{"className":7312,"style":7313},[2075],"height:0.9694em;vertical-align:-0.2861em;",[1865,7315,7317,7320],{"className":7316},[2080],[1865,7318,6896],{"className":7319,"style":7058},[2080,2154],[1865,7321,7323],{"className":7322},[2158],[1865,7324,7326,7351],{"className":7325},[2091,2092],[1865,7327,7329,7348],{"className":7328},[2096],[1865,7330,7332],{"className":7331,"style":3364},[2100],[1865,7333,7335,7338],{"style":7334},"top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;",[1865,7336],{"className":7337,"style":2175},[2108],[1865,7339,7341],{"className":7340},[2179,2180,2181,2182],[1865,7342,7344],{"className":7343},[2080,2182],[1865,7345,7347],{"className":7346,"style":3616},[2080,2154,2182],"ij",[1865,7349,2190],{"className":7350},[2189],[1865,7352,7354],{"className":7353},[2096],[1865,7355,7357],{"className":7356,"style":3626},[2100],[1865,7358],{},[1865,7360],{"className":7361,"style":2693},[2246],[1865,7363,1955],{"className":7364},[2697],[1865,7366],{"className":7367,"style":2693},[2246],[1865,7369,7371,7374],{"className":7370},[2071],[1865,7372],{"className":7373,"style":7313},[2075],[1865,7375,7377,7380],{"className":7376},[2080],[1865,7378,6896],{"className":7379,"style":7058},[2080,2154],[1865,7381,7383],{"className":7382},[2158],[1865,7384,7386,7412],{"className":7385},[2091,2092],[1865,7387,7389,7409],{"className":7388},[2096],[1865,7390,7392],{"className":7391,"style":3364},[2100],[1865,7393,7394,7397],{"style":7334},[1865,7395],{"className":7396,"style":2175},[2108],[1865,7398,7400],{"className":7399},[2179,2180,2181,2182],[1865,7401,7403,7406],{"className":7402},[2080,2182],[1865,7404,3471],{"className":7405,"style":3616},[2080,2154,2182],[1865,7407,3234],{"className":7408},[2080,2154,2182],[1865,7410,2190],{"className":7411},[2189],[1865,7413,7415],{"className":7414},[2096],[1865,7416,7418],{"className":7417,"style":3626},[2100],[1865,7419],{},"（由Young定理）",[1808,7422,7423,7426,7427,7457,7458],{},[3048,7424,7425],{},"负半定",": 对所有非零向量",[1865,7428,7430,7444],{"className":7429},[1872],[1865,7431,7433],{"className":7432},[1876],[1878,7434,7435],{"xmlns":1880},[1883,7436,7437,7442],{},[1903,7438,7439],{},[1911,7440,7441],{},"z",[2060,7443,7441],{"encoding":2062},[1865,7445,7447],{"className":7446,"ariaHidden":1901},[2067],[1865,7448,7450,7453],{"className":7449},[2071],[1865,7451],{"className":7452,"style":6852},[2075],[1865,7454,7441],{"className":7455,"style":7456},[2080,2154],"margin-right:0.044em;","，",[1865,7459,7461,7488],{"className":7460},[1872],[1865,7462,7464],{"className":7463},[1876],[1878,7465,7466],{"xmlns":1880},[1883,7467,7468,7485],{},[1903,7469,7470,7476,7478,7480,7483],{},[6885,7471,7472,7474],{},[1911,7473,7441],{},[1933,7475,6891],{"mathvariant":1913,"lspace":1890,"rspace":1890},[1911,7477,6896],{},[1911,7479,7441],{},[1933,7481,7482],{},"≤",[1929,7484,1900],{},[2060,7486,7487],{"encoding":2062},"z'Sz \\le 0",[1865,7489,7491,7547],{"className":7490,"ariaHidden":1901},[2067],[1865,7492,7494,7498,7532,7535,7538,7541,7544],{"className":7493},[2071],[1865,7495],{"className":7496,"style":7497},[2075],"height:0.8879em;vertical-align:-0.136em;",[1865,7499,7501,7504],{"className":7500},[2080],[1865,7502,7441],{"className":7503,"style":7456},[2080,2154],[1865,7505,7507],{"className":7506},[2158],[1865,7508,7510],{"className":7509},[2091],[1865,7511,7513],{"className":7512},[2096],[1865,7514,7517],{"className":7515,"style":7516},[2100],"height:0.7519em;",[1865,7518,7520,7523],{"style":7519},"top:-3.063em;margin-right:0.05em;",[1865,7521],{"className":7522,"style":2175},[2108],[1865,7524,7526],{"className":7525},[2179,2180,2181,2182],[1865,7527,7529],{"className":7528},[2080,2182],[1865,7530,6891],{"className":7531},[2080,2182],[1865,7533,6896],{"className":7534,"style":7058},[2080,2154],[1865,7536,7441],{"className":7537,"style":7456},[2080,2154],[1865,7539],{"className":7540,"style":2693},[2246],[1865,7542,7482],{"className":7543},[2697],[1865,7545],{"className":7546,"style":2693},[2246],[1865,7548,7550,7554],{"className":7549},[2071],[1865,7551],{"className":7552,"style":7553},[2075],"height:0.6444em;",[1865,7555,1900],{"className":7556},[2080],[1808,7558,7559,7266,7562,7619],{},[3048,7560,7561],{},"奇异性",[1865,7563,7565,7585],{"className":7564},[1872],[1865,7566,7568],{"className":7567},[1876],[1878,7569,7570],{"xmlns":1880},[1883,7571,7572,7582],{},[1903,7573,7574,7576,7578,7580],{},[1911,7575,6896],{},[1911,7577,1798],{},[1933,7579,1955],{},[1929,7581,1900],{},[2060,7583,7584],{"encoding":2062},"Sp = 0",[1865,7586,7588,7610],{"className":7587,"ariaHidden":1901},[2067],[1865,7589,7591,7595,7598,7601,7604,7607],{"className":7590},[2071],[1865,7592],{"className":7593,"style":7594},[2075],"height:0.8778em;vertical-align:-0.1944em;",[1865,7596,6896],{"className":7597,"style":7058},[2080,2154],[1865,7599,1798],{"className":7600},[2080,2154],[1865,7602],{"className":7603,"style":2693},[2246],[1865,7605,1955],{"className":7606},[2697],[1865,7608],{"className":7609,"style":2693},[2246],[1865,7611,7613,7616],{"className":7612},[2071],[1865,7614],{"className":7615,"style":7553},[2075],[1865,7617,1900],{"className":7618},[2080],"（因为齐次性）",[1854,7621,7623],{"id":7622},"_23-几何直观解释","2.3 几何直观解释",[1798,7625,7626],{},"价格变化的两步分解：",[1798,7628,7629],{},[3048,7630,7631],{},"第一步：替代效应",[1805,7633,7634,7637,7640],{},[1808,7635,7636],{},"保持效用不变（沿着原无差异曲线）",[1808,7638,7639],{},"旋转预算线以反映新的相对价格",[1808,7641,7642],{},"找到新的切点",[1798,7644,7645],{},[3048,7646,7647],{},"第二步：收入效应",[1805,7649,7650,7653,7656],{},[1808,7651,7652],{},"从假想的补偿预算线移动到实际的新预算线",[1808,7654,7655],{},"平行移动预算线",[1808,7657,7658],{},"效用水平发生变化",[7660,7661],"mermaid-diagram",{"code64":7662,"locale":7},"Z3JhcGggTFIKQVvljp\u002Flp4vlnYfooaEgReKCgF0gLS0+fOabv+S7o+aViOW6lHwgQlvlgYfmg7PlnYfooaEgRSddCkIgLS0+fOaUtuWFpeaViOW6lHwgQ1vmlrDlnYfooaEgReKCgV0=",[7664,7665],"model-curve-chart",{"props64":7666},"eyJ0aXRsZSI6IuaWr+WLkuiMqOWfuuWIhuino++8muaKiuS4gOasoeS7t+agvOWPmOWMluaLhuaIkOS4pOatpSIsInN1YnRpdGxlIjoi5ZWG5ZOBIHgg5Y+Y6LS15ZCO77yM5YWI55So6KGl5YG\u002F6aKE566X57q\u002F6ZqU56a75pu\u002F5Luj5pWI5bqU77yM5YaN5oqK5pS25YWl5pWI5bqU6KGl5Zue5p2l44CCIiwieExhYmVsIjoi5ZWG5ZOBIHgg55qE5pWw6YePIiwieUxhYmVsIjoi5YW25LuW5ZWG5ZOBIiwiaGVpZ2h0IjozOTAsIm1pblgiOjAsIm1heFgiOjcsIm1pblkiOjAsIm1heFkiOjE2LCJzZXJpZXMiOlt7Im5hbWUiOiLljp\u002FpooTnrpfnur8iLCJjb2xvciI6IiMyNTYzZWIiLCJzbW9vdGgiOmZhbHNlLCJwb2ludHMiOlt7IngiOjAsInkiOjEyfSx7IngiOjMuNSwieSI6NSwibGFiZWwiOiJFMCJ9LHsieCI6NiwieSI6MH1dfSx7Im5hbWUiOiLooaXlgb\u002FpooTnrpfnur8iLCJjb2xvciI6IiM5MzMzZWEiLCJkYXNoZWQiOnRydWUsInNtb290aCI6ZmFsc2UsInBvaW50cyI6W3sieCI6MCwieSI6MTV9LHsieCI6My4xLCJ5Ijo1LjcsImxhYmVsIjoiRScifSx7IngiOjUsInkiOjB9XX0seyJuYW1lIjoi5paw6aKE566X57q\u002FIiwiY29sb3IiOiIjZGMyNjI2Iiwic21vb3RoIjpmYWxzZSwicG9pbnRzIjpbeyJ4IjowLCJ5IjoxMn0seyJ4IjoyLjQsInkiOjQuOCwibGFiZWwiOiJFMSJ9LHsieCI6NCwieSI6MH1dfV0sInNlZ21lbnRzIjpbeyJ5IjoxLjE1LCJmcm9tIjozLjUsInRvIjozLjEsImxhYmVsIjoi5pu\u002F5Luj5pWI5bqUIiwiY29sb3IiOiIjOTMzM2VhIn0seyJ5IjowLjY1LCJmcm9tIjozLjEsInRvIjoyLjQsImxhYmVsIjoi5pS25YWl5pWI5bqUIiwiY29sb3IiOiIjZGMyNjI2In1dLCJjYXB0aW9uIjoi5Zu+5Lit55qEIEUnIOaYr+S4gOS4quWPjeS6i+WunueCue+8muWug+S4jeaYr+a2iOi0ueiAheecn+WunumdouWvueeahOmihOeul+e6v++8jOiAjOaYr+S4uuS6huaKiuabv+S7o+aViOW6lOWNleeLrOWIhuemu+WHuuadpeOAgiJ9",[1798,7668,7669],{},"斯勒茨基分解最容易混淆的地方，是把“真实的新选择”误认为一步到位。更清楚的读法是：先让消费者保持原来的效用水平，价格变化只改变相对价格，这一步得到替代效应；再把补偿拿走，让购买力回到真实水平，这一步得到收入效应。这样公式里的两个项就对应到图上的两个移动，而不是停留在抽象偏导数上。",[1854,7671,7673],{"id":7672},"_24-商品分类","2.4 商品分类",[1798,7675,7676],{},"根据替代效应和收入效应的符号，可以将商品分类：",[3406,7678,7679,7865,8051],{},[1808,7680,7681,7266,7684,7860],{},[3048,7682,7683],{},"正常品 (Normal Good)",[1865,7685,7687,7722],{"className":7686},[1872],[1865,7688,7690],{"className":7689},[1876],[1878,7691,7692],{"xmlns":1880},[1883,7693,7694,7719],{},[1903,7695,7696,7714,7717],{},[1906,7697,7698,7708],{},[1903,7699,7700,7702],{},[1911,7701,1914],{"mathvariant":1913},[1923,7703,7704,7706],{},[1911,7705,1927],{},[1911,7707,3234],{},[1903,7709,7710,7712],{},[1911,7711,1914],{"mathvariant":1913},[1911,7713,2046],{},[1933,7715,7716],{},">",[1929,7718,1900],{},[2060,7720,7721],{"encoding":2062},"\\frac{\\partial x_i}{\\partial m} > 0",[1865,7723,7725,7851],{"className":7724,"ariaHidden":1901},[2067],[1865,7726,7728,7731,7842,7845,7848],{"className":7727},[2071],[1865,7729],{"className":7730,"style":4751},[2075],[1865,7732,7734,7737,7839],{"className":7733},[2080],[1865,7735],{"className":7736},[2119,2120],[1865,7738,7740],{"className":7739},[1906],[1865,7741,7743,7831],{"className":7742},[2091,2092],[1865,7744,7746,7828],{"className":7745},[2096],[1865,7747,7749,7766,7774],{"className":7748,"style":4227},[2100],[1865,7750,7751,7754],{"style":4230},[1865,7752],{"className":7753,"style":2140},[2108],[1865,7755,7757],{"className":7756},[2179,2180,2181,2182],[1865,7758,7760,7763],{"className":7759},[2080,2182],[1865,7761,1914],{"className":7762,"style":2147},[2080,2182],[1865,7764,2046],{"className":7765},[2080,2154,2182],[1865,7767,7768,7771],{"style":2202},[1865,7769],{"className":7770,"style":2140},[2108],[1865,7772],{"className":7773,"style":2210},[2209],[1865,7775,7776,7779],{"style":4299},[1865,7777],{"className":7778,"style":2140},[2108],[1865,7780,7782],{"className":7781},[2179,2180,2181,2182],[1865,7783,7785,7788],{"className":7784},[2080,2182],[1865,7786,1914],{"className":7787,"style":2147},[2080,2182],[1865,7789,7791,7794],{"className":7790},[2080,2182],[1865,7792,1927],{"className":7793},[2080,2154,2182],[1865,7795,7797],{"className":7796},[2158],[1865,7798,7800,7820],{"className":7799},[2091,2092],[1865,7801,7803,7817],{"className":7802},[2096],[1865,7804,7806],{"className":7805,"style":4261},[2100],[1865,7807,7808,7811],{"style":4264},[1865,7809],{"className":7810,"style":4268},[2108],[1865,7812,7814],{"className":7813},[2179,4272,4273,2182],[1865,7815,3234],{"className":7816},[2080,2154,2182],[1865,7818,2190],{"className":7819},[2189],[1865,7821,7823],{"className":7822},[2096],[1865,7824,7826],{"className":7825,"style":4350},[2100],[1865,7827],{},[1865,7829,2190],{"className":7830},[2189],[1865,7832,7834],{"className":7833},[2096],[1865,7835,7837],{"className":7836,"style":4901},[2100],[1865,7838],{},[1865,7840],{"className":7841},[2242,2120],[1865,7843],{"className":7844,"style":2693},[2246],[1865,7846,7716],{"className":7847},[2697],[1865,7849],{"className":7850,"style":2693},[2246],[1865,7852,7854,7857],{"className":7853},[2071],[1865,7855],{"className":7856,"style":7553},[2075],[1865,7858,1900],{"className":7859},[2080],[1805,7861,7862],{},[1808,7863,7864],{},"收入增加，需求增加",[1808,7866,7867,7266,7870,8046],{},[3048,7868,7869],{},"劣等品 (Inferior Good)",[1865,7871,7873,7908],{"className":7872},[1872],[1865,7874,7876],{"className":7875},[1876],[1878,7877,7878],{"xmlns":1880},[1883,7879,7880,7905],{},[1903,7881,7882,7900,7903],{},[1906,7883,7884,7894],{},[1903,7885,7886,7888],{},[1911,7887,1914],{"mathvariant":1913},[1923,7889,7890,7892],{},[1911,7891,1927],{},[1911,7893,3234],{},[1903,7895,7896,7898],{},[1911,7897,1914],{"mathvariant":1913},[1911,7899,2046],{},[1933,7901,7902],{},"\u003C",[1929,7904,1900],{},[2060,7906,7907],{"encoding":2062},"\\frac{\\partial x_i}{\\partial m} \u003C 0",[1865,7909,7911,8037],{"className":7910,"ariaHidden":1901},[2067],[1865,7912,7914,7917,8028,8031,8034],{"className":7913},[2071],[1865,7915],{"className":7916,"style":4751},[2075],[1865,7918,7920,7923,8025],{"className":7919},[2080],[1865,7921],{"className":7922},[2119,2120],[1865,7924,7926],{"className":7925},[1906],[1865,7927,7929,8017],{"className":7928},[2091,2092],[1865,7930,7932,8014],{"className":7931},[2096],[1865,7933,7935,7952,7960],{"className":7934,"style":4227},[2100],[1865,7936,7937,7940],{"style":4230},[1865,7938],{"className":7939,"style":2140},[2108],[1865,7941,7943],{"className":7942},[2179,2180,2181,2182],[1865,7944,7946,7949],{"className":7945},[2080,2182],[1865,7947,1914],{"className":7948,"style":2147},[2080,2182],[1865,7950,2046],{"className":7951},[2080,2154,2182],[1865,7953,7954,7957],{"style":2202},[1865,7955],{"className":7956,"style":2140},[2108],[1865,7958],{"className":7959,"style":2210},[2209],[1865,7961,7962,7965],{"style":4299},[1865,7963],{"className":7964,"style":2140},[2108],[1865,7966,7968],{"className":7967},[2179,2180,2181,2182],[1865,7969,7971,7974],{"className":7970},[2080,2182],[1865,7972,1914],{"className":7973,"style":2147},[2080,2182],[1865,7975,7977,7980],{"className":7976},[2080,2182],[1865,7978,1927],{"className":7979},[2080,2154,2182],[1865,7981,7983],{"className":7982},[2158],[1865,7984,7986,8006],{"className":7985},[2091,2092],[1865,7987,7989,8003],{"className":7988},[2096],[1865,7990,7992],{"className":7991,"style":4261},[2100],[1865,7993,7994,7997],{"style":4264},[1865,7995],{"className":7996,"style":4268},[2108],[1865,7998,8000],{"className":7999},[2179,4272,4273,2182],[1865,8001,3234],{"className":8002},[2080,2154,2182],[1865,8004,2190],{"className":8005},[2189],[1865,8007,8009],{"className":8008},[2096],[1865,8010,8012],{"className":8011,"style":4350},[2100],[1865,8013],{},[1865,8015,2190],{"className":8016},[2189],[1865,8018,8020],{"className":8019},[2096],[1865,8021,8023],{"className":8022,"style":4901},[2100],[1865,8024],{},[1865,8026],{"className":8027},[2242,2120],[1865,8029],{"className":8030,"style":2693},[2246],[1865,8032,7902],{"className":8033},[2697],[1865,8035],{"className":8036,"style":2693},[2246],[1865,8038,8040,8043],{"className":8039},[2071],[1865,8041],{"className":8042,"style":7553},[2075],[1865,8044,1900],{"className":8045},[2080],[1805,8047,8048],{},[1808,8049,8050],{},"收入增加，需求减少（如方便面）",[1808,8052,8053,8056,8057],{},[3048,8054,8055],{},"吉芬品 (Giffen Good)",": 劣等品 + 价格上涨需求反而增加",[1805,8058,8059,8062,8283],{},[1808,8060,8061],{},"必须满足：收入效应的负向作用大于替代效应",[1808,8063,8064,8282],{},[1865,8065,8067,8105],{"className":8066},[1872],[1865,8068,8070],{"className":8069},[1876],[1878,8071,8072],{"xmlns":1880},[1883,8073,8074,8102],{},[1903,8075,8076,8098,8100],{},[1906,8077,8078,8088],{},[1903,8079,8080,8082],{},[1911,8081,1914],{"mathvariant":1913},[1923,8083,8084,8086],{},[1911,8085,1927],{},[1911,8087,3234],{},[1903,8089,8090,8092],{},[1911,8091,1914],{"mathvariant":1913},[1923,8093,8094,8096],{},[1911,8095,1798],{},[1911,8097,3234],{},[1933,8099,7716],{},[1929,8101,1900],{},[2060,8103,8104],{"encoding":2062},"\\frac{\\partial x_i}{\\partial p_i} > 0",[1865,8106,8108,8273],{"className":8107,"ariaHidden":1901},[2067],[1865,8109,8111,8115,8264,8267,8270],{"className":8110},[2071],[1865,8112],{"className":8113,"style":8114},[2075],"height:1.3773em;vertical-align:-0.4811em;",[1865,8116,8118,8121,8261],{"className":8117},[2080],[1865,8119],{"className":8120},[2119,2120],[1865,8122,8124],{"className":8123},[1906],[1865,8125,8127,8252],{"className":8126},[2091,2092],[1865,8128,8130,8249],{"className":8129},[2096],[1865,8131,8133,8187,8195],{"className":8132,"style":4227},[2100],[1865,8134,8135,8138],{"style":4230},[1865,8136],{"className":8137,"style":2140},[2108],[1865,8139,8141],{"className":8140},[2179,2180,2181,2182],[1865,8142,8144,8147],{"className":8143},[2080,2182],[1865,8145,1914],{"className":8146,"style":2147},[2080,2182],[1865,8148,8150,8153],{"className":8149},[2080,2182],[1865,8151,1798],{"className":8152},[2080,2154,2182],[1865,8154,8156],{"className":8155},[2158],[1865,8157,8159,8179],{"className":8158},[2091,2092],[1865,8160,8162,8176],{"className":8161},[2096],[1865,8163,8165],{"className":8164,"style":4261},[2100],[1865,8166,8167,8170],{"style":4264},[1865,8168],{"className":8169,"style":4268},[2108],[1865,8171,8173],{"className":8172},[2179,4272,4273,2182],[1865,8174,3234],{"className":8175},[2080,2154,2182],[1865,8177,2190],{"className":8178},[2189],[1865,8180,8182],{"className":8181},[2096],[1865,8183,8185],{"className":8184,"style":4350},[2100],[1865,8186],{},[1865,8188,8189,8192],{"style":2202},[1865,8190],{"className":8191,"style":2140},[2108],[1865,8193],{"className":8194,"style":2210},[2209],[1865,8196,8197,8200],{"style":4299},[1865,8198],{"className":8199,"style":2140},[2108],[1865,8201,8203],{"className":8202},[2179,2180,2181,2182],[1865,8204,8206,8209],{"className":8205},[2080,2182],[1865,8207,1914],{"className":8208,"style":2147},[2080,2182],[1865,8210,8212,8215],{"className":8211},[2080,2182],[1865,8213,1927],{"className":8214},[2080,2154,2182],[1865,8216,8218],{"className":8217},[2158],[1865,8219,8221,8241],{"className":8220},[2091,2092],[1865,8222,8224,8238],{"className":8223},[2096],[1865,8225,8227],{"className":8226,"style":4261},[2100],[1865,8228,8229,8232],{"style":4264},[1865,8230],{"className":8231,"style":4268},[2108],[1865,8233,8235],{"className":8234},[2179,4272,4273,2182],[1865,8236,3234],{"className":8237},[2080,2154,2182],[1865,8239,2190],{"className":8240},[2189],[1865,8242,8244],{"className":8243},[2096],[1865,8245,8247],{"className":8246,"style":4350},[2100],[1865,8248],{},[1865,8250,2190],{"className":8251},[2189],[1865,8253,8255],{"className":8254},[2096],[1865,8256,8259],{"className":8257,"style":8258},[2100],"height:0.4811em;",[1865,8260],{},[1865,8262],{"className":8263},[2242,2120],[1865,8265],{"className":8266,"style":2693},[2246],[1865,8268,7716],{"className":8269},[2697],[1865,8271],{"className":8272,"style":2693},[2246],[1865,8274,8276,8279],{"className":8275},[2071],[1865,8277],{"className":8278,"style":7553},[2075],[1865,8280,1900],{"className":8281},[2080],"（违反需求定律）",[1808,8284,8285],{},"实证中极为罕见",[1798,8287,8288,8291],{},[3048,8289,8290],{},"重要命题",": 对于自身价格，替代效应总是非正的：",[1865,8293,8295],{"className":8294},[1868],[1865,8296,8298,8336],{"className":8297},[1872],[1865,8299,8301],{"className":8300},[1876],[1878,8302,8303],{"xmlns":1880,"display":1881},[1883,8304,8305,8333],{},[1903,8306,8307,8329,8331],{},[1906,8308,8309,8319],{},[1903,8310,8311,8313],{},[1911,8312,1914],{"mathvariant":1913},[1923,8314,8315,8317],{},[1911,8316,3484],{},[1911,8318,3234],{},[1903,8320,8321,8323],{},[1911,8322,1914],{"mathvariant":1913},[1923,8324,8325,8327],{},[1911,8326,1798],{},[1911,8328,3234],{},[1933,8330,7482],{},[1929,8332,1900],{},[2060,8334,8335],{"encoding":2062},"\\frac{\\partial h_i}{\\partial p_i} \\le 0",[1865,8337,8339,8496],{"className":8338,"ariaHidden":1901},[2067],[1865,8340,8342,8345,8487,8490,8493],{"className":8341},[2071],[1865,8343],{"className":8344,"style":3257},[2075],[1865,8346,8348,8351,8484],{"className":8347},[2080],[1865,8349],{"className":8350},[2119,2120],[1865,8352,8354],{"className":8353},[1906],[1865,8355,8357,8476],{"className":8356},[2091,2092],[1865,8358,8360,8473],{"className":8359},[2096],[1865,8361,8363,8414,8422],{"className":8362,"style":2133},[2100],[1865,8364,8365,8368],{"style":2136},[1865,8366],{"className":8367,"style":2140},[2108],[1865,8369,8371,8374],{"className":8370},[2080],[1865,8372,1914],{"className":8373,"style":2147},[2080],[1865,8375,8377,8380],{"className":8376},[2080],[1865,8378,1798],{"className":8379},[2080,2154],[1865,8381,8383],{"className":8382},[2158],[1865,8384,8386,8406],{"className":8385},[2091,2092],[1865,8387,8389,8403],{"className":8388},[2096],[1865,8390,8392],{"className":8391,"style":3364},[2100],[1865,8393,8394,8397],{"style":2171},[1865,8395],{"className":8396,"style":2175},[2108],[1865,8398,8400],{"className":8399},[2179,2180,2181,2182],[1865,8401,3234],{"className":8402},[2080,2154,2182],[1865,8404,2190],{"className":8405},[2189],[1865,8407,8409],{"className":8408},[2096],[1865,8410,8412],{"className":8411,"style":2197},[2100],[1865,8413],{},[1865,8415,8416,8419],{"style":2202},[1865,8417],{"className":8418,"style":2140},[2108],[1865,8420],{"className":8421,"style":2210},[2209],[1865,8423,8424,8427],{"style":2213},[1865,8425],{"className":8426,"style":2140},[2108],[1865,8428,8430,8433],{"className":8429},[2080],[1865,8431,1914],{"className":8432,"style":2147},[2080],[1865,8434,8436,8439],{"className":8435},[2080],[1865,8437,3484],{"className":8438},[2080,2154],[1865,8440,8442],{"className":8441},[2158],[1865,8443,8445,8465],{"className":8444},[2091,2092],[1865,8446,8448,8462],{"className":8447},[2096],[1865,8449,8451],{"className":8450,"style":3364},[2100],[1865,8452,8453,8456],{"style":2171},[1865,8454],{"className":8455,"style":2175},[2108],[1865,8457,8459],{"className":8458},[2179,2180,2181,2182],[1865,8460,3234],{"className":8461},[2080,2154,2182],[1865,8463,2190],{"className":8464},[2189],[1865,8466,8468],{"className":8467},[2096],[1865,8469,8471],{"className":8470,"style":2197},[2100],[1865,8472],{},[1865,8474,2190],{"className":8475},[2189],[1865,8477,8479],{"className":8478},[2096],[1865,8480,8482],{"className":8481,"style":3396},[2100],[1865,8483],{},[1865,8485],{"className":8486},[2242,2120],[1865,8488],{"className":8489,"style":2693},[2246],[1865,8491,7482],{"className":8492},[2697],[1865,8494],{"className":8495,"style":2693},[2246],[1865,8497,8499,8502],{"className":8498},[2071],[1865,8500],{"className":8501,"style":7553},[2075],[1865,8503,1900],{"className":8504},[2080],[1798,8506,8507],{},"这保证了希克斯需求曲线总是向下倾斜。",[3421,8509],{},[1794,8511,8513],{"id":8512},"_3-福利变化的测度","3. 福利变化的测度",[1854,8515,8517],{"id":8516},"_31-问题的提出","3.1 问题的提出",[1798,8519,8520,8521,8609,8610,8693],{},"假设商品1的价格从",[1865,8522,8524,8545],{"className":8523},[1872],[1865,8525,8527],{"className":8526},[1876],[1878,8528,8529],{"xmlns":1880},[1883,8530,8531,8542],{},[1903,8532,8533],{},[8534,8535,8536,8538,8540],"msubsup",{},[1911,8537,1798],{},[1929,8539,1931],{},[1929,8541,1900],{},[2060,8543,8544],{"encoding":2062},"p_1^0",[1865,8546,8548],{"className":8547,"ariaHidden":1901},[2067],[1865,8549,8551,8555],{"className":8550},[2071],[1865,8552],{"className":8553,"style":8554},[2075],"height:1.0622em;vertical-align:-0.2481em;",[1865,8556,8558,8561],{"className":8557},[2080],[1865,8559,1798],{"className":8560},[2080,2154],[1865,8562,8564],{"className":8563},[2158],[1865,8565,8567,8600],{"className":8566},[2091,2092],[1865,8568,8570,8597],{"className":8569},[2096],[1865,8571,8574,8586],{"className":8572,"style":8573},[2100],"height:0.8141em;",[1865,8575,8577,8580],{"style":8576},"top:-2.4519em;margin-left:0em;margin-right:0.05em;",[1865,8578],{"className":8579,"style":2175},[2108],[1865,8581,8583],{"className":8582},[2179,2180,2181,2182],[1865,8584,1931],{"className":8585},[2080,2182],[1865,8587,8588,8591],{"style":7519},[1865,8589],{"className":8590,"style":2175},[2108],[1865,8592,8594],{"className":8593},[2179,2180,2181,2182],[1865,8595,1900],{"className":8596},[2080,2182],[1865,8598,2190],{"className":8599},[2189],[1865,8601,8603],{"className":8602},[2096],[1865,8604,8607],{"className":8605,"style":8606},[2100],"height:0.2481em;",[1865,8608],{},"上涨到",[1865,8611,8613,8633],{"className":8612},[1872],[1865,8614,8616],{"className":8615},[1876],[1878,8617,8618],{"xmlns":1880},[1883,8619,8620,8630],{},[1903,8621,8622],{},[8534,8623,8624,8626,8628],{},[1911,8625,1798],{},[1929,8627,1931],{},[1929,8629,1931],{},[2060,8631,8632],{"encoding":2062},"p_1^1",[1865,8634,8636],{"className":8635,"ariaHidden":1901},[2067],[1865,8637,8639,8642],{"className":8638},[2071],[1865,8640],{"className":8641,"style":8554},[2075],[1865,8643,8645,8648],{"className":8644},[2080],[1865,8646,1798],{"className":8647},[2080,2154],[1865,8649,8651],{"className":8650},[2158],[1865,8652,8654,8685],{"className":8653},[2091,2092],[1865,8655,8657,8682],{"className":8656},[2096],[1865,8658,8660,8671],{"className":8659,"style":8573},[2100],[1865,8661,8662,8665],{"style":8576},[1865,8663],{"className":8664,"style":2175},[2108],[1865,8666,8668],{"className":8667},[2179,2180,2181,2182],[1865,8669,1931],{"className":8670},[2080,2182],[1865,8672,8673,8676],{"style":7519},[1865,8674],{"className":8675,"style":2175},[2108],[1865,8677,8679],{"className":8678},[2179,2180,2181,2182],[1865,8680,1931],{"className":8681},[2080,2182],[1865,8683,2190],{"className":8684},[2189],[1865,8686,8688],{"className":8687},[2096],[1865,8689,8691],{"className":8690,"style":8606},[2100],[1865,8692],{},"。如何用货币单位来衡量这一价格变化对消费者福利的影响？",[1798,8695,8696,8697],{},"我们需要回答：",[3048,8698,8699],{},"消费者需要得到（或愿意放弃）多少钱，才能使其福利水平在价格变化后保持不变？",[1854,8701,8703],{"id":8702},"_32-补偿变差-compensating-variation-cv","3.2 补偿变差 (Compensating Variation, CV)",[1798,8705,8706,8709,8710,8713],{},[3048,8707,8708],{},"定义",": 价格变化后，为了让消费者恢复到",[3048,8711,8712],{},"原来的效用水平","，需要给予（或取走）的收入金额。",[1798,8715,8716],{},"数学表达：",[1865,8718,8720],{"className":8719},[1868],[1865,8721,8723,8806],{"className":8722},[1872],[1865,8724,8726],{"className":8725},[1876],[1878,8727,8728],{"xmlns":1880,"display":1881},[1883,8729,8730,8803],{},[1903,8731,8732,8735,8738,8740,8743,8745,8753,8755,8761,8763,8769,8771,8773,8775,8777,8785,8787,8793,8795,8801],{},[1911,8733,8734],{},"C",[1911,8736,8737],{},"V",[1933,8739,1955],{},[1911,8741,8742],{},"e",[1933,8744,4942],{"stretchy":3501},[8534,8746,8747,8749,8751],{},[1911,8748,1798],{},[1929,8750,1931],{},[1929,8752,1931],{},[1933,8754,2784],{"separator":1901},[1923,8756,8757,8759],{},[1911,8758,1798],{},[1929,8760,1984],{},[1933,8762,2784],{"separator":1901},[6885,8764,8765,8767],{},[1911,8766,3508],{},[1929,8768,1900],{},[1933,8770,4963],{"stretchy":3501},[1933,8772,1935],{},[1911,8774,8742],{},[1933,8776,4942],{"stretchy":3501},[8534,8778,8779,8781,8783],{},[1911,8780,1798],{},[1929,8782,1931],{},[1929,8784,1900],{},[1933,8786,2784],{"separator":1901},[1923,8788,8789,8791],{},[1911,8790,1798],{},[1929,8792,1984],{},[1933,8794,2784],{"separator":1901},[6885,8796,8797,8799],{},[1911,8798,3508],{},[1929,8800,1900],{},[1933,8802,4963],{"stretchy":3501},[2060,8804,8805],{"encoding":2062},"CV = e(p_1^1, p_2, u^0) - e(p_1^0, p_2, u^0)",[1865,8807,8809,8832,8992],{"className":8808,"ariaHidden":1901},[2067],[1865,8810,8812,8816,8820,8823,8826,8829],{"className":8811},[2071],[1865,8813],{"className":8814,"style":8815},[2075],"height:0.6833em;",[1865,8817,8734],{"className":8818,"style":8819},[2080,2154],"margin-right:0.0715em;",[1865,8821,8737],{"className":8822,"style":2247},[2080,2154],[1865,8824],{"className":8825,"style":2693},[2246],[1865,8827,1955],{"className":8828},[2697],[1865,8830],{"className":8831,"style":2693},[2246],[1865,8833,8835,8839,8842,8845,8899,8902,8905,8945,8948,8951,8980,8983,8986,8989],{"className":8834},[2071],[1865,8836],{"className":8837,"style":8838},[2075],"height:1.1141em;vertical-align:-0.25em;",[1865,8840,8742],{"className":8841},[2080,2154],[1865,8843,4942],{"className":8844},[2119],[1865,8846,8848,8851],{"className":8847},[2080],[1865,8849,1798],{"className":8850},[2080,2154],[1865,8852,8854],{"className":8853},[2158],[1865,8855,8857,8890],{"className":8856},[2091,2092],[1865,8858,8860,8887],{"className":8859},[2096],[1865,8861,8864,8876],{"className":8862,"style":8863},[2100],"height:0.8641em;",[1865,8865,8867,8870],{"style":8866},"top:-2.453em;margin-left:0em;margin-right:0.05em;",[1865,8868],{"className":8869,"style":2175},[2108],[1865,8871,8873],{"className":8872},[2179,2180,2181,2182],[1865,8874,1931],{"className":8875},[2080,2182],[1865,8877,8878,8881],{"style":7181},[1865,8879],{"className":8880,"style":2175},[2108],[1865,8882,8884],{"className":8883},[2179,2180,2181,2182],[1865,8885,1931],{"className":8886},[2080,2182],[1865,8888,2190],{"className":8889},[2189],[1865,8891,8893],{"className":8892},[2096],[1865,8894,8897],{"className":8895,"style":8896},[2100],"height:0.247em;",[1865,8898],{},[1865,8900,2784],{"className":8901},[2851],[1865,8903],{"className":8904,"style":2855},[2246],[1865,8906,8908,8911],{"className":8907},[2080],[1865,8909,1798],{"className":8910},[2080,2154],[1865,8912,8914],{"className":8913},[2158],[1865,8915,8917,8937],{"className":8916},[2091,2092],[1865,8918,8920,8934],{"className":8919},[2096],[1865,8921,8923],{"className":8922,"style":2168},[2100],[1865,8924,8925,8928],{"style":2171},[1865,8926],{"className":8927,"style":2175},[2108],[1865,8929,8931],{"className":8930},[2179,2180,2181,2182],[1865,8932,1984],{"className":8933},[2080,2182],[1865,8935,2190],{"className":8936},[2189],[1865,8938,8940],{"className":8939},[2096],[1865,8941,8943],{"className":8942,"style":2197},[2100],[1865,8944],{},[1865,8946,2784],{"className":8947},[2851],[1865,8949],{"className":8950,"style":2855},[2246],[1865,8952,8954,8957],{"className":8953},[2080],[1865,8955,3508],{"className":8956},[2080,2154],[1865,8958,8960],{"className":8959},[2158],[1865,8961,8963],{"className":8962},[2091],[1865,8964,8966],{"className":8965},[2096],[1865,8967,8969],{"className":8968,"style":8863},[2100],[1865,8970,8971,8974],{"style":7181},[1865,8972],{"className":8973,"style":2175},[2108],[1865,8975,8977],{"className":8976},[2179,2180,2181,2182],[1865,8978,1900],{"className":8979},[2080,2182],[1865,8981,4963],{"className":8982},[2242],[1865,8984],{"className":8985,"style":2247},[2246],[1865,8987,1935],{"className":8988},[2251],[1865,8990],{"className":8991,"style":2247},[2246],[1865,8993,8995,8998,9001,9004,9055,9058,9061,9101,9104,9107,9136],{"className":8994},[2071],[1865,8996],{"className":8997,"style":8838},[2075],[1865,8999,8742],{"className":9000},[2080,2154],[1865,9002,4942],{"className":9003},[2119],[1865,9005,9007,9010],{"className":9006},[2080],[1865,9008,1798],{"className":9009},[2080,2154],[1865,9011,9013],{"className":9012},[2158],[1865,9014,9016,9047],{"className":9015},[2091,2092],[1865,9017,9019,9044],{"className":9018},[2096],[1865,9020,9022,9033],{"className":9021,"style":8863},[2100],[1865,9023,9024,9027],{"style":8866},[1865,9025],{"className":9026,"style":2175},[2108],[1865,9028,9030],{"className":9029},[2179,2180,2181,2182],[1865,9031,1931],{"className":9032},[2080,2182],[1865,9034,9035,9038],{"style":7181},[1865,9036],{"className":9037,"style":2175},[2108],[1865,9039,9041],{"className":9040},[2179,2180,2181,2182],[1865,9042,1900],{"className":9043},[2080,2182],[1865,9045,2190],{"className":9046},[2189],[1865,9048,9050],{"className":9049},[2096],[1865,9051,9053],{"className":9052,"style":8896},[2100],[1865,9054],{},[1865,9056,2784],{"className":9057},[2851],[1865,9059],{"className":9060,"style":2855},[2246],[1865,9062,9064,9067],{"className":9063},[2080],[1865,9065,1798],{"className":9066},[2080,2154],[1865,9068,9070],{"className":9069},[2158],[1865,9071,9073,9093],{"className":9072},[2091,2092],[1865,9074,9076,9090],{"className":9075},[2096],[1865,9077,9079],{"className":9078,"style":2168},[2100],[1865,9080,9081,9084],{"style":2171},[1865,9082],{"className":9083,"style":2175},[2108],[1865,9085,9087],{"className":9086},[2179,2180,2181,2182],[1865,9088,1984],{"className":9089},[2080,2182],[1865,9091,2190],{"className":9092},[2189],[1865,9094,9096],{"className":9095},[2096],[1865,9097,9099],{"className":9098,"style":2197},[2100],[1865,9100],{},[1865,9102,2784],{"className":9103},[2851],[1865,9105],{"className":9106,"style":2855},[2246],[1865,9108,9110,9113],{"className":9109},[2080],[1865,9111,3508],{"className":9112},[2080,2154],[1865,9114,9116],{"className":9115},[2158],[1865,9117,9119],{"className":9118},[2091],[1865,9120,9122],{"className":9121},[2096],[1865,9123,9125],{"className":9124,"style":8863},[2100],[1865,9126,9127,9130],{"style":7181},[1865,9128],{"className":9129,"style":2175},[2108],[1865,9131,9133],{"className":9132},[2179,2180,2181,2182],[1865,9134,1900],{"className":9135},[2080,2182],[1865,9137,4963],{"className":9138},[2242],[1798,9140,7196,9141,9359],{},[1865,9142,9144,9190],{"className":9143},[1872],[1865,9145,9147],{"className":9146},[1876],[1878,9148,9149],{"xmlns":1880},[1883,9150,9151,9187],{},[1903,9152,9153,9159,9161,9163,9165,9173,9175,9181,9183,9185],{},[6885,9154,9155,9157],{},[1911,9156,3508],{},[1929,9158,1900],{},[1933,9160,1955],{},[1911,9162,4993],{},[1933,9164,4942],{"stretchy":3501},[8534,9166,9167,9169,9171],{},[1911,9168,1798],{},[1929,9170,1931],{},[1929,9172,1900],{},[1933,9174,2784],{"separator":1901},[1923,9176,9177,9179],{},[1911,9178,1798],{},[1929,9180,1984],{},[1933,9182,2784],{"separator":1901},[1911,9184,2046],{},[1933,9186,4963],{"stretchy":3501},[2060,9188,9189],{"encoding":2062},"u^0 = v(p_1^0, p_2, m)",[1865,9191,9193,9237],{"className":9192,"ariaHidden":1901},[2067],[1865,9194,9196,9199,9228,9231,9234],{"className":9195},[2071],[1865,9197],{"className":9198,"style":8573},[2075],[1865,9200,9202,9205],{"className":9201},[2080],[1865,9203,3508],{"className":9204},[2080,2154],[1865,9206,9208],{"className":9207},[2158],[1865,9209,9211],{"className":9210},[2091],[1865,9212,9214],{"className":9213},[2096],[1865,9215,9217],{"className":9216,"style":8573},[2100],[1865,9218,9219,9222],{"style":7519},[1865,9220],{"className":9221,"style":2175},[2108],[1865,9223,9225],{"className":9224},[2179,2180,2181,2182],[1865,9226,1900],{"className":9227},[2080,2182],[1865,9229],{"className":9230,"style":2693},[2246],[1865,9232,1955],{"className":9233},[2697],[1865,9235],{"className":9236,"style":2693},[2246],[1865,9238,9240,9244,9247,9250,9301,9304,9307,9347,9350,9353,9356],{"className":9239},[2071],[1865,9241],{"className":9242,"style":9243},[2075],"height:1.0641em;vertical-align:-0.25em;",[1865,9245,4993],{"className":9246,"style":5325},[2080,2154],[1865,9248,4942],{"className":9249},[2119],[1865,9251,9253,9256],{"className":9252},[2080],[1865,9254,1798],{"className":9255},[2080,2154],[1865,9257,9259],{"className":9258},[2158],[1865,9260,9262,9293],{"className":9261},[2091,2092],[1865,9263,9265,9290],{"className":9264},[2096],[1865,9266,9268,9279],{"className":9267,"style":8573},[2100],[1865,9269,9270,9273],{"style":8576},[1865,9271],{"className":9272,"style":2175},[2108],[1865,9274,9276],{"className":9275},[2179,2180,2181,2182],[1865,9277,1931],{"className":9278},[2080,2182],[1865,9280,9281,9284],{"style":7519},[1865,9282],{"className":9283,"style":2175},[2108],[1865,9285,9287],{"className":9286},[2179,2180,2181,2182],[1865,9288,1900],{"className":9289},[2080,2182],[1865,9291,2190],{"className":9292},[2189],[1865,9294,9296],{"className":9295},[2096],[1865,9297,9299],{"className":9298,"style":8606},[2100],[1865,9300],{},[1865,9302,2784],{"className":9303},[2851],[1865,9305],{"className":9306,"style":2855},[2246],[1865,9308,9310,9313],{"className":9309},[2080],[1865,9311,1798],{"className":9312},[2080,2154],[1865,9314,9316],{"className":9315},[2158],[1865,9317,9319,9339],{"className":9318},[2091,2092],[1865,9320,9322,9336],{"className":9321},[2096],[1865,9323,9325],{"className":9324,"style":2168},[2100],[1865,9326,9327,9330],{"style":2171},[1865,9328],{"className":9329,"style":2175},[2108],[1865,9331,9333],{"className":9332},[2179,2180,2181,2182],[1865,9334,1984],{"className":9335},[2080,2182],[1865,9337,2190],{"className":9338},[2189],[1865,9340,9342],{"className":9341},[2096],[1865,9343,9345],{"className":9344,"style":2197},[2100],[1865,9346],{},[1865,9348,2784],{"className":9349},[2851],[1865,9351],{"className":9352,"style":2855},[2246],[1865,9354,2046],{"className":9355},[2080,2154],[1865,9357,4963],{"className":9358},[2242],"是初始效用水平。",[1798,9361,9362],{},"等价地：",[1865,9364,9366],{"className":9365},[1868],[1865,9367,9369,9421],{"className":9368},[1872],[1865,9370,9372],{"className":9371},[1876],[1878,9373,9374],{"xmlns":1880,"display":1881},[1883,9375,9376,9418],{},[1903,9377,9378,9380,9382,9384,9386,9388,9396,9398,9404,9406,9412,9414,9416],{},[1911,9379,8734],{},[1911,9381,8737],{},[1933,9383,1955],{},[1911,9385,8742],{},[1933,9387,4942],{"stretchy":3501},[8534,9389,9390,9392,9394],{},[1911,9391,1798],{},[1929,9393,1931],{},[1929,9395,1931],{},[1933,9397,2784],{"separator":1901},[1923,9399,9400,9402],{},[1911,9401,1798],{},[1929,9403,1984],{},[1933,9405,2784],{"separator":1901},[6885,9407,9408,9410],{},[1911,9409,3508],{},[1929,9411,1900],{},[1933,9413,4963],{"stretchy":3501},[1933,9415,1935],{},[1911,9417,2046],{},[2060,9419,9420],{"encoding":2062},"CV = e(p_1^1, p_2, u^0) - m",[1865,9422,9424,9445,9601],{"className":9423,"ariaHidden":1901},[2067],[1865,9425,9427,9430,9433,9436,9439,9442],{"className":9426},[2071],[1865,9428],{"className":9429,"style":8815},[2075],[1865,9431,8734],{"className":9432,"style":8819},[2080,2154],[1865,9434,8737],{"className":9435,"style":2247},[2080,2154],[1865,9437],{"className":9438,"style":2693},[2246],[1865,9440,1955],{"className":9441},[2697],[1865,9443],{"className":9444,"style":2693},[2246],[1865,9446,9448,9451,9454,9457,9508,9511,9514,9554,9557,9560,9589,9592,9595,9598],{"className":9447},[2071],[1865,9449],{"className":9450,"style":8838},[2075],[1865,9452,8742],{"className":9453},[2080,2154],[1865,9455,4942],{"className":9456},[2119],[1865,9458,9460,9463],{"className":9459},[2080],[1865,9461,1798],{"className":9462},[2080,2154],[1865,9464,9466],{"className":9465},[2158],[1865,9467,9469,9500],{"className":9468},[2091,2092],[1865,9470,9472,9497],{"className":9471},[2096],[1865,9473,9475,9486],{"className":9474,"style":8863},[2100],[1865,9476,9477,9480],{"style":8866},[1865,9478],{"className":9479,"style":2175},[2108],[1865,9481,9483],{"className":9482},[2179,2180,2181,2182],[1865,9484,1931],{"className":9485},[2080,2182],[1865,9487,9488,9491],{"style":7181},[1865,9489],{"className":9490,"style":2175},[2108],[1865,9492,9494],{"className":9493},[2179,2180,2181,2182],[1865,9495,1931],{"className":9496},[2080,2182],[1865,9498,2190],{"className":9499},[2189],[1865,9501,9503],{"className":9502},[2096],[1865,9504,9506],{"className":9505,"style":8896},[2100],[1865,9507],{},[1865,9509,2784],{"className":9510},[2851],[1865,9512],{"className":9513,"style":2855},[2246],[1865,9515,9517,9520],{"className":9516},[2080],[1865,9518,1798],{"className":9519},[2080,2154],[1865,9521,9523],{"className":9522},[2158],[1865,9524,9526,9546],{"className":9525},[2091,2092],[1865,9527,9529,9543],{"className":9528},[2096],[1865,9530,9532],{"className":9531,"style":2168},[2100],[1865,9533,9534,9537],{"style":2171},[1865,9535],{"className":9536,"style":2175},[2108],[1865,9538,9540],{"className":9539},[2179,2180,2181,2182],[1865,9541,1984],{"className":9542},[2080,2182],[1865,9544,2190],{"className":9545},[2189],[1865,9547,9549],{"className":9548},[2096],[1865,9550,9552],{"className":9551,"style":2197},[2100],[1865,9553],{},[1865,9555,2784],{"className":9556},[2851],[1865,9558],{"className":9559,"style":2855},[2246],[1865,9561,9563,9566],{"className":9562},[2080],[1865,9564,3508],{"className":9565},[2080,2154],[1865,9567,9569],{"className":9568},[2158],[1865,9570,9572],{"className":9571},[2091],[1865,9573,9575],{"className":9574},[2096],[1865,9576,9578],{"className":9577,"style":8863},[2100],[1865,9579,9580,9583],{"style":7181},[1865,9581],{"className":9582,"style":2175},[2108],[1865,9584,9586],{"className":9585},[2179,2180,2181,2182],[1865,9587,1900],{"className":9588},[2080,2182],[1865,9590,4963],{"className":9591},[2242],[1865,9593],{"className":9594,"style":2247},[2246],[1865,9596,1935],{"className":9597},[2251],[1865,9599],{"className":9600,"style":2247},[2246],[1865,9602,9604,9607],{"className":9603},[2071],[1865,9605],{"className":9606,"style":6852},[2075],[1865,9608,2046],{"className":9609},[2080,2154],[1798,9611,9612,4915],{},[3048,9613,9614],{},"直观理解",[1805,9616,9617,9838],{},[1808,9618,9619,9620,9779,9780,9837],{},"如果价格上涨（",[1865,9621,9623,9653],{"className":9622},[1872],[1865,9624,9626],{"className":9625},[1876],[1878,9627,9628],{"xmlns":1880},[1883,9629,9630,9650],{},[1903,9631,9632,9640,9642],{},[8534,9633,9634,9636,9638],{},[1911,9635,1798],{},[1929,9637,1931],{},[1929,9639,1931],{},[1933,9641,7716],{},[8534,9643,9644,9646,9648],{},[1911,9645,1798],{},[1929,9647,1931],{},[1929,9649,1900],{},[2060,9651,9652],{"encoding":2062},"p_1^1 > p_1^0",[1865,9654,9656,9722],{"className":9655,"ariaHidden":1901},[2067],[1865,9657,9659,9662,9713,9716,9719],{"className":9658},[2071],[1865,9660],{"className":9661,"style":8554},[2075],[1865,9663,9665,9668],{"className":9664},[2080],[1865,9666,1798],{"className":9667},[2080,2154],[1865,9669,9671],{"className":9670},[2158],[1865,9672,9674,9705],{"className":9673},[2091,2092],[1865,9675,9677,9702],{"className":9676},[2096],[1865,9678,9680,9691],{"className":9679,"style":8573},[2100],[1865,9681,9682,9685],{"style":8576},[1865,9683],{"className":9684,"style":2175},[2108],[1865,9686,9688],{"className":9687},[2179,2180,2181,2182],[1865,9689,1931],{"className":9690},[2080,2182],[1865,9692,9693,9696],{"style":7519},[1865,9694],{"className":9695,"style":2175},[2108],[1865,9697,9699],{"className":9698},[2179,2180,2181,2182],[1865,9700,1931],{"className":9701},[2080,2182],[1865,9703,2190],{"className":9704},[2189],[1865,9706,9708],{"className":9707},[2096],[1865,9709,9711],{"className":9710,"style":8606},[2100],[1865,9712],{},[1865,9714],{"className":9715,"style":2693},[2246],[1865,9717,7716],{"className":9718},[2697],[1865,9720],{"className":9721,"style":2693},[2246],[1865,9723,9725,9728],{"className":9724},[2071],[1865,9726],{"className":9727,"style":8554},[2075],[1865,9729,9731,9734],{"className":9730},[2080],[1865,9732,1798],{"className":9733},[2080,2154],[1865,9735,9737],{"className":9736},[2158],[1865,9738,9740,9771],{"className":9739},[2091,2092],[1865,9741,9743,9768],{"className":9742},[2096],[1865,9744,9746,9757],{"className":9745,"style":8573},[2100],[1865,9747,9748,9751],{"style":8576},[1865,9749],{"className":9750,"style":2175},[2108],[1865,9752,9754],{"className":9753},[2179,2180,2181,2182],[1865,9755,1931],{"className":9756},[2080,2182],[1865,9758,9759,9762],{"style":7519},[1865,9760],{"className":9761,"style":2175},[2108],[1865,9763,9765],{"className":9764},[2179,2180,2181,2182],[1865,9766,1900],{"className":9767},[2080,2182],[1865,9769,2190],{"className":9770},[2189],[1865,9772,9774],{"className":9773},[2096],[1865,9775,9777],{"className":9776,"style":8606},[2100],[1865,9778],{},"），",[1865,9781,9783,9803],{"className":9782},[1872],[1865,9784,9786],{"className":9785},[1876],[1878,9787,9788],{"xmlns":1880},[1883,9789,9790,9800],{},[1903,9791,9792,9794,9796,9798],{},[1911,9793,8734],{},[1911,9795,8737],{},[1933,9797,7716],{},[1929,9799,1900],{},[2060,9801,9802],{"encoding":2062},"CV > 0",[1865,9804,9806,9828],{"className":9805,"ariaHidden":1901},[2067],[1865,9807,9809,9813,9816,9819,9822,9825],{"className":9808},[2071],[1865,9810],{"className":9811,"style":9812},[2075],"height:0.7224em;vertical-align:-0.0391em;",[1865,9814,8734],{"className":9815,"style":8819},[2080,2154],[1865,9817,8737],{"className":9818,"style":2247},[2080,2154],[1865,9820],{"className":9821,"style":2693},[2246],[1865,9823,7716],{"className":9824},[2697],[1865,9826],{"className":9827,"style":2693},[2246],[1865,9829,9831,9834],{"className":9830},[2071],[1865,9832],{"className":9833,"style":7553},[2075],[1865,9835,1900],{"className":9836},[2080],"：需要补偿消费者",[1808,9839,9840,9841,9897],{},"如果价格下降，",[1865,9842,9844,9864],{"className":9843},[1872],[1865,9845,9847],{"className":9846},[1876],[1878,9848,9849],{"xmlns":1880},[1883,9850,9851,9861],{},[1903,9852,9853,9855,9857,9859],{},[1911,9854,8734],{},[1911,9856,8737],{},[1933,9858,7902],{},[1929,9860,1900],{},[2060,9862,9863],{"encoding":2062},"CV \u003C 0",[1865,9865,9867,9888],{"className":9866,"ariaHidden":1901},[2067],[1865,9868,9870,9873,9876,9879,9882,9885],{"className":9869},[2071],[1865,9871],{"className":9872,"style":9812},[2075],[1865,9874,8734],{"className":9875,"style":8819},[2080,2154],[1865,9877,8737],{"className":9878,"style":2247},[2080,2154],[1865,9880],{"className":9881,"style":2693},[2246],[1865,9883,7902],{"className":9884},[2697],[1865,9886],{"className":9887,"style":2693},[2246],[1865,9889,9891,9894],{"className":9890},[2071],[1865,9892],{"className":9893,"style":7553},[2075],[1865,9895,1900],{"className":9896},[2080],"：消费者愿意支付这么多来享受降价",[1854,9899,9901],{"id":9900},"_33-等价变差-equivalent-variation-ev","3.3 等价变差 (Equivalent Variation, EV)",[1798,9903,9904,9906,9907,9910],{},[3048,9905,8708],{},": 在价格",[3048,9908,9909],{},"未发生变化","的情况下，取走（或给予）多少收入，能让消费者的效用变化等同于价格变化带来的效用变化。",[1798,9912,8716],{},[1865,9914,9916],{"className":9915},[1868],[1865,9917,9919,10000],{"className":9918},[1872],[1865,9920,9922],{"className":9921},[1876],[1878,9923,9924],{"xmlns":1880,"display":1881},[1883,9925,9926,9997],{},[1903,9927,9928,9931,9933,9935,9937,9939,9947,9949,9955,9957,9963,9965,9967,9969,9971,9979,9981,9987,9989,9995],{},[1911,9929,9930],{},"E",[1911,9932,8737],{},[1933,9934,1955],{},[1911,9936,8742],{},[1933,9938,4942],{"stretchy":3501},[8534,9940,9941,9943,9945],{},[1911,9942,1798],{},[1929,9944,1931],{},[1929,9946,1900],{},[1933,9948,2784],{"separator":1901},[1923,9950,9951,9953],{},[1911,9952,1798],{},[1929,9954,1984],{},[1933,9956,2784],{"separator":1901},[6885,9958,9959,9961],{},[1911,9960,3508],{},[1929,9962,1931],{},[1933,9964,4963],{"stretchy":3501},[1933,9966,1935],{},[1911,9968,8742],{},[1933,9970,4942],{"stretchy":3501},[8534,9972,9973,9975,9977],{},[1911,9974,1798],{},[1929,9976,1931],{},[1929,9978,1900],{},[1933,9980,2784],{"separator":1901},[1923,9982,9983,9985],{},[1911,9984,1798],{},[1929,9986,1984],{},[1933,9988,2784],{"separator":1901},[6885,9990,9991,9993],{},[1911,9992,3508],{},[1929,9994,1900],{},[1933,9996,4963],{"stretchy":3501},[2060,9998,9999],{"encoding":2062},"EV = e(p_1^0, p_2, u^1) - e(p_1^0, p_2, u^0)",[1865,10001,10003,10024,10180],{"className":10002,"ariaHidden":1901},[2067],[1865,10004,10006,10009,10012,10015,10018,10021],{"className":10005},[2071],[1865,10007],{"className":10008,"style":8815},[2075],[1865,10010,9930],{"className":10011,"style":7058},[2080,2154],[1865,10013,8737],{"className":10014,"style":2247},[2080,2154],[1865,10016],{"className":10017,"style":2693},[2246],[1865,10019,1955],{"className":10020},[2697],[1865,10022],{"className":10023,"style":2693},[2246],[1865,10025,10027,10030,10033,10036,10087,10090,10093,10133,10136,10139,10168,10171,10174,10177],{"className":10026},[2071],[1865,10028],{"className":10029,"style":8838},[2075],[1865,10031,8742],{"className":10032},[2080,2154],[1865,10034,4942],{"className":10035},[2119],[1865,10037,10039,10042],{"className":10038},[2080],[1865,10040,1798],{"className":10041},[2080,2154],[1865,10043,10045],{"className":10044},[2158],[1865,10046,10048,10079],{"className":10047},[2091,2092],[1865,10049,10051,10076],{"className":10050},[2096],[1865,10052,10054,10065],{"className":10053,"style":8863},[2100],[1865,10055,10056,10059],{"style":8866},[1865,10057],{"className":10058,"style":2175},[2108],[1865,10060,10062],{"className":10061},[2179,2180,2181,2182],[1865,10063,1931],{"className":10064},[2080,2182],[1865,10066,10067,10070],{"style":7181},[1865,10068],{"className":10069,"style":2175},[2108],[1865,10071,10073],{"className":10072},[2179,2180,2181,2182],[1865,10074,1900],{"className":10075},[2080,2182],[1865,10077,2190],{"className":10078},[2189],[1865,10080,10082],{"className":10081},[2096],[1865,10083,10085],{"className":10084,"style":8896},[2100],[1865,10086],{},[1865,10088,2784],{"className":10089},[2851],[1865,10091],{"className":10092,"style":2855},[2246],[1865,10094,10096,10099],{"className":10095},[2080],[1865,10097,1798],{"className":10098},[2080,2154],[1865,10100,10102],{"className":10101},[2158],[1865,10103,10105,10125],{"className":10104},[2091,2092],[1865,10106,10108,10122],{"className":10107},[2096],[1865,10109,10111],{"className":10110,"style":2168},[2100],[1865,10112,10113,10116],{"style":2171},[1865,10114],{"className":10115,"style":2175},[2108],[1865,10117,10119],{"className":10118},[2179,2180,2181,2182],[1865,10120,1984],{"className":10121},[2080,2182],[1865,10123,2190],{"className":10124},[2189],[1865,10126,10128],{"className":10127},[2096],[1865,10129,10131],{"className":10130,"style":2197},[2100],[1865,10132],{},[1865,10134,2784],{"className":10135},[2851],[1865,10137],{"className":10138,"style":2855},[2246],[1865,10140,10142,10145],{"className":10141},[2080],[1865,10143,3508],{"className":10144},[2080,2154],[1865,10146,10148],{"className":10147},[2158],[1865,10149,10151],{"className":10150},[2091],[1865,10152,10154],{"className":10153},[2096],[1865,10155,10157],{"className":10156,"style":8863},[2100],[1865,10158,10159,10162],{"style":7181},[1865,10160],{"className":10161,"style":2175},[2108],[1865,10163,10165],{"className":10164},[2179,2180,2181,2182],[1865,10166,1931],{"className":10167},[2080,2182],[1865,10169,4963],{"className":10170},[2242],[1865,10172],{"className":10173,"style":2247},[2246],[1865,10175,1935],{"className":10176},[2251],[1865,10178],{"className":10179,"style":2247},[2246],[1865,10181,10183,10186,10189,10192,10243,10246,10249,10289,10292,10295,10324],{"className":10182},[2071],[1865,10184],{"className":10185,"style":8838},[2075],[1865,10187,8742],{"className":10188},[2080,2154],[1865,10190,4942],{"className":10191},[2119],[1865,10193,10195,10198],{"className":10194},[2080],[1865,10196,1798],{"className":10197},[2080,2154],[1865,10199,10201],{"className":10200},[2158],[1865,10202,10204,10235],{"className":10203},[2091,2092],[1865,10205,10207,10232],{"className":10206},[2096],[1865,10208,10210,10221],{"className":10209,"style":8863},[2100],[1865,10211,10212,10215],{"style":8866},[1865,10213],{"className":10214,"style":2175},[2108],[1865,10216,10218],{"className":10217},[2179,2180,2181,2182],[1865,10219,1931],{"className":10220},[2080,2182],[1865,10222,10223,10226],{"style":7181},[1865,10224],{"className":10225,"style":2175},[2108],[1865,10227,10229],{"className":10228},[2179,2180,2181,2182],[1865,10230,1900],{"className":10231},[2080,2182],[1865,10233,2190],{"className":10234},[2189],[1865,10236,10238],{"className":10237},[2096],[1865,10239,10241],{"className":10240,"style":8896},[2100],[1865,10242],{},[1865,10244,2784],{"className":10245},[2851],[1865,10247],{"className":10248,"style":2855},[2246],[1865,10250,10252,10255],{"className":10251},[2080],[1865,10253,1798],{"className":10254},[2080,2154],[1865,10256,10258],{"className":10257},[2158],[1865,10259,10261,10281],{"className":10260},[2091,2092],[1865,10262,10264,10278],{"className":10263},[2096],[1865,10265,10267],{"className":10266,"style":2168},[2100],[1865,10268,10269,10272],{"style":2171},[1865,10270],{"className":10271,"style":2175},[2108],[1865,10273,10275],{"className":10274},[2179,2180,2181,2182],[1865,10276,1984],{"className":10277},[2080,2182],[1865,10279,2190],{"className":10280},[2189],[1865,10282,10284],{"className":10283},[2096],[1865,10285,10287],{"className":10286,"style":2197},[2100],[1865,10288],{},[1865,10290,2784],{"className":10291},[2851],[1865,10293],{"className":10294,"style":2855},[2246],[1865,10296,10298,10301],{"className":10297},[2080],[1865,10299,3508],{"className":10300},[2080,2154],[1865,10302,10304],{"className":10303},[2158],[1865,10305,10307],{"className":10306},[2091],[1865,10308,10310],{"className":10309},[2096],[1865,10311,10313],{"className":10312,"style":8863},[2100],[1865,10314,10315,10318],{"style":7181},[1865,10316],{"className":10317,"style":2175},[2108],[1865,10319,10321],{"className":10320},[2179,2180,2181,2182],[1865,10322,1900],{"className":10323},[2080,2182],[1865,10325,4963],{"className":10326},[2242],[1798,10328,7196,10329,10546],{},[1865,10330,10332,10378],{"className":10331},[1872],[1865,10333,10335],{"className":10334},[1876],[1878,10336,10337],{"xmlns":1880},[1883,10338,10339,10375],{},[1903,10340,10341,10347,10349,10351,10353,10361,10363,10369,10371,10373],{},[6885,10342,10343,10345],{},[1911,10344,3508],{},[1929,10346,1931],{},[1933,10348,1955],{},[1911,10350,4993],{},[1933,10352,4942],{"stretchy":3501},[8534,10354,10355,10357,10359],{},[1911,10356,1798],{},[1929,10358,1931],{},[1929,10360,1931],{},[1933,10362,2784],{"separator":1901},[1923,10364,10365,10367],{},[1911,10366,1798],{},[1929,10368,1984],{},[1933,10370,2784],{"separator":1901},[1911,10372,2046],{},[1933,10374,4963],{"stretchy":3501},[2060,10376,10377],{"encoding":2062},"u^1 = v(p_1^1, p_2, m)",[1865,10379,10381,10425],{"className":10380,"ariaHidden":1901},[2067],[1865,10382,10384,10387,10416,10419,10422],{"className":10383},[2071],[1865,10385],{"className":10386,"style":8573},[2075],[1865,10388,10390,10393],{"className":10389},[2080],[1865,10391,3508],{"className":10392},[2080,2154],[1865,10394,10396],{"className":10395},[2158],[1865,10397,10399],{"className":10398},[2091],[1865,10400,10402],{"className":10401},[2096],[1865,10403,10405],{"className":10404,"style":8573},[2100],[1865,10406,10407,10410],{"style":7519},[1865,10408],{"className":10409,"style":2175},[2108],[1865,10411,10413],{"className":10412},[2179,2180,2181,2182],[1865,10414,1931],{"className":10415},[2080,2182],[1865,10417],{"className":10418,"style":2693},[2246],[1865,10420,1955],{"className":10421},[2697],[1865,10423],{"className":10424,"style":2693},[2246],[1865,10426,10428,10431,10434,10437,10488,10491,10494,10534,10537,10540,10543],{"className":10427},[2071],[1865,10429],{"className":10430,"style":9243},[2075],[1865,10432,4993],{"className":10433,"style":5325},[2080,2154],[1865,10435,4942],{"className":10436},[2119],[1865,10438,10440,10443],{"className":10439},[2080],[1865,10441,1798],{"className":10442},[2080,2154],[1865,10444,10446],{"className":10445},[2158],[1865,10447,10449,10480],{"className":10448},[2091,2092],[1865,10450,10452,10477],{"className":10451},[2096],[1865,10453,10455,10466],{"className":10454,"style":8573},[2100],[1865,10456,10457,10460],{"style":8576},[1865,10458],{"className":10459,"style":2175},[2108],[1865,10461,10463],{"className":10462},[2179,2180,2181,2182],[1865,10464,1931],{"className":10465},[2080,2182],[1865,10467,10468,10471],{"style":7519},[1865,10469],{"className":10470,"style":2175},[2108],[1865,10472,10474],{"className":10473},[2179,2180,2181,2182],[1865,10475,1931],{"className":10476},[2080,2182],[1865,10478,2190],{"className":10479},[2189],[1865,10481,10483],{"className":10482},[2096],[1865,10484,10486],{"className":10485,"style":8606},[2100],[1865,10487],{},[1865,10489,2784],{"className":10490},[2851],[1865,10492],{"className":10493,"style":2855},[2246],[1865,10495,10497,10500],{"className":10496},[2080],[1865,10498,1798],{"className":10499},[2080,2154],[1865,10501,10503],{"className":10502},[2158],[1865,10504,10506,10526],{"className":10505},[2091,2092],[1865,10507,10509,10523],{"className":10508},[2096],[1865,10510,10512],{"className":10511,"style":2168},[2100],[1865,10513,10514,10517],{"style":2171},[1865,10515],{"className":10516,"style":2175},[2108],[1865,10518,10520],{"className":10519},[2179,2180,2181,2182],[1865,10521,1984],{"className":10522},[2080,2182],[1865,10524,2190],{"className":10525},[2189],[1865,10527,10529],{"className":10528},[2096],[1865,10530,10532],{"className":10531,"style":2197},[2100],[1865,10533],{},[1865,10535,2784],{"className":10536},[2851],[1865,10538],{"className":10539,"style":2855},[2246],[1865,10541,2046],{"className":10542},[2080,2154],[1865,10544,4963],{"className":10545},[2242],"是价格变化后的效用水平。",[1798,10548,10549],{},"如果把价格上涨造成的福利损失记为正数，常用写法是：",[1865,10551,10553],{"className":10552},[1868],[1865,10554,10556,10608],{"className":10555},[1872],[1865,10557,10559],{"className":10558},[1876],[1878,10560,10561],{"xmlns":1880,"display":1881},[1883,10562,10563,10605],{},[1903,10564,10565,10567,10569,10571,10573,10575,10577,10579,10587,10589,10595,10597,10603],{},[1911,10566,9930],{},[1911,10568,8737],{},[1933,10570,1955],{},[1911,10572,2046],{},[1933,10574,1935],{},[1911,10576,8742],{},[1933,10578,4942],{"stretchy":3501},[8534,10580,10581,10583,10585],{},[1911,10582,1798],{},[1929,10584,1931],{},[1929,10586,1900],{},[1933,10588,2784],{"separator":1901},[1923,10590,10591,10593],{},[1911,10592,1798],{},[1929,10594,1984],{},[1933,10596,2784],{"separator":1901},[6885,10598,10599,10601],{},[1911,10600,3508],{},[1929,10602,1931],{},[1933,10604,4963],{"stretchy":3501},[2060,10606,10607],{"encoding":2062},"EV = m - e(p_1^0, p_2, u^1)",[1865,10609,10611,10632,10651],{"className":10610,"ariaHidden":1901},[2067],[1865,10612,10614,10617,10620,10623,10626,10629],{"className":10613},[2071],[1865,10615],{"className":10616,"style":8815},[2075],[1865,10618,9930],{"className":10619,"style":7058},[2080,2154],[1865,10621,8737],{"className":10622,"style":2247},[2080,2154],[1865,10624],{"className":10625,"style":2693},[2246],[1865,10627,1955],{"className":10628},[2697],[1865,10630],{"className":10631,"style":2693},[2246],[1865,10633,10635,10639,10642,10645,10648],{"className":10634},[2071],[1865,10636],{"className":10637,"style":10638},[2075],"height:0.6667em;vertical-align:-0.0833em;",[1865,10640,2046],{"className":10641},[2080,2154],[1865,10643],{"className":10644,"style":2247},[2246],[1865,10646,1935],{"className":10647},[2251],[1865,10649],{"className":10650,"style":2247},[2246],[1865,10652,10654,10657,10660,10663,10714,10717,10720,10760,10763,10766,10795],{"className":10653},[2071],[1865,10655],{"className":10656,"style":8838},[2075],[1865,10658,8742],{"className":10659},[2080,2154],[1865,10661,4942],{"className":10662},[2119],[1865,10664,10666,10669],{"className":10665},[2080],[1865,10667,1798],{"className":10668},[2080,2154],[1865,10670,10672],{"className":10671},[2158],[1865,10673,10675,10706],{"className":10674},[2091,2092],[1865,10676,10678,10703],{"className":10677},[2096],[1865,10679,10681,10692],{"className":10680,"style":8863},[2100],[1865,10682,10683,10686],{"style":8866},[1865,10684],{"className":10685,"style":2175},[2108],[1865,10687,10689],{"className":10688},[2179,2180,2181,2182],[1865,10690,1931],{"className":10691},[2080,2182],[1865,10693,10694,10697],{"style":7181},[1865,10695],{"className":10696,"style":2175},[2108],[1865,10698,10700],{"className":10699},[2179,2180,2181,2182],[1865,10701,1900],{"className":10702},[2080,2182],[1865,10704,2190],{"className":10705},[2189],[1865,10707,10709],{"className":10708},[2096],[1865,10710,10712],{"className":10711,"style":8896},[2100],[1865,10713],{},[1865,10715,2784],{"className":10716},[2851],[1865,10718],{"className":10719,"style":2855},[2246],[1865,10721,10723,10726],{"className":10722},[2080],[1865,10724,1798],{"className":10725},[2080,2154],[1865,10727,10729],{"className":10728},[2158],[1865,10730,10732,10752],{"className":10731},[2091,2092],[1865,10733,10735,10749],{"className":10734},[2096],[1865,10736,10738],{"className":10737,"style":2168},[2100],[1865,10739,10740,10743],{"style":2171},[1865,10741],{"className":10742,"style":2175},[2108],[1865,10744,10746],{"className":10745},[2179,2180,2181,2182],[1865,10747,1984],{"className":10748},[2080,2182],[1865,10750,2190],{"className":10751},[2189],[1865,10753,10755],{"className":10754},[2096],[1865,10756,10758],{"className":10757,"style":2197},[2100],[1865,10759],{},[1865,10761,2784],{"className":10762},[2851],[1865,10764],{"className":10765,"style":2855},[2246],[1865,10767,10769,10772],{"className":10768},[2080],[1865,10770,3508],{"className":10771},[2080,2154],[1865,10773,10775],{"className":10774},[2158],[1865,10776,10778],{"className":10777},[2091],[1865,10779,10781],{"className":10780},[2096],[1865,10782,10784],{"className":10783,"style":8863},[2100],[1865,10785,10786,10789],{"style":7181},[1865,10787],{"className":10788,"style":2175},[2108],[1865,10790,10792],{"className":10791},[2179,2180,2181,2182],[1865,10793,1931],{"className":10794},[2080,2182],[1865,10796,4963],{"className":10797},[2242],[1798,10799,10800],{},"前一个式子是“在旧价格下达到新效用所需的有符号收入变化”，后一个式子是“愿意支付多少来避免这次价格上涨”。做题时先说明采用哪一种符号约定。",[1854,10802,10804],{"id":10803},"_34-cv与ev的比较","3.4 CV与EV的比较",[10806,10807,10808,10823],"table",{},[10809,10810,10811],"thead",{},[10812,10813,10814,10817,10820],"tr",{},[10815,10816],"th",{},[10815,10818,10819],{},"补偿变差 (CV)",[10815,10821,10822],{},"等价变差 (EV)",[10824,10825,10826,10958,11090],"tbody",{},[10812,10827,10828,10834,10896],{},[10829,10830,10831],"td",{},[3048,10832,10833],{},"参考效用水平",[10829,10835,10836,10837],{},"原始效用 ",[1865,10838,10840,10858],{"className":10839},[1872],[1865,10841,10843],{"className":10842},[1876],[1878,10844,10845],{"xmlns":1880},[1883,10846,10847,10855],{},[1903,10848,10849],{},[6885,10850,10851,10853],{},[1911,10852,3508],{},[1929,10854,1900],{},[2060,10856,10857],{"encoding":2062},"u^0",[1865,10859,10861],{"className":10860,"ariaHidden":1901},[2067],[1865,10862,10864,10867],{"className":10863},[2071],[1865,10865],{"className":10866,"style":8573},[2075],[1865,10868,10870,10873],{"className":10869},[2080],[1865,10871,3508],{"className":10872},[2080,2154],[1865,10874,10876],{"className":10875},[2158],[1865,10877,10879],{"className":10878},[2091],[1865,10880,10882],{"className":10881},[2096],[1865,10883,10885],{"className":10884,"style":8573},[2100],[1865,10886,10887,10890],{"style":7519},[1865,10888],{"className":10889,"style":2175},[2108],[1865,10891,10893],{"className":10892},[2179,2180,2181,2182],[1865,10894,1900],{"className":10895},[2080,2182],[10829,10897,10898,10899],{},"新效用 ",[1865,10900,10902,10920],{"className":10901},[1872],[1865,10903,10905],{"className":10904},[1876],[1878,10906,10907],{"xmlns":1880},[1883,10908,10909,10917],{},[1903,10910,10911],{},[6885,10912,10913,10915],{},[1911,10914,3508],{},[1929,10916,1931],{},[2060,10918,10919],{"encoding":2062},"u^1",[1865,10921,10923],{"className":10922,"ariaHidden":1901},[2067],[1865,10924,10926,10929],{"className":10925},[2071],[1865,10927],{"className":10928,"style":8573},[2075],[1865,10930,10932,10935],{"className":10931},[2080],[1865,10933,3508],{"className":10934},[2080,2154],[1865,10936,10938],{"className":10937},[2158],[1865,10939,10941],{"className":10940},[2091],[1865,10942,10944],{"className":10943},[2096],[1865,10945,10947],{"className":10946,"style":8573},[2100],[1865,10948,10949,10952],{"style":7519},[1865,10950],{"className":10951,"style":2175},[2108],[1865,10953,10955],{"className":10954},[2179,2180,2181,2182],[1865,10956,1931],{"className":10957},[2080,2182],[10812,10959,10960,10965,11028],{},[10829,10961,10962],{},[3048,10963,10964],{},"评估价格",[10829,10966,10967,10968],{},"新价格 ",[1865,10969,10971,10989],{"className":10970},[1872],[1865,10972,10974],{"className":10973},[1876],[1878,10975,10976],{"xmlns":1880},[1883,10977,10978,10986],{},[1903,10979,10980],{},[6885,10981,10982,10984],{},[1911,10983,1798],{},[1929,10985,1931],{},[2060,10987,10988],{"encoding":2062},"p^1",[1865,10990,10992],{"className":10991,"ariaHidden":1901},[2067],[1865,10993,10995,10999],{"className":10994},[2071],[1865,10996],{"className":10997,"style":10998},[2075],"height:1.0085em;vertical-align:-0.1944em;",[1865,11000,11002,11005],{"className":11001},[2080],[1865,11003,1798],{"className":11004},[2080,2154],[1865,11006,11008],{"className":11007},[2158],[1865,11009,11011],{"className":11010},[2091],[1865,11012,11014],{"className":11013},[2096],[1865,11015,11017],{"className":11016,"style":8573},[2100],[1865,11018,11019,11022],{"style":7519},[1865,11020],{"className":11021,"style":2175},[2108],[1865,11023,11025],{"className":11024},[2179,2180,2181,2182],[1865,11026,1931],{"className":11027},[2080,2182],[10829,11029,11030,11031],{},"原价格 ",[1865,11032,11034,11052],{"className":11033},[1872],[1865,11035,11037],{"className":11036},[1876],[1878,11038,11039],{"xmlns":1880},[1883,11040,11041,11049],{},[1903,11042,11043],{},[6885,11044,11045,11047],{},[1911,11046,1798],{},[1929,11048,1900],{},[2060,11050,11051],{"encoding":2062},"p^0",[1865,11053,11055],{"className":11054,"ariaHidden":1901},[2067],[1865,11056,11058,11061],{"className":11057},[2071],[1865,11059],{"className":11060,"style":10998},[2075],[1865,11062,11064,11067],{"className":11063},[2080],[1865,11065,1798],{"className":11066},[2080,2154],[1865,11068,11070],{"className":11069},[2158],[1865,11071,11073],{"className":11072},[2091],[1865,11074,11076],{"className":11075},[2096],[1865,11077,11079],{"className":11078,"style":8573},[2100],[1865,11080,11081,11084],{"style":7519},[1865,11082],{"className":11083,"style":2175},[2108],[1865,11085,11087],{"className":11086},[2179,2180,2181,2182],[1865,11088,1900],{"className":11089},[2080,2182],[10812,11091,11092,11097,11100],{},[10829,11093,11094],{},[3048,11095,11096],{},"问题",[10829,11098,11099],{},"需要多少钱补偿？",[10829,11101,11102],{},"等价于放弃多少钱？",[1798,11104,11105,4915],{},[3048,11106,11107],{},"关系",[1805,11109,11110,11197,11200],{},[1808,11111,11112,11113],{},"对于正常品且价格上涨：",[1865,11114,11116,11142],{"className":11115},[1872],[1865,11117,11119],{"className":11118},[1876],[1878,11120,11121],{"xmlns":1880},[1883,11122,11123,11139],{},[1903,11124,11125,11127,11129,11131,11133,11135,11137],{},[1929,11126,1900],{},[1933,11128,7902],{},[1911,11130,8734],{},[1911,11132,8737],{},[1933,11134,7902],{},[1911,11136,9930],{},[1911,11138,8737],{},[2060,11140,11141],{"encoding":2062},"0 \u003C CV \u003C EV",[1865,11143,11145,11164,11185],{"className":11144,"ariaHidden":1901},[2067],[1865,11146,11148,11152,11155,11158,11161],{"className":11147},[2071],[1865,11149],{"className":11150,"style":11151},[2075],"height:0.6835em;vertical-align:-0.0391em;",[1865,11153,1900],{"className":11154},[2080],[1865,11156],{"className":11157,"style":2693},[2246],[1865,11159,7902],{"className":11160},[2697],[1865,11162],{"className":11163,"style":2693},[2246],[1865,11165,11167,11170,11173,11176,11179,11182],{"className":11166},[2071],[1865,11168],{"className":11169,"style":9812},[2075],[1865,11171,8734],{"className":11172,"style":8819},[2080,2154],[1865,11174,8737],{"className":11175,"style":2247},[2080,2154],[1865,11177],{"className":11178,"style":2693},[2246],[1865,11180,7902],{"className":11181},[2697],[1865,11183],{"className":11184,"style":2693},[2246],[1865,11186,11188,11191,11194],{"className":11187},[2071],[1865,11189],{"className":11190,"style":8815},[2075],[1865,11192,9930],{"className":11193,"style":7058},[2080,2154],[1865,11195,8737],{"className":11196,"style":2247},[2080,2154],[1808,11198,11199],{},"对于劣等品：大小关系可能颠倒",[1808,11201,11202,11203,11264],{},"对于拟线性效用函数：",[1865,11204,11206,11228],{"className":11205},[1872],[1865,11207,11209],{"className":11208},[1876],[1878,11210,11211],{"xmlns":1880},[1883,11212,11213,11225],{},[1903,11214,11215,11217,11219,11221,11223],{},[1911,11216,8734],{},[1911,11218,8737],{},[1933,11220,1955],{},[1911,11222,9930],{},[1911,11224,8737],{},[2060,11226,11227],{"encoding":2062},"CV = EV",[1865,11229,11231,11252],{"className":11230,"ariaHidden":1901},[2067],[1865,11232,11234,11237,11240,11243,11246,11249],{"className":11233},[2071],[1865,11235],{"className":11236,"style":8815},[2075],[1865,11238,8734],{"className":11239,"style":8819},[2080,2154],[1865,11241,8737],{"className":11242,"style":2247},[2080,2154],[1865,11244],{"className":11245,"style":2693},[2246],[1865,11247,1955],{"className":11248},[2697],[1865,11250],{"className":11251,"style":2693},[2246],[1865,11253,11255,11258,11261],{"className":11254},[2071],[1865,11256],{"className":11257,"style":8815},[2075],[1865,11259,9930],{"className":11260,"style":7058},[2080,2154],[1865,11262,8737],{"className":11263,"style":2247},[2080,2154],"（无收入效应）",[1854,11266,11268],{"id":11267},"_35-几何表示","3.5 几何表示",[1798,11270,11271],{},"考虑商品1价格上涨的情况：",[11273,11274,11279],"pre",{"className":11275,"code":11277,"language":11278},[11276],"language-text","效用\n ↑\n │     E₁ (新均衡, u¹)\n u¹├──────●\n │       \u002F│\n │      \u002F │  ← EV: 在旧价格下达到u¹需要的额外收入\n │     \u002F  │\n u⁰├────●─┤ E₀ (原均衡, u⁰)\n │   \u002F    │\n │  \u002F     │  ← CV: 在新价格下维持u⁰需要的补偿\n │ ●──────┤ E'\n │        │\n └────────┴──→ 收入\n","text",[11280,11281,11277],"code",{"__ignoreMap":10},[3421,11283],{},[1794,11285,11287],{"id":11286},"_4-消费者剩余-consumer-surplus-cs","4. 消费者剩余 (Consumer Surplus, CS)",[1854,11289,11291],{"id":11290},"_41-定义","4.1 定义",[1798,11293,11294],{},"消费者剩余是消费者愿意为某种商品支付的总金额与实际支付金额之间的差额。",[1798,11296,11297,11298,11366],{},"在需求曲线",[1865,11299,11301,11326],{"className":11300},[1872],[1865,11302,11304],{"className":11303},[1876],[1878,11305,11306],{"xmlns":1880},[1883,11307,11308,11323],{},[1903,11309,11310,11312,11314,11317,11319,11321],{},[1911,11311,1798],{},[1933,11313,1955],{},[1911,11315,11316],{},"D",[1933,11318,4942],{"stretchy":3501},[1911,11320,1927],{},[1933,11322,4963],{"stretchy":3501},[2060,11324,11325],{"encoding":2062},"p = D(x)",[1865,11327,11329,11347],{"className":11328,"ariaHidden":1901},[2067],[1865,11330,11332,11335,11338,11341,11344],{"className":11331},[2071],[1865,11333],{"className":11334,"style":2948},[2075],[1865,11336,1798],{"className":11337},[2080,2154],[1865,11339],{"className":11340,"style":2693},[2246],[1865,11342,1955],{"className":11343},[2697],[1865,11345],{"className":11346,"style":2693},[2246],[1865,11348,11350,11353,11357,11360,11363],{"className":11349},[2071],[1865,11351],{"className":11352,"style":5030},[2075],[1865,11354,11316],{"className":11355,"style":11356},[2080,2154],"margin-right:0.0278em;",[1865,11358,4942],{"className":11359},[2119],[1865,11361,1927],{"className":11362},[2080,2154],[1865,11364,4963],{"className":11365},[2242],"下：",[1865,11368,11370],{"className":11369},[1868],[1865,11371,11373,11431],{"className":11372},[1872],[1865,11374,11376],{"className":11375},[1876],[1878,11377,11378],{"xmlns":1880,"display":1881},[1883,11379,11380,11428],{},[1903,11381,11382,11384,11386,11388,11402,11404,11406,11408,11410,11412,11414,11416,11422],{},[1911,11383,8734],{},[1911,11385,6896],{},[1933,11387,1955],{},[8534,11389,11390,11393,11395],{},[1933,11391,11392],{},"∫",[1929,11394,1900],{},[6885,11396,11397,11399],{},[1911,11398,1927],{},[1933,11400,11401],{},"∗",[1911,11403,11316],{},[1933,11405,4942],{"stretchy":3501},[1911,11407,1927],{},[1933,11409,4963],{"stretchy":3501},[1911,11411,3144],{},[1911,11413,1927],{},[1933,11415,1935],{},[6885,11417,11418,11420],{},[1911,11419,1798],{},[1933,11421,11401],{},[6885,11423,11424,11426],{},[1911,11425,1927],{},[1933,11427,11401],{},[2060,11429,11430],{"encoding":2062},"CS = \\int_0^{x^*} D(x)dx - p^* x^*",[1865,11432,11434,11455,11582],{"className":11433,"ariaHidden":1901},[2067],[1865,11435,11437,11440,11443,11446,11449,11452],{"className":11436},[2071],[1865,11438],{"className":11439,"style":8815},[2075],[1865,11441,8734],{"className":11442,"style":8819},[2080,2154],[1865,11444,6896],{"className":11445,"style":7058},[2080,2154],[1865,11447],{"className":11448,"style":2693},[2246],[1865,11450,1955],{"className":11451},[2697],[1865,11453],{"className":11454,"style":2693},[2246],[1865,11456,11458,11462,11552,11555,11558,11561,11564,11567,11570,11573,11576,11579],{"className":11457},[2071],[1865,11459],{"className":11460,"style":11461},[2075],"height:2.5592em;vertical-align:-0.9119em;",[1865,11463,11466,11472],{"className":11464},[11465],"mop",[1865,11467,11392],{"className":11468,"style":11471},[11465,11469,11470],"op-symbol","large-op","margin-right:0.4445em;position:relative;top:-0.0011em;",[1865,11473,11475],{"className":11474},[2158],[1865,11476,11478,11543],{"className":11477},[2091,2092],[1865,11479,11481,11540],{"className":11480},[2096],[1865,11482,11485,11497],{"className":11483,"style":11484},[2100],"height:1.6472em;",[1865,11486,11488,11491],{"style":11487},"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;",[1865,11489],{"className":11490,"style":2175},[2108],[1865,11492,11494],{"className":11493},[2179,2180,2181,2182],[1865,11495,1900],{"className":11496},[2080,2182],[1865,11498,11500,11503],{"style":11499},"top:-3.8129em;margin-right:0.05em;",[1865,11501],{"className":11502,"style":2175},[2108],[1865,11504,11506],{"className":11505},[2179,2180,2181,2182],[1865,11507,11509],{"className":11508},[2080,2182],[1865,11510,11512,11515],{"className":11511},[2080,2182],[1865,11513,1927],{"className":11514},[2080,2154,2182],[1865,11516,11518],{"className":11517},[2158],[1865,11519,11521],{"className":11520},[2091],[1865,11522,11524],{"className":11523},[2096],[1865,11525,11528],{"className":11526,"style":11527},[2100],"height:0.7633em;",[1865,11529,11531,11534],{"style":11530},"top:-2.931em;margin-right:0.0714em;",[1865,11532],{"className":11533,"style":4268},[2108],[1865,11535,11537],{"className":11536},[2179,4272,4273,2182],[1865,11538,11401],{"className":11539},[2251,2182],[1865,11541,2190],{"className":11542},[2189],[1865,11544,11546],{"className":11545},[2096],[1865,11547,11550],{"className":11548,"style":11549},[2100],"height:0.9119em;",[1865,11551],{},[1865,11553],{"className":11554,"style":2855},[2246],[1865,11556,11316],{"className":11557,"style":11356},[2080,2154],[1865,11559,4942],{"className":11560},[2119],[1865,11562,1927],{"className":11563},[2080,2154],[1865,11565,4963],{"className":11566},[2242],[1865,11568,3144],{"className":11569},[2080,2154],[1865,11571,1927],{"className":11572},[2080,2154],[1865,11574],{"className":11575,"style":2247},[2246],[1865,11577,1935],{"className":11578},[2251],[1865,11580],{"className":11581,"style":2247},[2246],[1865,11583,11585,11589,11619],{"className":11584},[2071],[1865,11586],{"className":11587,"style":11588},[2075],"height:0.9331em;vertical-align:-0.1944em;",[1865,11590,11592,11595],{"className":11591},[2080],[1865,11593,1798],{"className":11594},[2080,2154],[1865,11596,11598],{"className":11597},[2158],[1865,11599,11601],{"className":11600},[2091],[1865,11602,11604],{"className":11603},[2096],[1865,11605,11608],{"className":11606,"style":11607},[2100],"height:0.7387em;",[1865,11609,11610,11613],{"style":7181},[1865,11611],{"className":11612,"style":2175},[2108],[1865,11614,11616],{"className":11615},[2179,2180,2181,2182],[1865,11617,11401],{"className":11618},[2251,2182],[1865,11620,11622,11625],{"className":11621},[2080],[1865,11623,1927],{"className":11624},[2080,2154],[1865,11626,11628],{"className":11627},[2158],[1865,11629,11631],{"className":11630},[2091],[1865,11632,11634],{"className":11633},[2096],[1865,11635,11637],{"className":11636,"style":11607},[2100],[1865,11638,11639,11642],{"style":7181},[1865,11640],{"className":11641,"style":2175},[2108],[1865,11643,11645],{"className":11644},[2179,2180,2181,2182],[1865,11646,11401],{"className":11647},[2251,2182],[1798,11649,11650],{},"几何上，这是需求曲线下方、价格线上方的面积。",[1854,11652,11654],{"id":11653},"_42-消费者剩余的变化","4.2 消费者剩余的变化",[1798,11656,11657,11658,11716,11717,11775],{},"当价格从",[1865,11659,11661,11678],{"className":11660},[1872],[1865,11662,11664],{"className":11663},[1876],[1878,11665,11666],{"xmlns":1880},[1883,11667,11668,11676],{},[1903,11669,11670],{},[6885,11671,11672,11674],{},[1911,11673,1798],{},[1929,11675,1900],{},[2060,11677,11051],{"encoding":2062},[1865,11679,11681],{"className":11680,"ariaHidden":1901},[2067],[1865,11682,11684,11687],{"className":11683},[2071],[1865,11685],{"className":11686,"style":10998},[2075],[1865,11688,11690,11693],{"className":11689},[2080],[1865,11691,1798],{"className":11692},[2080,2154],[1865,11694,11696],{"className":11695},[2158],[1865,11697,11699],{"className":11698},[2091],[1865,11700,11702],{"className":11701},[2096],[1865,11703,11705],{"className":11704,"style":8573},[2100],[1865,11706,11707,11710],{"style":7519},[1865,11708],{"className":11709,"style":2175},[2108],[1865,11711,11713],{"className":11712},[2179,2180,2181,2182],[1865,11714,1900],{"className":11715},[2080,2182],"变为",[1865,11718,11720,11737],{"className":11719},[1872],[1865,11721,11723],{"className":11722},[1876],[1878,11724,11725],{"xmlns":1880},[1883,11726,11727,11735],{},[1903,11728,11729],{},[6885,11730,11731,11733],{},[1911,11732,1798],{},[1929,11734,1931],{},[2060,11736,10988],{"encoding":2062},[1865,11738,11740],{"className":11739,"ariaHidden":1901},[2067],[1865,11741,11743,11746],{"className":11742},[2071],[1865,11744],{"className":11745,"style":10998},[2075],[1865,11747,11749,11752],{"className":11748},[2080],[1865,11750,1798],{"className":11751},[2080,2154],[1865,11753,11755],{"className":11754},[2158],[1865,11756,11758],{"className":11757},[2091],[1865,11759,11761],{"className":11760},[2096],[1865,11762,11764],{"className":11763,"style":8573},[2100],[1865,11765,11766,11769],{"style":7519},[1865,11767],{"className":11768,"style":2175},[2108],[1865,11770,11772],{"className":11771},[2179,2180,2181,2182],[1865,11773,1931],{"className":11774},[2080,2182],"时：",[1865,11777,11779],{"className":11778},[1868],[1865,11780,11782,11837],{"className":11781},[1872],[1865,11783,11785],{"className":11784},[1876],[1878,11786,11787],{"xmlns":1880,"display":1881},[1883,11788,11789,11834],{},[1903,11790,11791,11794,11796,11798,11800,11816,11818,11820,11822,11824,11826,11830,11832],{},[1911,11792,11793],{"mathvariant":1913},"Δ",[1911,11795,8734],{},[1911,11797,6896],{},[1933,11799,1955],{},[8534,11801,11802,11804,11810],{},[1933,11803,11392],{},[6885,11805,11806,11808],{},[1911,11807,1798],{},[1929,11809,1900],{},[6885,11811,11812,11814],{},[1911,11813,1798],{},[1929,11815,1931],{},[1933,11817,1935],{},[1911,11819,1927],{},[1933,11821,4942],{"stretchy":3501},[1911,11823,1798],{},[1933,11825,4963],{"stretchy":3501},[11827,11828,11829],"mtext",{}," ",[1911,11831,3144],{},[1911,11833,1798],{},[2060,11835,11836],{"encoding":2062},"\\Delta CS = \\int_{p^0}^{p^1} -x(p)\\,dp",[1865,11838,11840,11864],{"className":11839,"ariaHidden":1901},[2067],[1865,11841,11843,11846,11849,11852,11855,11858,11861],{"className":11842},[2071],[1865,11844],{"className":11845,"style":8815},[2075],[1865,11847,11793],{"className":11848},[2080],[1865,11850,8734],{"className":11851,"style":8819},[2080,2154],[1865,11853,6896],{"className":11854,"style":7058},[2080,2154],[1865,11856],{"className":11857,"style":2693},[2246],[1865,11859,1955],{"className":11860},[2697],[1865,11862],{"className":11863,"style":2693},[2246],[1865,11865,11867,11871,11985,11988,11991,11994,11997,12000,12003,12006,12009],{"className":11866},[2071],[1865,11868],{"className":11869,"style":11870},[2075],"height:2.7849em;vertical-align:-1.0481em;",[1865,11872,11874,11877],{"className":11873},[11465],[1865,11875,11392],{"className":11876,"style":11471},[11465,11469,11470],[1865,11878,11880],{"className":11879},[2158],[1865,11881,11883,11976],{"className":11882},[2091,2092],[1865,11884,11886,11973],{"className":11885},[2096],[1865,11887,11890,11932],{"className":11888,"style":11889},[2100],"height:1.7368em;",[1865,11891,11892,11895],{"style":11487},[1865,11893],{"className":11894,"style":2175},[2108],[1865,11896,11898],{"className":11897},[2179,2180,2181,2182],[1865,11899,11901],{"className":11900},[2080,2182],[1865,11902,11904,11907],{"className":11903},[2080,2182],[1865,11905,1798],{"className":11906},[2080,2154,2182],[1865,11908,11910],{"className":11909},[2158],[1865,11911,11913],{"className":11912},[2091],[1865,11914,11916],{"className":11915},[2096],[1865,11917,11920],{"className":11918,"style":11919},[2100],"height:0.7463em;",[1865,11921,11923,11926],{"style":11922},"top:-2.786em;margin-right:0.0714em;",[1865,11924],{"className":11925,"style":4268},[2108],[1865,11927,11929],{"className":11928},[2179,4272,4273,2182],[1865,11930,1900],{"className":11931},[2080,2182],[1865,11933,11934,11937],{"style":11499},[1865,11935],{"className":11936,"style":2175},[2108],[1865,11938,11940],{"className":11939},[2179,2180,2181,2182],[1865,11941,11943],{"className":11942},[2080,2182],[1865,11944,11946,11949],{"className":11945},[2080,2182],[1865,11947,1798],{"className":11948},[2080,2154,2182],[1865,11950,11952],{"className":11951},[2158],[1865,11953,11955],{"className":11954},[2091],[1865,11956,11958],{"className":11957},[2096],[1865,11959,11962],{"className":11960,"style":11961},[2100],"height:0.8913em;",[1865,11963,11964,11967],{"style":11530},[1865,11965],{"className":11966,"style":4268},[2108],[1865,11968,11970],{"className":11969},[2179,4272,4273,2182],[1865,11971,1931],{"className":11972},[2080,2182],[1865,11974,2190],{"className":11975},[2189],[1865,11977,11979],{"className":11978},[2096],[1865,11980,11983],{"className":11981,"style":11982},[2100],"height:1.0481em;",[1865,11984],{},[1865,11986],{"className":11987,"style":2855},[2246],[1865,11989,1935],{"className":11990},[2080],[1865,11992,1927],{"className":11993},[2080,2154],[1865,11995,4942],{"className":11996},[2119],[1865,11998,1798],{"className":11999},[2080,2154],[1865,12001,4963],{"className":12002},[2242],[1865,12004],{"className":12005,"style":2855},[2246],[1865,12007,3144],{"className":12008},[2080,2154],[1865,12010,1798],{"className":12011},[2080,2154],[1798,12013,12014],{},"若价格上涨，并把消费者剩余损失记为正数，则：",[1865,12016,12018],{"className":12017},[1868],[1865,12019,12021,12068],{"className":12020},[1872],[1865,12022,12024],{"className":12023},[1876],[1878,12025,12026],{"xmlns":1880,"display":1881},[1883,12027,12028,12065],{},[1903,12029,12030,12033,12035,12051,12053,12055,12057,12059,12061,12063],{},[11827,12031,12032],{},"CS 损失",[1933,12034,1955],{},[8534,12036,12037,12039,12045],{},[1933,12038,11392],{},[6885,12040,12041,12043],{},[1911,12042,1798],{},[1929,12044,1900],{},[6885,12046,12047,12049],{},[1911,12048,1798],{},[1929,12050,1931],{},[1911,12052,1927],{},[1933,12054,4942],{"stretchy":3501},[1911,12056,1798],{},[1933,12058,4963],{"stretchy":3501},[11827,12060,11829],{},[1911,12062,3144],{},[1911,12064,1798],{},[2060,12066,12067],{"encoding":2062},"\\text{CS 损失} = \\int_{p^0}^{p^1} x(p)\\,dp",[1865,12069,12071,12098],{"className":12070,"ariaHidden":1901},[2067],[1865,12072,12074,12077,12089,12092,12095],{"className":12073},[2071],[1865,12075],{"className":12076,"style":8815},[2075],[1865,12078,12080,12084],{"className":12079},[2080,11278],[1865,12081,12083],{"className":12082},[2080],"CS ",[1865,12085,12088],{"className":12086},[2080,12087],"cjk_fallback","损失",[1865,12090],{"className":12091,"style":2693},[2246],[1865,12093,1955],{"className":12094},[2697],[1865,12096],{"className":12097,"style":2693},[2246],[1865,12099,12101,12104,12213,12216,12219,12222,12225,12228,12231,12234],{"className":12100},[2071],[1865,12102],{"className":12103,"style":11870},[2075],[1865,12105,12107,12110],{"className":12106},[11465],[1865,12108,11392],{"className":12109,"style":11471},[11465,11469,11470],[1865,12111,12113],{"className":12112},[2158],[1865,12114,12116,12205],{"className":12115},[2091,2092],[1865,12117,12119,12202],{"className":12118},[2096],[1865,12120,12122,12162],{"className":12121,"style":11889},[2100],[1865,12123,12124,12127],{"style":11487},[1865,12125],{"className":12126,"style":2175},[2108],[1865,12128,12130],{"className":12129},[2179,2180,2181,2182],[1865,12131,12133],{"className":12132},[2080,2182],[1865,12134,12136,12139],{"className":12135},[2080,2182],[1865,12137,1798],{"className":12138},[2080,2154,2182],[1865,12140,12142],{"className":12141},[2158],[1865,12143,12145],{"className":12144},[2091],[1865,12146,12148],{"className":12147},[2096],[1865,12149,12151],{"className":12150,"style":11919},[2100],[1865,12152,12153,12156],{"style":11922},[1865,12154],{"className":12155,"style":4268},[2108],[1865,12157,12159],{"className":12158},[2179,4272,4273,2182],[1865,12160,1900],{"className":12161},[2080,2182],[1865,12163,12164,12167],{"style":11499},[1865,12165],{"className":12166,"style":2175},[2108],[1865,12168,12170],{"className":12169},[2179,2180,2181,2182],[1865,12171,12173],{"className":12172},[2080,2182],[1865,12174,12176,12179],{"className":12175},[2080,2182],[1865,12177,1798],{"className":12178},[2080,2154,2182],[1865,12180,12182],{"className":12181},[2158],[1865,12183,12185],{"className":12184},[2091],[1865,12186,12188],{"className":12187},[2096],[1865,12189,12191],{"className":12190,"style":11961},[2100],[1865,12192,12193,12196],{"style":11530},[1865,12194],{"className":12195,"style":4268},[2108],[1865,12197,12199],{"className":12198},[2179,4272,4273,2182],[1865,12200,1931],{"className":12201},[2080,2182],[1865,12203,2190],{"className":12204},[2189],[1865,12206,12208],{"className":12207},[2096],[1865,12209,12211],{"className":12210,"style":11982},[2100],[1865,12212],{},[1865,12214],{"className":12215,"style":2855},[2246],[1865,12217,1927],{"className":12218},[2080,2154],[1865,12220,4942],{"className":12221},[2119],[1865,12223,1798],{"className":12224},[2080,2154],[1865,12226,4963],{"className":12227},[2242],[1865,12229],{"className":12230,"style":2855},[2246],[1865,12232,3144],{"className":12233},[2080,2154],[1865,12235,1798],{"className":12236},[2080,2154],[1798,12238,12239,4915],{},[3048,12240,12241],{},"近似关系",[1865,12243,12245],{"className":12244},[1868],[1865,12246,12248,12279],{"className":12247},[1872],[1865,12249,12251],{"className":12250},[1876],[1878,12252,12253],{"xmlns":1880,"display":1881},[1883,12254,12255,12276],{},[1903,12256,12257,12259,12261,12264,12266,12268,12270,12272,12274],{},[1911,12258,8734],{},[1911,12260,8737],{},[1933,12262,12263],{},"≈",[1911,12265,11793],{"mathvariant":1913},[1911,12267,8734],{},[1911,12269,6896],{},[1933,12271,12263],{},[1911,12273,9930],{},[1911,12275,8737],{},[2060,12277,12278],{"encoding":2062},"CV \\approx \\Delta CS \\approx EV",[1865,12280,12282,12303,12327],{"className":12281,"ariaHidden":1901},[2067],[1865,12283,12285,12288,12291,12294,12297,12300],{"className":12284},[2071],[1865,12286],{"className":12287,"style":8815},[2075],[1865,12289,8734],{"className":12290,"style":8819},[2080,2154],[1865,12292,8737],{"className":12293,"style":2247},[2080,2154],[1865,12295],{"className":12296,"style":2693},[2246],[1865,12298,12263],{"className":12299},[2697],[1865,12301],{"className":12302,"style":2693},[2246],[1865,12304,12306,12309,12312,12315,12318,12321,12324],{"className":12305},[2071],[1865,12307],{"className":12308,"style":8815},[2075],[1865,12310,11793],{"className":12311},[2080],[1865,12313,8734],{"className":12314,"style":8819},[2080,2154],[1865,12316,6896],{"className":12317,"style":7058},[2080,2154],[1865,12319],{"className":12320,"style":2693},[2246],[1865,12322,12263],{"className":12323},[2697],[1865,12325],{"className":12326,"style":2693},[2246],[1865,12328,12330,12333,12336],{"className":12329},[2071],[1865,12331],{"className":12332,"style":8815},[2075],[1865,12334,9930],{"className":12335,"style":7058},[2080,2154],[1865,12337,8737],{"className":12338,"style":2247},[2080,2154],[1798,12340,12341],{},"这个近似在以下情况下精确成立：",[3406,12343,12344,12630],{},[1808,12345,12346,7266,12349,11264],{},[3048,12347,12348],{},"拟线性效用",[1865,12350,12352,12406],{"className":12351},[1872],[1865,12353,12355],{"className":12354},[1876],[1878,12356,12357],{"xmlns":1880},[1883,12358,12359,12403],{},[1903,12360,12361,12363,12365,12371,12373,12379,12381,12383,12385,12387,12393,12395,12397],{},[1911,12362,1917],{},[1933,12364,4942],{"stretchy":3501},[1923,12366,12367,12369],{},[1911,12368,1927],{},[1929,12370,1931],{},[1933,12372,2784],{"separator":1901},[1923,12374,12375,12377],{},[1911,12376,1927],{},[1929,12378,1984],{},[1933,12380,4963],{"stretchy":3501},[1933,12382,1955],{},[1911,12384,4993],{},[1933,12386,4942],{"stretchy":3501},[1923,12388,12389,12391],{},[1911,12390,1927],{},[1929,12392,1931],{},[1933,12394,4963],{"stretchy":3501},[1933,12396,2029],{},[1923,12398,12399,12401],{},[1911,12400,1927],{},[1929,12402,1984],{},[2060,12404,12405],{"encoding":2062},"U(x_1, x_2) = v(x_1) + x_2",[1865,12407,12409,12519,12583],{"className":12408,"ariaHidden":1901},[2067],[1865,12410,12412,12415,12418,12421,12461,12464,12467,12507,12510,12513,12516],{"className":12411},[2071],[1865,12413],{"className":12414,"style":5030},[2075],[1865,12416,1917],{"className":12417,"style":2226},[2080,2154],[1865,12419,4942],{"className":12420},[2119],[1865,12422,12424,12427],{"className":12423},[2080],[1865,12425,1927],{"className":12426},[2080,2154],[1865,12428,12430],{"className":12429},[2158],[1865,12431,12433,12453],{"className":12432},[2091,2092],[1865,12434,12436,12450],{"className":12435},[2096],[1865,12437,12439],{"className":12438,"style":2168},[2100],[1865,12440,12441,12444],{"style":2171},[1865,12442],{"className":12443,"style":2175},[2108],[1865,12445,12447],{"className":12446},[2179,2180,2181,2182],[1865,12448,1931],{"className":12449},[2080,2182],[1865,12451,2190],{"className":12452},[2189],[1865,12454,12456],{"className":12455},[2096],[1865,12457,12459],{"className":12458,"style":2197},[2100],[1865,12460],{},[1865,12462,2784],{"className":12463},[2851],[1865,12465],{"className":12466,"style":2855},[2246],[1865,12468,12470,12473],{"className":12469},[2080],[1865,12471,1927],{"className":12472},[2080,2154],[1865,12474,12476],{"className":12475},[2158],[1865,12477,12479,12499],{"className":12478},[2091,2092],[1865,12480,12482,12496],{"className":12481},[2096],[1865,12483,12485],{"className":12484,"style":2168},[2100],[1865,12486,12487,12490],{"style":2171},[1865,12488],{"className":12489,"style":2175},[2108],[1865,12491,12493],{"className":12492},[2179,2180,2181,2182],[1865,12494,1984],{"className":12495},[2080,2182],[1865,12497,2190],{"className":12498},[2189],[1865,12500,12502],{"className":12501},[2096],[1865,12503,12505],{"className":12504,"style":2197},[2100],[1865,12506],{},[1865,12508,4963],{"className":12509},[2242],[1865,12511],{"className":12512,"style":2693},[2246],[1865,12514,1955],{"className":12515},[2697],[1865,12517],{"className":12518,"style":2693},[2246],[1865,12520,12522,12525,12528,12531,12571,12574,12577,12580],{"className":12521},[2071],[1865,12523],{"className":12524,"style":5030},[2075],[1865,12526,4993],{"className":12527,"style":5325},[2080,2154],[1865,12529,4942],{"className":12530},[2119],[1865,12532,12534,12537],{"className":12533},[2080],[1865,12535,1927],{"className":12536},[2080,2154],[1865,12538,12540],{"className":12539},[2158],[1865,12541,12543,12563],{"className":12542},[2091,2092],[1865,12544,12546,12560],{"className":12545},[2096],[1865,12547,12549],{"className":12548,"style":2168},[2100],[1865,12550,12551,12554],{"style":2171},[1865,12552],{"className":12553,"style":2175},[2108],[1865,12555,12557],{"className":12556},[2179,2180,2181,2182],[1865,12558,1931],{"className":12559},[2080,2182],[1865,12561,2190],{"className":12562},[2189],[1865,12564,12566],{"className":12565},[2096],[1865,12567,12569],{"className":12568,"style":2197},[2100],[1865,12570],{},[1865,12572,4963],{"className":12573},[2242],[1865,12575],{"className":12576,"style":2247},[2246],[1865,12578,2029],{"className":12579},[2251],[1865,12581],{"className":12582,"style":2247},[2246],[1865,12584,12586,12590],{"className":12585},[2071],[1865,12587],{"className":12588,"style":12589},[2075],"height:0.5806em;vertical-align:-0.15em;",[1865,12591,12593,12596],{"className":12592},[2080],[1865,12594,1927],{"className":12595},[2080,2154],[1865,12597,12599],{"className":12598},[2158],[1865,12600,12602,12622],{"className":12601},[2091,2092],[1865,12603,12605,12619],{"className":12604},[2096],[1865,12606,12608],{"className":12607,"style":2168},[2100],[1865,12609,12610,12613],{"style":2171},[1865,12611],{"className":12612,"style":2175},[2108],[1865,12614,12616],{"className":12615},[2179,2180,2181,2182],[1865,12617,1984],{"className":12618},[2080,2182],[1865,12620,2190],{"className":12621},[2189],[1865,12623,12625],{"className":12624},[2096],[1865,12626,12628],{"className":12627,"style":2197},[2100],[1865,12629],{},[1808,12631,12632,12635],{},[3048,12633,12634],{},"价格变化很小",": 泰勒展开的一阶近似",[1854,12637,12639],{"id":12638},"_43-为什么消费者剩余被广泛使用","4.3 为什么消费者剩余被广泛使用？",[1798,12641,12642],{},"尽管CV和EV在理论上更精确，消费者剩余在实践中更常用，因为：",[3406,12644,12645,12651,12657],{},[1808,12646,12647,12650],{},[3048,12648,12649],{},"易于计算",": 只需要观察需求曲线",[1808,12652,12653,12656],{},[3048,12654,12655],{},"足够准确",": 在大多数应用中，误差很小",[1808,12658,12659,12662],{},[3048,12660,12661],{},"可加性",": 对于独立商品，总CS = 各商品CS之和",[1798,12664,12665,4915],{},[3048,12666,12667],{},"Marshall vs. Hicks",[1805,12669,12670,12673],{},[1808,12671,12672],{},"马歇尔需求曲线（普通需求）下的面积 = 消费者剩余",[1808,12674,12675],{},"希克斯需求曲线（补偿需求）下的面积 = CV（精确）",[3421,12677],{},[1794,12679,12681],{"id":12680},"_5-完整例题","5. 完整例题",[1854,12683,12685],{"id":12684},"例题-1-拟线性效用下的cvev和cs","例题 1: 拟线性效用下的CV、EV和CS",[1798,12687,12688,12691,12692,13024,13025,13207,13208,13260,13261,13330,13331,13437,13438,13477],{},[3048,12689,12690],{},"题目",": 效用函数 ",[1865,12693,12695,12748],{"className":12694},[1872],[1865,12696,12698],{"className":12697},[1876],[1878,12699,12700],{"xmlns":1880},[1883,12701,12702,12745],{},[1903,12703,12704,12706,12708,12714,12716,12722,12724,12726,12728,12737,12739],{},[1911,12705,1917],{},[1933,12707,4942],{"stretchy":3501},[1923,12709,12710,12712],{},[1911,12711,1927],{},[1929,12713,1931],{},[1933,12715,2784],{"separator":1901},[1923,12717,12718,12720],{},[1911,12719,1927],{},[1929,12721,1984],{},[1933,12723,4963],{"stretchy":3501},[1933,12725,1955],{},[1929,12727,1984],{},[12729,12730,12731],"msqrt",{},[1923,12732,12733,12735],{},[1911,12734,1927],{},[1929,12736,1931],{},[1933,12738,2029],{},[1923,12740,12741,12743],{},[1911,12742,1927],{},[1929,12744,1984],{},[2060,12746,12747],{"encoding":2062},"U(x_1, x_2) = 2\\sqrt{x_1} + x_2",[1865,12749,12751,12861,12978],{"className":12750,"ariaHidden":1901},[2067],[1865,12752,12754,12757,12760,12763,12803,12806,12809,12849,12852,12855,12858],{"className":12753},[2071],[1865,12755],{"className":12756,"style":5030},[2075],[1865,12758,1917],{"className":12759,"style":2226},[2080,2154],[1865,12761,4942],{"className":12762},[2119],[1865,12764,12766,12769],{"className":12765},[2080],[1865,12767,1927],{"className":12768},[2080,2154],[1865,12770,12772],{"className":12771},[2158],[1865,12773,12775,12795],{"className":12774},[2091,2092],[1865,12776,12778,12792],{"className":12777},[2096],[1865,12779,12781],{"className":12780,"style":2168},[2100],[1865,12782,12783,12786],{"style":2171},[1865,12784],{"className":12785,"style":2175},[2108],[1865,12787,12789],{"className":12788},[2179,2180,2181,2182],[1865,12790,1931],{"className":12791},[2080,2182],[1865,12793,2190],{"className":12794},[2189],[1865,12796,12798],{"className":12797},[2096],[1865,12799,12801],{"className":12800,"style":2197},[2100],[1865,12802],{},[1865,12804,2784],{"className":12805},[2851],[1865,12807],{"className":12808,"style":2855},[2246],[1865,12810,12812,12815],{"className":12811},[2080],[1865,12813,1927],{"className":12814},[2080,2154],[1865,12816,12818],{"className":12817},[2158],[1865,12819,12821,12841],{"className":12820},[2091,2092],[1865,12822,12824,12838],{"className":12823},[2096],[1865,12825,12827],{"className":12826,"style":2168},[2100],[1865,12828,12829,12832],{"style":2171},[1865,12830],{"className":12831,"style":2175},[2108],[1865,12833,12835],{"className":12834},[2179,2180,2181,2182],[1865,12836,1984],{"className":12837},[2080,2182],[1865,12839,2190],{"className":12840},[2189],[1865,12842,12844],{"className":12843},[2096],[1865,12845,12847],{"className":12846,"style":2197},[2100],[1865,12848],{},[1865,12850,4963],{"className":12851},[2242],[1865,12853],{"className":12854,"style":2693},[2246],[1865,12856,1955],{"className":12857},[2697],[1865,12859],{"className":12860,"style":2693},[2246],[1865,12862,12864,12868,12871,12969,12972,12975],{"className":12863},[2071],[1865,12865],{"className":12866,"style":12867},[2075],"height:1.04em;vertical-align:-0.3147em;",[1865,12869,1984],{"className":12870},[2080],[1865,12872,12875],{"className":12873},[2080,12874],"sqrt",[1865,12876,12878,12960],{"className":12877},[2091,2092],[1865,12879,12881,12957],{"className":12880},[2096],[1865,12882,12885,12937],{"className":12883,"style":12884},[2100],"height:0.7253em;",[1865,12886,12890,12893],{"className":12887,"style":12889},[12888],"svg-align","top:-3em;",[1865,12891],{"className":12892,"style":2140},[2108],[1865,12894,12897],{"className":12895,"style":12896},[2080],"padding-left:0.833em;",[1865,12898,12900,12903],{"className":12899},[2080],[1865,12901,1927],{"className":12902},[2080,2154],[1865,12904,12906],{"className":12905},[2158],[1865,12907,12909,12929],{"className":12908},[2091,2092],[1865,12910,12912,12926],{"className":12911},[2096],[1865,12913,12915],{"className":12914,"style":2168},[2100],[1865,12916,12917,12920],{"style":2171},[1865,12918],{"className":12919,"style":2175},[2108],[1865,12921,12923],{"className":12922},[2179,2180,2181,2182],[1865,12924,1931],{"className":12925},[2080,2182],[1865,12927,2190],{"className":12928},[2189],[1865,12930,12932],{"className":12931},[2096],[1865,12933,12935],{"className":12934,"style":2197},[2100],[1865,12936],{},[1865,12938,12940,12943],{"style":12939},"top:-2.6853em;",[1865,12941],{"className":12942,"style":2140},[2108],[1865,12944,12948],{"className":12945,"style":12947},[12946],"hide-tail","min-width:0.853em;height:1.08em;",[3893,12949,12954],{"xmlns":3895,"width":12950,"height":12951,"viewBox":12952,"preserveAspectRatio":12953},"400em","1.08em","0 0 400000 1080","xMinYMin slice",[3899,12955],{"d":12956},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[1865,12958,2190],{"className":12959},[2189],[1865,12961,12963],{"className":12962},[2096],[1865,12964,12967],{"className":12965,"style":12966},[2100],"height:0.3147em;",[1865,12968],{},[1865,12970],{"className":12971,"style":2247},[2246],[1865,12973,2029],{"className":12974},[2251],[1865,12976],{"className":12977,"style":2247},[2246],[1865,12979,12981,12984],{"className":12980},[2071],[1865,12982],{"className":12983,"style":12589},[2075],[1865,12985,12987,12990],{"className":12986},[2080],[1865,12988,1927],{"className":12989},[2080,2154],[1865,12991,12993],{"className":12992},[2158],[1865,12994,12996,13016],{"className":12995},[2091,2092],[1865,12997,12999,13013],{"className":12998},[2096],[1865,13000,13002],{"className":13001,"style":2168},[2100],[1865,13003,13004,13007],{"style":2171},[1865,13005],{"className":13006,"style":2175},[2108],[1865,13008,13010],{"className":13009},[2179,2180,2181,2182],[1865,13011,1984],{"className":13012},[2080,2182],[1865,13014,2190],{"className":13015},[2189],[1865,13017,13019],{"className":13018},[2096],[1865,13020,13022],{"className":13021,"style":2197},[2100],[1865,13023],{},"，初始价格 ",[1865,13026,13028,13064],{"className":13027},[1872],[1865,13029,13031],{"className":13030},[1876],[1878,13032,13033],{"xmlns":1880},[1883,13034,13035,13061],{},[1903,13036,13037,13045,13047,13049,13051,13057,13059],{},[8534,13038,13039,13041,13043],{},[1911,13040,1798],{},[1929,13042,1931],{},[1929,13044,1900],{},[1933,13046,1955],{},[1929,13048,1931],{},[1933,13050,2784],{"separator":1901},[1923,13052,13053,13055],{},[1911,13054,1798],{},[1929,13056,1984],{},[1933,13058,1955],{},[1929,13060,1931],{},[2060,13062,13063],{"encoding":2062},"p_1^0 = 1, p_2 = 1",[1865,13065,13067,13133,13198],{"className":13066,"ariaHidden":1901},[2067],[1865,13068,13070,13073,13124,13127,13130],{"className":13069},[2071],[1865,13071],{"className":13072,"style":8554},[2075],[1865,13074,13076,13079],{"className":13075},[2080],[1865,13077,1798],{"className":13078},[2080,2154],[1865,13080,13082],{"className":13081},[2158],[1865,13083,13085,13116],{"className":13084},[2091,2092],[1865,13086,13088,13113],{"className":13087},[2096],[1865,13089,13091,13102],{"className":13090,"style":8573},[2100],[1865,13092,13093,13096],{"style":8576},[1865,13094],{"className":13095,"style":2175},[2108],[1865,13097,13099],{"className":13098},[2179,2180,2181,2182],[1865,13100,1931],{"className":13101},[2080,2182],[1865,13103,13104,13107],{"style":7519},[1865,13105],{"className":13106,"style":2175},[2108],[1865,13108,13110],{"className":13109},[2179,2180,2181,2182],[1865,13111,1900],{"className":13112},[2080,2182],[1865,13114,2190],{"className":13115},[2189],[1865,13117,13119],{"className":13118},[2096],[1865,13120,13122],{"className":13121,"style":8606},[2100],[1865,13123],{},[1865,13125],{"className":13126,"style":2693},[2246],[1865,13128,1955],{"className":13129},[2697],[1865,13131],{"className":13132,"style":2693},[2246],[1865,13134,13136,13140,13143,13146,13149,13189,13192,13195],{"className":13135},[2071],[1865,13137],{"className":13138,"style":13139},[2075],"height:0.8389em;vertical-align:-0.1944em;",[1865,13141,1931],{"className":13142},[2080],[1865,13144,2784],{"className":13145},[2851],[1865,13147],{"className":13148,"style":2855},[2246],[1865,13150,13152,13155],{"className":13151},[2080],[1865,13153,1798],{"className":13154},[2080,2154],[1865,13156,13158],{"className":13157},[2158],[1865,13159,13161,13181],{"className":13160},[2091,2092],[1865,13162,13164,13178],{"className":13163},[2096],[1865,13165,13167],{"className":13166,"style":2168},[2100],[1865,13168,13169,13172],{"style":2171},[1865,13170],{"className":13171,"style":2175},[2108],[1865,13173,13175],{"className":13174},[2179,2180,2181,2182],[1865,13176,1984],{"className":13177},[2080,2182],[1865,13179,2190],{"className":13180},[2189],[1865,13182,13184],{"className":13183},[2096],[1865,13185,13187],{"className":13186,"style":2197},[2100],[1865,13188],{},[1865,13190],{"className":13191,"style":2693},[2246],[1865,13193,1955],{"className":13194},[2697],[1865,13196],{"className":13197,"style":2693},[2246],[1865,13199,13201,13204],{"className":13200},[2071],[1865,13202],{"className":13203,"style":7553},[2075],[1865,13205,1931],{"className":13206},[2080],"，收入 ",[1865,13209,13211,13230],{"className":13210},[1872],[1865,13212,13214],{"className":13213},[1876],[1878,13215,13216],{"xmlns":1880},[1883,13217,13218,13227],{},[1903,13219,13220,13222,13224],{},[1911,13221,2046],{},[1933,13223,1955],{},[1929,13225,13226],{},"20",[2060,13228,13229],{"encoding":2062},"m = 20",[1865,13231,13233,13251],{"className":13232,"ariaHidden":1901},[2067],[1865,13234,13236,13239,13242,13245,13248],{"className":13235},[2071],[1865,13237],{"className":13238,"style":6852},[2075],[1865,13240,2046],{"className":13241},[2080,2154],[1865,13243],{"className":13244,"style":2693},[2246],[1865,13246,1955],{"className":13247},[2697],[1865,13249],{"className":13250,"style":2693},[2246],[1865,13252,13254,13257],{"className":13253},[2071],[1865,13255],{"className":13256,"style":7553},[2075],[1865,13258,13226],{"className":13259},[2080],"。现在",[1865,13262,13264,13281],{"className":13263},[1872],[1865,13265,13267],{"className":13266},[1876],[1878,13268,13269],{"xmlns":1880},[1883,13270,13271,13279],{},[1903,13272,13273],{},[1923,13274,13275,13277],{},[1911,13276,1798],{},[1929,13278,1931],{},[2060,13280,3079],{"encoding":2062},[1865,13282,13284],{"className":13283,"ariaHidden":1901},[2067],[1865,13285,13287,13290],{"className":13286},[2071],[1865,13288],{"className":13289,"style":2948},[2075],[1865,13291,13293,13296],{"className":13292},[2080],[1865,13294,1798],{"className":13295},[2080,2154],[1865,13297,13299],{"className":13298},[2158],[1865,13300,13302,13322],{"className":13301},[2091,2092],[1865,13303,13305,13319],{"className":13304},[2096],[1865,13306,13308],{"className":13307,"style":2168},[2100],[1865,13309,13310,13313],{"style":2171},[1865,13311],{"className":13312,"style":2175},[2108],[1865,13314,13316],{"className":13315},[2179,2180,2181,2182],[1865,13317,1931],{"className":13318},[2080,2182],[1865,13320,2190],{"className":13321},[2189],[1865,13323,13325],{"className":13324},[2096],[1865,13326,13328],{"className":13327,"style":2197},[2100],[1865,13329],{},"涨到",[1865,13332,13334,13359],{"className":13333},[1872],[1865,13335,13337],{"className":13336},[1876],[1878,13338,13339],{"xmlns":1880},[1883,13340,13341,13356],{},[1903,13342,13343,13351,13353],{},[8534,13344,13345,13347,13349],{},[1911,13346,1798],{},[1929,13348,1931],{},[1929,13350,1931],{},[1933,13352,1955],{},[1929,13354,13355],{},"4",[2060,13357,13358],{"encoding":2062},"p_1^1 = 4",[1865,13360,13362,13428],{"className":13361,"ariaHidden":1901},[2067],[1865,13363,13365,13368,13419,13422,13425],{"className":13364},[2071],[1865,13366],{"className":13367,"style":8554},[2075],[1865,13369,13371,13374],{"className":13370},[2080],[1865,13372,1798],{"className":13373},[2080,2154],[1865,13375,13377],{"className":13376},[2158],[1865,13378,13380,13411],{"className":13379},[2091,2092],[1865,13381,13383,13408],{"className":13382},[2096],[1865,13384,13386,13397],{"className":13385,"style":8573},[2100],[1865,13387,13388,13391],{"style":8576},[1865,13389],{"className":13390,"style":2175},[2108],[1865,13392,13394],{"className":13393},[2179,2180,2181,2182],[1865,13395,1931],{"className":13396},[2080,2182],[1865,13398,13399,13402],{"style":7519},[1865,13400],{"className":13401,"style":2175},[2108],[1865,13403,13405],{"className":13404},[2179,2180,2181,2182],[1865,13406,1931],{"className":13407},[2080,2182],[1865,13409,2190],{"className":13410},[2189],[1865,13412,13414],{"className":13413},[2096],[1865,13415,13417],{"className":13416,"style":8606},[2100],[1865,13418],{},[1865,13420],{"className":13421,"style":2693},[2246],[1865,13423,1955],{"className":13424},[2697],[1865,13426],{"className":13427,"style":2693},[2246],[1865,13429,13431,13434],{"className":13430},[2071],[1865,13432],{"className":13433,"style":7553},[2075],[1865,13435,13355],{"className":13436},[2080],"。计算CV、EV和",[1865,13439,13441,13459],{"className":13440},[1872],[1865,13442,13444],{"className":13443},[1876],[1878,13445,13446],{"xmlns":1880},[1883,13447,13448,13456],{},[1903,13449,13450,13452,13454],{},[1911,13451,11793],{"mathvariant":1913},[1911,13453,8734],{},[1911,13455,6896],{},[2060,13457,13458],{"encoding":2062},"\\Delta CS",[1865,13460,13462],{"className":13461,"ariaHidden":1901},[2067],[1865,13463,13465,13468,13471,13474],{"className":13464},[2071],[1865,13466],{"className":13467,"style":8815},[2075],[1865,13469,11793],{"className":13470},[2080],[1865,13472,8734],{"className":13473,"style":8819},[2080,2154],[1865,13475,6896],{"className":13476,"style":7058},[2080,2154],"。",[1798,13479,13480,4915],{},[3048,13481,13482],{},"解答",[1798,13484,13485],{},[3048,13486,13487],{},"(1) 求马歇尔需求函数",[1798,13489,13490],{},"拉格朗日函数：",[1865,13492,13494],{"className":13493},[1868],[1865,13495,13497,13565],{"className":13496},[1872],[1865,13498,13500],{"className":13499},[1876],[1878,13501,13502],{"xmlns":1880,"display":1881},[1883,13503,13504,13562],{},[1903,13505,13506,13510,13512,13514,13522,13524,13530,13532,13534,13536,13538,13540,13546,13552,13554,13560],{},[1911,13507,13509],{"mathvariant":13508},"script","L",[1933,13511,1955],{},[1929,13513,1984],{},[12729,13515,13516],{},[1923,13517,13518,13520],{},[1911,13519,1927],{},[1929,13521,1931],{},[1933,13523,2029],{},[1923,13525,13526,13528],{},[1911,13527,1927],{},[1929,13529,1984],{},[1933,13531,2029],{},[1911,13533,1938],{},[1933,13535,4942],{"stretchy":3501},[1929,13537,13226],{},[1933,13539,1935],{},[1923,13541,13542,13544],{},[1911,13543,1798],{},[1929,13545,1931],{},[1923,13547,13548,13550],{},[1911,13549,1927],{},[1929,13551,1931],{},[1933,13553,1935],{},[1923,13555,13556,13558],{},[1911,13557,1927],{},[1929,13559,1984],{},[1933,13561,4963],{"stretchy":3501},[2060,13563,13564],{"encoding":2062},"\\mathcal{L} = 2\\sqrt{x_1} + x_2 + \\lambda(20 - p_1 x_1 - x_2)",[1865,13566,13568,13587,13693,13749,13773,13869],{"className":13567,"ariaHidden":1901},[2067],[1865,13569,13571,13574,13578,13581,13584],{"className":13570},[2071],[1865,13572],{"className":13573,"style":8815},[2075],[1865,13575,13509],{"className":13576},[2080,13577],"mathcal",[1865,13579],{"className":13580,"style":2693},[2246],[1865,13582,1955],{"className":13583},[2697],[1865,13585],{"className":13586,"style":2693},[2246],[1865,13588,13590,13594,13597,13684,13687,13690],{"className":13589},[2071],[1865,13591],{"className":13592,"style":13593},[2075],"height:1.04em;vertical-align:-0.2658em;",[1865,13595,1984],{"className":13596},[2080],[1865,13598,13600],{"className":13599},[2080,12874],[1865,13601,13603,13675],{"className":13602},[2091,2092],[1865,13604,13606,13672],{"className":13605},[2096],[1865,13607,13610,13659],{"className":13608,"style":13609},[2100],"height:0.7742em;",[1865,13611,13613,13616],{"className":13612,"style":12889},[12888],[1865,13614],{"className":13615,"style":2140},[2108],[1865,13617,13619],{"className":13618,"style":12896},[2080],[1865,13620,13622,13625],{"className":13621},[2080],[1865,13623,1927],{"className":13624},[2080,2154],[1865,13626,13628],{"className":13627},[2158],[1865,13629,13631,13651],{"className":13630},[2091,2092],[1865,13632,13634,13648],{"className":13633},[2096],[1865,13635,13637],{"className":13636,"style":2168},[2100],[1865,13638,13639,13642],{"style":2171},[1865,13640],{"className":13641,"style":2175},[2108],[1865,13643,13645],{"className":13644},[2179,2180,2181,2182],[1865,13646,1931],{"className":13647},[2080,2182],[1865,13649,2190],{"className":13650},[2189],[1865,13652,13654],{"className":13653},[2096],[1865,13655,13657],{"className":13656,"style":2197},[2100],[1865,13658],{},[1865,13660,13662,13665],{"style":13661},"top:-2.7342em;",[1865,13663],{"className":13664,"style":2140},[2108],[1865,13666,13668],{"className":13667,"style":12947},[12946],[3893,13669,13670],{"xmlns":3895,"width":12950,"height":12951,"viewBox":12952,"preserveAspectRatio":12953},[3899,13671],{"d":12956},[1865,13673,2190],{"className":13674},[2189],[1865,13676,13678],{"className":13677},[2096],[1865,13679,13682],{"className":13680,"style":13681},[2100],"height:0.2658em;",[1865,13683],{},[1865,13685],{"className":13686,"style":2247},[2246],[1865,13688,2029],{"className":13689},[2251],[1865,13691],{"className":13692,"style":2247},[2246],[1865,13694,13696,13700,13740,13743,13746],{"className":13695},[2071],[1865,13697],{"className":13698,"style":13699},[2075],"height:0.7333em;vertical-align:-0.15em;",[1865,13701,13703,13706],{"className":13702},[2080],[1865,13704,1927],{"className":13705},[2080,2154],[1865,13707,13709],{"className":13708},[2158],[1865,13710,13712,13732],{"className":13711},[2091,2092],[1865,13713,13715,13729],{"className":13714},[2096],[1865,13716,13718],{"className":13717,"style":2168},[2100],[1865,13719,13720,13723],{"style":2171},[1865,13721],{"className":13722,"style":2175},[2108],[1865,13724,13726],{"className":13725},[2179,2180,2181,2182],[1865,13727,1984],{"className":13728},[2080,2182],[1865,13730,2190],{"className":13731},[2189],[1865,13733,13735],{"className":13734},[2096],[1865,13736,13738],{"className":13737,"style":2197},[2100],[1865,13739],{},[1865,13741],{"className":13742,"style":2247},[2246],[1865,13744,2029],{"className":13745},[2251],[1865,13747],{"className":13748,"style":2247},[2246],[1865,13750,13752,13755,13758,13761,13764,13767,13770],{"className":13751},[2071],[1865,13753],{"className":13754,"style":5030},[2075],[1865,13756,1938],{"className":13757},[2080,2154],[1865,13759,4942],{"className":13760},[2119],[1865,13762,13226],{"className":13763},[2080],[1865,13765],{"className":13766,"style":2247},[2246],[1865,13768,1935],{"className":13769},[2251],[1865,13771],{"className":13772,"style":2247},[2246],[1865,13774,13776,13780,13820,13860,13863,13866],{"className":13775},[2071],[1865,13777],{"className":13778,"style":13779},[2075],"height:0.7778em;vertical-align:-0.1944em;",[1865,13781,13783,13786],{"className":13782},[2080],[1865,13784,1798],{"className":13785},[2080,2154],[1865,13787,13789],{"className":13788},[2158],[1865,13790,13792,13812],{"className":13791},[2091,2092],[1865,13793,13795,13809],{"className":13794},[2096],[1865,13796,13798],{"className":13797,"style":2168},[2100],[1865,13799,13800,13803],{"style":2171},[1865,13801],{"className":13802,"style":2175},[2108],[1865,13804,13806],{"className":13805},[2179,2180,2181,2182],[1865,13807,1931],{"className":13808},[2080,2182],[1865,13810,2190],{"className":13811},[2189],[1865,13813,13815],{"className":13814},[2096],[1865,13816,13818],{"className":13817,"style":2197},[2100],[1865,13819],{},[1865,13821,13823,13826],{"className":13822},[2080],[1865,13824,1927],{"className":13825},[2080,2154],[1865,13827,13829],{"className":13828},[2158],[1865,13830,13832,13852],{"className":13831},[2091,2092],[1865,13833,13835,13849],{"className":13834},[2096],[1865,13836,13838],{"className":13837,"style":2168},[2100],[1865,13839,13840,13843],{"style":2171},[1865,13841],{"className":13842,"style":2175},[2108],[1865,13844,13846],{"className":13845},[2179,2180,2181,2182],[1865,13847,1931],{"className":13848},[2080,2182],[1865,13850,2190],{"className":13851},[2189],[1865,13853,13855],{"className":13854},[2096],[1865,13856,13858],{"className":13857,"style":2197},[2100],[1865,13859],{},[1865,13861],{"className":13862,"style":2247},[2246],[1865,13864,1935],{"className":13865},[2251],[1865,13867],{"className":13868,"style":2247},[2246],[1865,13870,13872,13875,13915],{"className":13871},[2071],[1865,13873],{"className":13874,"style":5030},[2075],[1865,13876,13878,13881],{"className":13877},[2080],[1865,13879,1927],{"className":13880},[2080,2154],[1865,13882,13884],{"className":13883},[2158],[1865,13885,13887,13907],{"className":13886},[2091,2092],[1865,13888,13890,13904],{"className":13889},[2096],[1865,13891,13893],{"className":13892,"style":2168},[2100],[1865,13894,13895,13898],{"style":2171},[1865,13896],{"className":13897,"style":2175},[2108],[1865,13899,13901],{"className":13900},[2179,2180,2181,2182],[1865,13902,1984],{"className":13903},[2080,2182],[1865,13905,2190],{"className":13906},[2189],[1865,13908,13910],{"className":13909},[2096],[1865,13911,13913],{"className":13912,"style":2197},[2100],[1865,13914],{},[1865,13916,4963],{"className":13917},[2242],[1798,13919,13920],{},"一阶条件：",[1865,13922,13924],{"className":13923},[1868],[1865,13925,13927,14007],{"className":13926},[1872],[1865,13928,13930],{"className":13929},[1876],[1878,13931,13932],{"xmlns":1880,"display":1881},[1883,13933,13934,14004],{},[1886,13935,13936,13978],{"rowspacing":1888,"columnalign":1889,"columnspacing":1890},[1892,13937,13938,13966],{},[1895,13939,13940],{},[1898,13941,13942],{"scriptlevel":1900,"displaystyle":1901},[1903,13943,13944,13956,13958,13960],{},[1906,13945,13946,13948],{},[1929,13947,1931],{},[12729,13949,13950],{},[1923,13951,13952,13954],{},[1911,13953,1927],{},[1929,13955,1931],{},[1933,13957,1935],{},[1911,13959,1938],{},[1923,13961,13962,13964],{},[1911,13963,1798],{},[1929,13965,1931],{},[1895,13967,13968],{},[1898,13969,13970],{"scriptlevel":1900,"displaystyle":1901},[1903,13971,13972,13974,13976],{},[1903,13973],{},[1933,13975,1955],{},[1929,13977,1900],{},[1892,13979,13980,13992],{},[1895,13981,13982],{},[1898,13983,13984],{"scriptlevel":1900,"displaystyle":1901},[1903,13985,13986,13988,13990],{},[1929,13987,1931],{},[1933,13989,1935],{},[1911,13991,1938],{},[1895,13993,13994],{},[1898,13995,13996],{"scriptlevel":1900,"displaystyle":1901},[1903,13997,13998,14000,14002],{},[1903,13999],{},[1933,14001,1955],{},[1929,14003,1900],{},[2060,14005,14006],{"encoding":2062},"\\begin{align*}\n\\frac{1}{\\sqrt{x_1}} - \\lambda p_1 &= 0 \\\\\n1 - \\lambda &= 0\n\\end{align*}",[1865,14008,14010],{"className":14009,"ariaHidden":1901},[2067],[1865,14011,14013,14017],{"className":14012},[2071],[1865,14014],{"className":14015,"style":14016},[2075],"height:3.8222em;vertical-align:-1.6611em;",[1865,14018,14020],{"className":14019},[2080],[1865,14021,14023,14278],{"className":14022},[1886],[1865,14024,14026],{"className":14025},[2087],[1865,14027,14029,14269],{"className":14028},[2091,2092],[1865,14030,14032,14266],{"className":14031},[2096],[1865,14033,14036,14242],{"className":14034,"style":14035},[2100],"height:2.1611em;",[1865,14037,14039,14043],{"style":14038},"top:-4.1611em;",[1865,14040],{"className":14041,"style":14042},[2108],"height:3.3214em;",[1865,14044,14046,14190,14193,14196,14199,14202],{"className":14045},[2080],[1865,14047,14049,14052,14187],{"className":14048},[2080],[1865,14050],{"className":14051},[2119,2120],[1865,14053,14055],{"className":14054},[1906],[1865,14056,14058,14178],{"className":14057},[2091,2092],[1865,14059,14061,14175],{"className":14060},[2096],[1865,14062,14064,14156,14164],{"className":14063,"style":6666},[2100],[1865,14065,14066,14069],{"style":2136},[1865,14067],{"className":14068,"style":2140},[2108],[1865,14070,14072],{"className":14071},[2080],[1865,14073,14075],{"className":14074},[2080,12874],[1865,14076,14078,14148],{"className":14077},[2091,2092],[1865,14079,14081,14145],{"className":14080},[2096],[1865,14082,14084,14133],{"className":14083,"style":12884},[2100],[1865,14085,14087,14090],{"className":14086,"style":12889},[12888],[1865,14088],{"className":14089,"style":2140},[2108],[1865,14091,14093],{"className":14092,"style":12896},[2080],[1865,14094,14096,14099],{"className":14095},[2080],[1865,14097,1927],{"className":14098},[2080,2154],[1865,14100,14102],{"className":14101},[2158],[1865,14103,14105,14125],{"className":14104},[2091,2092],[1865,14106,14108,14122],{"className":14107},[2096],[1865,14109,14111],{"className":14110,"style":2168},[2100],[1865,14112,14113,14116],{"style":2171},[1865,14114],{"className":14115,"style":2175},[2108],[1865,14117,14119],{"className":14118},[2179,2180,2181,2182],[1865,14120,1931],{"className":14121},[2080,2182],[1865,14123,2190],{"className":14124},[2189],[1865,14126,14128],{"className":14127},[2096],[1865,14129,14131],{"className":14130,"style":2197},[2100],[1865,14132],{},[1865,14134,14135,14138],{"style":12939},[1865,14136],{"className":14137,"style":2140},[2108],[1865,14139,14141],{"className":14140,"style":12947},[12946],[3893,14142,14143],{"xmlns":3895,"width":12950,"height":12951,"viewBox":12952,"preserveAspectRatio":12953},[3899,14144],{"d":12956},[1865,14146,2190],{"className":14147},[2189],[1865,14149,14151],{"className":14150},[2096],[1865,14152,14154],{"className":14153,"style":12966},[2100],[1865,14155],{},[1865,14157,14158,14161],{"style":2202},[1865,14159],{"className":14160,"style":2140},[2108],[1865,14162],{"className":14163,"style":2210},[2209],[1865,14165,14166,14169],{"style":2213},[1865,14167],{"className":14168,"style":2140},[2108],[1865,14170,14172],{"className":14171},[2080],[1865,14173,1931],{"className":14174},[2080],[1865,14176,2190],{"className":14177},[2189],[1865,14179,14181],{"className":14180},[2096],[1865,14182,14185],{"className":14183,"style":14184},[2100],"height:1.0007em;",[1865,14186],{},[1865,14188],{"className":14189},[2242,2120],[1865,14191],{"className":14192,"style":2247},[2246],[1865,14194,1935],{"className":14195},[2251],[1865,14197],{"className":14198,"style":2247},[2246],[1865,14200,1938],{"className":14201},[2080,2154],[1865,14203,14205,14208],{"className":14204},[2080],[1865,14206,1798],{"className":14207},[2080,2154],[1865,14209,14211],{"className":14210},[2158],[1865,14212,14214,14234],{"className":14213},[2091,2092],[1865,14215,14217,14231],{"className":14216},[2096],[1865,14218,14220],{"className":14219,"style":2168},[2100],[1865,14221,14222,14225],{"style":2171},[1865,14223],{"className":14224,"style":2175},[2108],[1865,14226,14228],{"className":14227},[2179,2180,2181,2182],[1865,14229,1931],{"className":14230},[2080,2182],[1865,14232,2190],{"className":14233},[2189],[1865,14235,14237],{"className":14236},[2096],[1865,14238,14240],{"className":14239,"style":2197},[2100],[1865,14241],{},[1865,14243,14245,14248],{"style":14244},"top:-2.0204em;",[1865,14246],{"className":14247,"style":14042},[2108],[1865,14249,14251,14254,14257,14260,14263],{"className":14250},[2080],[1865,14252,1931],{"className":14253},[2080],[1865,14255],{"className":14256,"style":2247},[2246],[1865,14258,1935],{"className":14259},[2251],[1865,14261],{"className":14262,"style":2247},[2246],[1865,14264,1938],{"className":14265},[2080,2154],[1865,14267,2190],{"className":14268},[2189],[1865,14270,14272],{"className":14271},[2096],[1865,14273,14276],{"className":14274,"style":14275},[2100],"height:1.6611em;",[1865,14277],{},[1865,14279,14281],{"className":14280},[2669],[1865,14282,14284,14339],{"className":14283},[2091,2092],[1865,14285,14287,14336],{"className":14286},[2096],[1865,14288,14290,14313],{"className":14289,"style":14035},[2100],[1865,14291,14292,14295],{"style":14038},[1865,14293],{"className":14294,"style":14042},[2108],[1865,14296,14298,14301,14304,14307,14310],{"className":14297},[2080],[1865,14299],{"className":14300},[2080],[1865,14302],{"className":14303,"style":2693},[2246],[1865,14305,1955],{"className":14306},[2697],[1865,14308],{"className":14309,"style":2693},[2246],[1865,14311,1900],{"className":14312},[2080],[1865,14314,14315,14318],{"style":14244},[1865,14316],{"className":14317,"style":14042},[2108],[1865,14319,14321,14324,14327,14330,14333],{"className":14320},[2080],[1865,14322],{"className":14323},[2080],[1865,14325],{"className":14326,"style":2693},[2246],[1865,14328,1955],{"className":14329},[2697],[1865,14331],{"className":14332,"style":2693},[2246],[1865,14334,1900],{"className":14335},[2080],[1865,14337,2190],{"className":14338},[2189],[1865,14340,14342],{"className":14341},[2096],[1865,14343,14345],{"className":14344,"style":14275},[2100],[1865,14346],{},[1798,14348,14349,14350,14402],{},"从第二个方程得",[1865,14351,14353,14371],{"className":14352},[1872],[1865,14354,14356],{"className":14355},[1876],[1878,14357,14358],{"xmlns":1880},[1883,14359,14360,14368],{},[1903,14361,14362,14364,14366],{},[1911,14363,1938],{},[1933,14365,1955],{},[1929,14367,1931],{},[2060,14369,14370],{"encoding":2062},"\\lambda = 1",[1865,14372,14374,14393],{"className":14373,"ariaHidden":1901},[2067],[1865,14375,14377,14381,14384,14387,14390],{"className":14376},[2071],[1865,14378],{"className":14379,"style":14380},[2075],"height:0.6944em;",[1865,14382,1938],{"className":14383},[2080,2154],[1865,14385],{"className":14386,"style":2693},[2246],[1865,14388,1955],{"className":14389},[2697],[1865,14391],{"className":14392,"style":2693},[2246],[1865,14394,14396,14399],{"className":14395},[2071],[1865,14397],{"className":14398,"style":7553},[2075],[1865,14400,1931],{"className":14401},[2080],"，代入第一个：",[1865,14404,14406],{"className":14405},[1868],[1865,14407,14409,14469],{"className":14408},[1872],[1865,14410,14412],{"className":14411},[1876],[1878,14413,14414],{"xmlns":1880,"display":1881},[1883,14415,14416,14466],{},[1903,14417,14418,14430,14432,14438,14441,14444,14446,14452,14454],{},[1906,14419,14420,14422],{},[1929,14421,1931],{},[12729,14423,14424],{},[1923,14425,14426,14428],{},[1911,14427,1927],{},[1929,14429,1931],{},[1933,14431,1955],{},[1923,14433,14434,14436],{},[1911,14435,1798],{},[1929,14437,1931],{},[11827,14439,14440],{},"  ",[1933,14442,14443],{},"⟹",[11827,14445,14440],{},[1923,14447,14448,14450],{},[1911,14449,1927],{},[1929,14451,1931],{},[1933,14453,1955],{},[1906,14455,14456,14458],{},[1929,14457,1931],{},[8534,14459,14460,14462,14464],{},[1911,14461,1798],{},[1929,14463,1931],{},[1929,14465,1984],{},[2060,14467,14468],{"encoding":2062},"\\frac{1}{\\sqrt{x_1}} = p_1 \\implies x_1 = \\frac{1}{p_1^2}",[1865,14470,14472,14631,14693,14748],{"className":14471,"ariaHidden":1901},[2067],[1865,14473,14475,14479,14622,14625,14628],{"className":14474},[2071],[1865,14476],{"className":14477,"style":14478},[2075],"height:2.3222em;vertical-align:-1.0007em;",[1865,14480,14482,14485,14619],{"className":14481},[2080],[1865,14483],{"className":14484},[2119,2120],[1865,14486,14488],{"className":14487},[1906],[1865,14489,14491,14611],{"className":14490},[2091,2092],[1865,14492,14494,14608],{"className":14493},[2096],[1865,14495,14497,14589,14597],{"className":14496,"style":6666},[2100],[1865,14498,14499,14502],{"style":2136},[1865,14500],{"className":14501,"style":2140},[2108],[1865,14503,14505],{"className":14504},[2080],[1865,14506,14508],{"className":14507},[2080,12874],[1865,14509,14511,14581],{"className":14510},[2091,2092],[1865,14512,14514,14578],{"className":14513},[2096],[1865,14515,14517,14566],{"className":14516,"style":12884},[2100],[1865,14518,14520,14523],{"className":14519,"style":12889},[12888],[1865,14521],{"className":14522,"style":2140},[2108],[1865,14524,14526],{"className":14525,"style":12896},[2080],[1865,14527,14529,14532],{"className":14528},[2080],[1865,14530,1927],{"className":14531},[2080,2154],[1865,14533,14535],{"className":14534},[2158],[1865,14536,14538,14558],{"className":14537},[2091,2092],[1865,14539,14541,14555],{"className":14540},[2096],[1865,14542,14544],{"className":14543,"style":2168},[2100],[1865,14545,14546,14549],{"style":2171},[1865,14547],{"className":14548,"style":2175},[2108],[1865,14550,14552],{"className":14551},[2179,2180,2181,2182],[1865,14553,1931],{"className":14554},[2080,2182],[1865,14556,2190],{"className":14557},[2189],[1865,14559,14561],{"className":14560},[2096],[1865,14562,14564],{"className":14563,"style":2197},[2100],[1865,14565],{},[1865,14567,14568,14571],{"style":12939},[1865,14569],{"className":14570,"style":2140},[2108],[1865,14572,14574],{"className":14573,"style":12947},[12946],[3893,14575,14576],{"xmlns":3895,"width":12950,"height":12951,"viewBox":12952,"preserveAspectRatio":12953},[3899,14577],{"d":12956},[1865,14579,2190],{"className":14580},[2189],[1865,14582,14584],{"className":14583},[2096],[1865,14585,14587],{"className":14586,"style":12966},[2100],[1865,14588],{},[1865,14590,14591,14594],{"style":2202},[1865,14592],{"className":14593,"style":2140},[2108],[1865,14595],{"className":14596,"style":2210},[2209],[1865,14598,14599,14602],{"style":2213},[1865,14600],{"className":14601,"style":2140},[2108],[1865,14603,14605],{"className":14604},[2080],[1865,14606,1931],{"className":14607},[2080],[1865,14609,2190],{"className":14610},[2189],[1865,14612,14614],{"className":14613},[2096],[1865,14615,14617],{"className":14616,"style":14184},[2100],[1865,14618],{},[1865,14620],{"className":14621},[2242,2120],[1865,14623],{"className":14624,"style":2693},[2246],[1865,14626,1955],{"className":14627},[2697],[1865,14629],{"className":14630,"style":2693},[2246],[1865,14632,14634,14638,14678,14681,14684,14687,14690],{"className":14633},[2071],[1865,14635],{"className":14636,"style":14637},[2075],"height:0.7194em;vertical-align:-0.1944em;",[1865,14639,14641,14644],{"className":14640},[2080],[1865,14642,1798],{"className":14643},[2080,2154],[1865,14645,14647],{"className":14646},[2158],[1865,14648,14650,14670],{"className":14649},[2091,2092],[1865,14651,14653,14667],{"className":14652},[2096],[1865,14654,14656],{"className":14655,"style":2168},[2100],[1865,14657,14658,14661],{"style":2171},[1865,14659],{"className":14660,"style":2175},[2108],[1865,14662,14664],{"className":14663},[2179,2180,2181,2182],[1865,14665,1931],{"className":14666},[2080,2182],[1865,14668,2190],{"className":14669},[2189],[1865,14671,14673],{"className":14672},[2096],[1865,14674,14676],{"className":14675,"style":2197},[2100],[1865,14677],{},[1865,14679],{"className":14680,"style":2693},[2246],[1865,14682],{"className":14683,"style":2693},[2246],[1865,14685,14443],{"className":14686},[2697],[1865,14688],{"className":14689,"style":2693},[2246],[1865,14691],{"className":14692,"style":2693},[2246],[1865,14694,14696,14699,14739,14742,14745],{"className":14695},[2071],[1865,14697],{"className":14698,"style":12589},[2075],[1865,14700,14702,14705],{"className":14701},[2080],[1865,14703,1927],{"className":14704},[2080,2154],[1865,14706,14708],{"className":14707},[2158],[1865,14709,14711,14731],{"className":14710},[2091,2092],[1865,14712,14714,14728],{"className":14713},[2096],[1865,14715,14717],{"className":14716,"style":2168},[2100],[1865,14718,14719,14722],{"style":2171},[1865,14720],{"className":14721,"style":2175},[2108],[1865,14723,14725],{"className":14724},[2179,2180,2181,2182],[1865,14726,1931],{"className":14727},[2080,2182],[1865,14729,2190],{"className":14730},[2189],[1865,14732,14734],{"className":14733},[2096],[1865,14735,14737],{"className":14736,"style":2197},[2100],[1865,14738],{},[1865,14740],{"className":14741,"style":2693},[2246],[1865,14743,1955],{"className":14744},[2697],[1865,14746],{"className":14747,"style":2693},[2246],[1865,14749,14751,14755],{"className":14750},[2071],[1865,14752],{"className":14753,"style":14754},[2075],"height:2.2737em;vertical-align:-0.9523em;",[1865,14756,14758,14761,14867],{"className":14757},[2080],[1865,14759],{"className":14760},[2119,2120],[1865,14762,14764],{"className":14763},[1906],[1865,14765,14767,14858],{"className":14766},[2091,2092],[1865,14768,14770,14855],{"className":14769},[2096],[1865,14771,14773,14836,14844],{"className":14772,"style":6666},[2100],[1865,14774,14775,14778],{"style":2136},[1865,14776],{"className":14777,"style":2140},[2108],[1865,14779,14781],{"className":14780},[2080],[1865,14782,14784,14787],{"className":14783},[2080],[1865,14785,1798],{"className":14786},[2080,2154],[1865,14788,14790],{"className":14789},[2158],[1865,14791,14793,14827],{"className":14792},[2091,2092],[1865,14794,14796,14824],{"className":14795},[2096],[1865,14797,14800,14812],{"className":14798,"style":14799},[2100],"height:0.7959em;",[1865,14801,14803,14806],{"style":14802},"top:-2.4337em;margin-left:0em;margin-right:0.05em;",[1865,14804],{"className":14805,"style":2175},[2108],[1865,14807,14809],{"className":14808},[2179,2180,2181,2182],[1865,14810,1931],{"className":14811},[2080,2182],[1865,14813,14815,14818],{"style":14814},"top:-3.0448em;margin-right:0.05em;",[1865,14816],{"className":14817,"style":2175},[2108],[1865,14819,14821],{"className":14820},[2179,2180,2181,2182],[1865,14822,1984],{"className":14823},[2080,2182],[1865,14825,2190],{"className":14826},[2189],[1865,14828,14830],{"className":14829},[2096],[1865,14831,14834],{"className":14832,"style":14833},[2100],"height:0.2663em;",[1865,14835],{},[1865,14837,14838,14841],{"style":2202},[1865,14839],{"className":14840,"style":2140},[2108],[1865,14842],{"className":14843,"style":2210},[2209],[1865,14845,14846,14849],{"style":2213},[1865,14847],{"className":14848,"style":2140},[2108],[1865,14850,14852],{"className":14851},[2080],[1865,14853,1931],{"className":14854},[2080],[1865,14856,2190],{"className":14857},[2189],[1865,14859,14861],{"className":14860},[2096],[1865,14862,14865],{"className":14863,"style":14864},[2100],"height:0.9523em;",[1865,14866],{},[1865,14868],{"className":14869},[2242,2120],[1798,14871,14872],{},"代入预算约束：",[1865,14874,14876],{"className":14875},[1868],[1865,14877,14879,14939],{"className":14878},[1872],[1865,14880,14882],{"className":14881},[1876],[1878,14883,14884],{"xmlns":1880,"display":1881},[1883,14885,14886,14936],{},[1903,14887,14888,14894,14896,14898,14900,14906,14908,14920,14922,14924,14926],{},[1923,14889,14890,14892],{},[1911,14891,1927],{},[1929,14893,1984],{},[1933,14895,1955],{},[1929,14897,13226],{},[1933,14899,1935],{},[1923,14901,14902,14904],{},[1911,14903,1798],{},[1929,14905,1931],{},[1933,14907,5600],{},[1906,14909,14910,14912],{},[1929,14911,1931],{},[8534,14913,14914,14916,14918],{},[1911,14915,1798],{},[1929,14917,1931],{},[1929,14919,1984],{},[1933,14921,1955],{},[1929,14923,13226],{},[1933,14925,1935],{},[1906,14927,14928,14930],{},[1929,14929,1931],{},[1923,14931,14932,14934],{},[1911,14933,1798],{},[1929,14935,1931],{},[2060,14937,14938],{"encoding":2062},"x_2 = 20 - p_1 \\cdot \\frac{1}{p_1^2} = 20 - \\frac{1}{p_1}",[1865,14940,14942,14997,15016,15072,15197,15215],{"className":14941,"ariaHidden":1901},[2067],[1865,14943,14945,14948,14988,14991,14994],{"className":14944},[2071],[1865,14946],{"className":14947,"style":12589},[2075],[1865,14949,14951,14954],{"className":14950},[2080],[1865,14952,1927],{"className":14953},[2080,2154],[1865,14955,14957],{"className":14956},[2158],[1865,14958,14960,14980],{"className":14959},[2091,2092],[1865,14961,14963,14977],{"className":14962},[2096],[1865,14964,14966],{"className":14965,"style":2168},[2100],[1865,14967,14968,14971],{"style":2171},[1865,14969],{"className":14970,"style":2175},[2108],[1865,14972,14974],{"className":14973},[2179,2180,2181,2182],[1865,14975,1984],{"className":14976},[2080,2182],[1865,14978,2190],{"className":14979},[2189],[1865,14981,14983],{"className":14982},[2096],[1865,14984,14986],{"className":14985,"style":2197},[2100],[1865,14987],{},[1865,14989],{"className":14990,"style":2693},[2246],[1865,14992,1955],{"className":14993},[2697],[1865,14995],{"className":14996,"style":2693},[2246],[1865,14998,15000,15004,15007,15010,15013],{"className":14999},[2071],[1865,15001],{"className":15002,"style":15003},[2075],"height:0.7278em;vertical-align:-0.0833em;",[1865,15005,13226],{"className":15006},[2080],[1865,15008],{"className":15009,"style":2247},[2246],[1865,15011,1935],{"className":15012},[2251],[1865,15014],{"className":15015,"style":2247},[2246],[1865,15017,15019,15023,15063,15066,15069],{"className":15018},[2071],[1865,15020],{"className":15021,"style":15022},[2075],"height:0.6389em;vertical-align:-0.1944em;",[1865,15024,15026,15029],{"className":15025},[2080],[1865,15027,1798],{"className":15028},[2080,2154],[1865,15030,15032],{"className":15031},[2158],[1865,15033,15035,15055],{"className":15034},[2091,2092],[1865,15036,15038,15052],{"className":15037},[2096],[1865,15039,15041],{"className":15040,"style":2168},[2100],[1865,15042,15043,15046],{"style":2171},[1865,15044],{"className":15045,"style":2175},[2108],[1865,15047,15049],{"className":15048},[2179,2180,2181,2182],[1865,15050,1931],{"className":15051},[2080,2182],[1865,15053,2190],{"className":15054},[2189],[1865,15056,15058],{"className":15057},[2096],[1865,15059,15061],{"className":15060,"style":2197},[2100],[1865,15062],{},[1865,15064],{"className":15065,"style":2247},[2246],[1865,15067,5600],{"className":15068},[2251],[1865,15070],{"className":15071,"style":2247},[2246],[1865,15073,15075,15078,15188,15191,15194],{"className":15074},[2071],[1865,15076],{"className":15077,"style":14754},[2075],[1865,15079,15081,15084,15185],{"className":15080},[2080],[1865,15082],{"className":15083},[2119,2120],[1865,15085,15087],{"className":15086},[1906],[1865,15088,15090,15177],{"className":15089},[2091,2092],[1865,15091,15093,15174],{"className":15092},[2096],[1865,15094,15096,15155,15163],{"className":15095,"style":6666},[2100],[1865,15097,15098,15101],{"style":2136},[1865,15099],{"className":15100,"style":2140},[2108],[1865,15102,15104],{"className":15103},[2080],[1865,15105,15107,15110],{"className":15106},[2080],[1865,15108,1798],{"className":15109},[2080,2154],[1865,15111,15113],{"className":15112},[2158],[1865,15114,15116,15147],{"className":15115},[2091,2092],[1865,15117,15119,15144],{"className":15118},[2096],[1865,15120,15122,15133],{"className":15121,"style":14799},[2100],[1865,15123,15124,15127],{"style":14802},[1865,15125],{"className":15126,"style":2175},[2108],[1865,15128,15130],{"className":15129},[2179,2180,2181,2182],[1865,15131,1931],{"className":15132},[2080,2182],[1865,15134,15135,15138],{"style":14814},[1865,15136],{"className":15137,"style":2175},[2108],[1865,15139,15141],{"className":15140},[2179,2180,2181,2182],[1865,15142,1984],{"className":15143},[2080,2182],[1865,15145,2190],{"className":15146},[2189],[1865,15148,15150],{"className":15149},[2096],[1865,15151,15153],{"className":15152,"style":14833},[2100],[1865,15154],{},[1865,15156,15157,15160],{"style":2202},[1865,15158],{"className":15159,"style":2140},[2108],[1865,15161],{"className":15162,"style":2210},[2209],[1865,15164,15165,15168],{"style":2213},[1865,15166],{"className":15167,"style":2140},[2108],[1865,15169,15171],{"className":15170},[2080],[1865,15172,1931],{"className":15173},[2080],[1865,15175,2190],{"className":15176},[2189],[1865,15178,15180],{"className":15179},[2096],[1865,15181,15183],{"className":15182,"style":14864},[2100],[1865,15184],{},[1865,15186],{"className":15187},[2242,2120],[1865,15189],{"className":15190,"style":2693},[2246],[1865,15192,1955],{"className":15193},[2697],[1865,15195],{"className":15196,"style":2693},[2246],[1865,15198,15200,15203,15206,15209,15212],{"className":15199},[2071],[1865,15201],{"className":15202,"style":15003},[2075],[1865,15204,13226],{"className":15205},[2080],[1865,15207],{"className":15208,"style":2247},[2246],[1865,15210,1935],{"className":15211},[2251],[1865,15213],{"className":15214,"style":2247},[2246],[1865,15216,15218,15222],{"className":15217},[2071],[1865,15219],{"className":15220,"style":15221},[2075],"height:2.2019em;vertical-align:-0.8804em;",[1865,15223,15225,15228,15318],{"className":15224},[2080],[1865,15226],{"className":15227},[2119,2120],[1865,15229,15231],{"className":15230},[1906],[1865,15232,15234,15310],{"className":15233},[2091,2092],[1865,15235,15237,15307],{"className":15236},[2096],[1865,15238,15240,15288,15296],{"className":15239,"style":6666},[2100],[1865,15241,15242,15245],{"style":2136},[1865,15243],{"className":15244,"style":2140},[2108],[1865,15246,15248],{"className":15247},[2080],[1865,15249,15251,15254],{"className":15250},[2080],[1865,15252,1798],{"className":15253},[2080,2154],[1865,15255,15257],{"className":15256},[2158],[1865,15258,15260,15280],{"className":15259},[2091,2092],[1865,15261,15263,15277],{"className":15262},[2096],[1865,15264,15266],{"className":15265,"style":2168},[2100],[1865,15267,15268,15271],{"style":2171},[1865,15269],{"className":15270,"style":2175},[2108],[1865,15272,15274],{"className":15273},[2179,2180,2181,2182],[1865,15275,1931],{"className":15276},[2080,2182],[1865,15278,2190],{"className":15279},[2189],[1865,15281,15283],{"className":15282},[2096],[1865,15284,15286],{"className":15285,"style":2197},[2100],[1865,15287],{},[1865,15289,15290,15293],{"style":2202},[1865,15291],{"className":15292,"style":2140},[2108],[1865,15294],{"className":15295,"style":2210},[2209],[1865,15297,15298,15301],{"style":2213},[1865,15299],{"className":15300,"style":2140},[2108],[1865,15302,15304],{"className":15303},[2080],[1865,15305,1931],{"className":15306},[2080],[1865,15308,2190],{"className":15309},[2189],[1865,15311,15313],{"className":15312},[2096],[1865,15314,15316],{"className":15315,"style":3396},[2100],[1865,15317],{},[1865,15319],{"className":15320},[2242,2120],[1798,15322,15323],{},"马歇尔需求：",[1865,15325,15327],{"className":15326},[1868],[1865,15328,15330,15409],{"className":15329},[1872],[1865,15331,15333],{"className":15332},[1876],[1878,15334,15335],{"xmlns":1880,"display":1881},[1883,15336,15337,15406],{},[1903,15338,15339,15345,15347,15353,15355,15357,15369,15371,15374,15380,15382,15388,15390,15392,15394,15396],{},[1923,15340,15341,15343],{},[1911,15342,1927],{},[1929,15344,1931],{},[1933,15346,4942],{"stretchy":3501},[1923,15348,15349,15351],{},[1911,15350,1798],{},[1929,15352,1931],{},[1933,15354,4963],{"stretchy":3501},[1933,15356,1955],{},[1906,15358,15359,15361],{},[1929,15360,1931],{},[8534,15362,15363,15365,15367],{},[1911,15364,1798],{},[1929,15366,1931],{},[1929,15368,1984],{},[1933,15370,2784],{"separator":1901},[2246,15372],{"width":15373},"1em",[1923,15375,15376,15378],{},[1911,15377,1927],{},[1929,15379,1984],{},[1933,15381,4942],{"stretchy":3501},[1923,15383,15384,15386],{},[1911,15385,1798],{},[1929,15387,1931],{},[1933,15389,4963],{"stretchy":3501},[1933,15391,1955],{},[1929,15393,13226],{},[1933,15395,1935],{},[1906,15397,15398,15400],{},[1929,15399,1931],{},[1923,15401,15402,15404],{},[1911,15403,1798],{},[1929,15405,1931],{},[2060,15407,15408],{"encoding":2062},"x_1(p_1) = \\frac{1}{p_1^2}, \\quad x_2(p_1) = 20 - \\frac{1}{p_1}",[1865,15410,15412,15513,15734,15752],{"className":15411,"ariaHidden":1901},[2067],[1865,15413,15415,15418,15458,15461,15501,15504,15507,15510],{"className":15414},[2071],[1865,15416],{"className":15417,"style":5030},[2075],[1865,15419,15421,15424],{"className":15420},[2080],[1865,15422,1927],{"className":15423},[2080,2154],[1865,15425,15427],{"className":15426},[2158],[1865,15428,15430,15450],{"className":15429},[2091,2092],[1865,15431,15433,15447],{"className":15432},[2096],[1865,15434,15436],{"className":15435,"style":2168},[2100],[1865,15437,15438,15441],{"style":2171},[1865,15439],{"className":15440,"style":2175},[2108],[1865,15442,15444],{"className":15443},[2179,2180,2181,2182],[1865,15445,1931],{"className":15446},[2080,2182],[1865,15448,2190],{"className":15449},[2189],[1865,15451,15453],{"className":15452},[2096],[1865,15454,15456],{"className":15455,"style":2197},[2100],[1865,15457],{},[1865,15459,4942],{"className":15460},[2119],[1865,15462,15464,15467],{"className":15463},[2080],[1865,15465,1798],{"className":15466},[2080,2154],[1865,15468,15470],{"className":15469},[2158],[1865,15471,15473,15493],{"className":15472},[2091,2092],[1865,15474,15476,15490],{"className":15475},[2096],[1865,15477,15479],{"className":15478,"style":2168},[2100],[1865,15480,15481,15484],{"style":2171},[1865,15482],{"className":15483,"style":2175},[2108],[1865,15485,15487],{"className":15486},[2179,2180,2181,2182],[1865,15488,1931],{"className":15489},[2080,2182],[1865,15491,2190],{"className":15492},[2189],[1865,15494,15496],{"className":15495},[2096],[1865,15497,15499],{"className":15498,"style":2197},[2100],[1865,15500],{},[1865,15502,4963],{"className":15503},[2242],[1865,15505],{"className":15506,"style":2693},[2246],[1865,15508,1955],{"className":15509},[2697],[1865,15511],{"className":15512,"style":2693},[2246],[1865,15514,15516,15519,15629,15632,15636,15639,15679,15682,15722,15725,15728,15731],{"className":15515},[2071],[1865,15517],{"className":15518,"style":14754},[2075],[1865,15520,15522,15525,15626],{"className":15521},[2080],[1865,15523],{"className":15524},[2119,2120],[1865,15526,15528],{"className":15527},[1906],[1865,15529,15531,15618],{"className":15530},[2091,2092],[1865,15532,15534,15615],{"className":15533},[2096],[1865,15535,15537,15596,15604],{"className":15536,"style":6666},[2100],[1865,15538,15539,15542],{"style":2136},[1865,15540],{"className":15541,"style":2140},[2108],[1865,15543,15545],{"className":15544},[2080],[1865,15546,15548,15551],{"className":15547},[2080],[1865,15549,1798],{"className":15550},[2080,2154],[1865,15552,15554],{"className":15553},[2158],[1865,15555,15557,15588],{"className":15556},[2091,2092],[1865,15558,15560,15585],{"className":15559},[2096],[1865,15561,15563,15574],{"className":15562,"style":14799},[2100],[1865,15564,15565,15568],{"style":14802},[1865,15566],{"className":15567,"style":2175},[2108],[1865,15569,15571],{"className":15570},[2179,2180,2181,2182],[1865,15572,1931],{"className":15573},[2080,2182],[1865,15575,15576,15579],{"style":14814},[1865,15577],{"className":15578,"style":2175},[2108],[1865,15580,15582],{"className":15581},[2179,2180,2181,2182],[1865,15583,1984],{"className":15584},[2080,2182],[1865,15586,2190],{"className":15587},[2189],[1865,15589,15591],{"className":15590},[2096],[1865,15592,15594],{"className":15593,"style":14833},[2100],[1865,15595],{},[1865,15597,15598,15601],{"style":2202},[1865,15599],{"className":15600,"style":2140},[2108],[1865,15602],{"className":15603,"style":2210},[2209],[1865,15605,15606,15609],{"style":2213},[1865,15607],{"className":15608,"style":2140},[2108],[1865,15610,15612],{"className":15611},[2080],[1865,15613,1931],{"className":15614},[2080],[1865,15616,2190],{"className":15617},[2189],[1865,15619,15621],{"className":15620},[2096],[1865,15622,15624],{"className":15623,"style":14864},[2100],[1865,15625],{},[1865,15627],{"className":15628},[2242,2120],[1865,15630,2784],{"className":15631},[2851],[1865,15633],{"className":15634,"style":15635},[2246],"margin-right:1em;",[1865,15637],{"className":15638,"style":2855},[2246],[1865,15640,15642,15645],{"className":15641},[2080],[1865,15643,1927],{"className":15644},[2080,2154],[1865,15646,15648],{"className":15647},[2158],[1865,15649,15651,15671],{"className":15650},[2091,2092],[1865,15652,15654,15668],{"className":15653},[2096],[1865,15655,15657],{"className":15656,"style":2168},[2100],[1865,15658,15659,15662],{"style":2171},[1865,15660],{"className":15661,"style":2175},[2108],[1865,15663,15665],{"className":15664},[2179,2180,2181,2182],[1865,15666,1984],{"className":15667},[2080,2182],[1865,15669,2190],{"className":15670},[2189],[1865,15672,15674],{"className":15673},[2096],[1865,15675,15677],{"className":15676,"style":2197},[2100],[1865,15678],{},[1865,15680,4942],{"className":15681},[2119],[1865,15683,15685,15688],{"className":15684},[2080],[1865,15686,1798],{"className":15687},[2080,2154],[1865,15689,15691],{"className":15690},[2158],[1865,15692,15694,15714],{"className":15693},[2091,2092],[1865,15695,15697,15711],{"className":15696},[2096],[1865,15698,15700],{"className":15699,"style":2168},[2100],[1865,15701,15702,15705],{"style":2171},[1865,15703],{"className":15704,"style":2175},[2108],[1865,15706,15708],{"className":15707},[2179,2180,2181,2182],[1865,15709,1931],{"className":15710},[2080,2182],[1865,15712,2190],{"className":15713},[2189],[1865,15715,15717],{"className":15716},[2096],[1865,15718,15720],{"className":15719,"style":2197},[2100],[1865,15721],{},[1865,15723,4963],{"className":15724},[2242],[1865,15726],{"className":15727,"style":2693},[2246],[1865,15729,1955],{"className":15730},[2697],[1865,15732],{"className":15733,"style":2693},[2246],[1865,15735,15737,15740,15743,15746,15749],{"className":15736},[2071],[1865,15738],{"className":15739,"style":15003},[2075],[1865,15741,13226],{"className":15742},[2080],[1865,15744],{"className":15745,"style":2247},[2246],[1865,15747,1935],{"className":15748},[2251],[1865,15750],{"className":15751,"style":2247},[2246],[1865,15753,15755,15758],{"className":15754},[2071],[1865,15756],{"className":15757,"style":15221},[2075],[1865,15759,15761,15764,15854],{"className":15760},[2080],[1865,15762],{"className":15763},[2119,2120],[1865,15765,15767],{"className":15766},[1906],[1865,15768,15770,15846],{"className":15769},[2091,2092],[1865,15771,15773,15843],{"className":15772},[2096],[1865,15774,15776,15824,15832],{"className":15775,"style":6666},[2100],[1865,15777,15778,15781],{"style":2136},[1865,15779],{"className":15780,"style":2140},[2108],[1865,15782,15784],{"className":15783},[2080],[1865,15785,15787,15790],{"className":15786},[2080],[1865,15788,1798],{"className":15789},[2080,2154],[1865,15791,15793],{"className":15792},[2158],[1865,15794,15796,15816],{"className":15795},[2091,2092],[1865,15797,15799,15813],{"className":15798},[2096],[1865,15800,15802],{"className":15801,"style":2168},[2100],[1865,15803,15804,15807],{"style":2171},[1865,15805],{"className":15806,"style":2175},[2108],[1865,15808,15810],{"className":15809},[2179,2180,2181,2182],[1865,15811,1931],{"className":15812},[2080,2182],[1865,15814,2190],{"className":15815},[2189],[1865,15817,15819],{"className":15818},[2096],[1865,15820,15822],{"className":15821,"style":2197},[2100],[1865,15823],{},[1865,15825,15826,15829],{"style":2202},[1865,15827],{"className":15828,"style":2140},[2108],[1865,15830],{"className":15831,"style":2210},[2209],[1865,15833,15834,15837],{"style":2213},[1865,15835],{"className":15836,"style":2140},[2108],[1865,15838,15840],{"className":15839},[2080],[1865,15841,1931],{"className":15842},[2080],[1865,15844,2190],{"className":15845},[2189],[1865,15847,15849],{"className":15848},[2096],[1865,15850,15852],{"className":15851,"style":3396},[2100],[1865,15853],{},[1865,15855],{"className":15856},[2242,2120],[1798,15858,15859],{},[3048,15860,15861],{},"(2) 计算初始和最终消费",[1805,15863,15864,16310],{},[1808,15865,15866,15867,15972,15973,16168,16169],{},"初始 (",[1865,15868,15870,15894],{"className":15869},[1872],[1865,15871,15873],{"className":15872},[1876],[1878,15874,15875],{"xmlns":1880},[1883,15876,15877,15891],{},[1903,15878,15879,15887,15889],{},[8534,15880,15881,15883,15885],{},[1911,15882,1798],{},[1929,15884,1931],{},[1929,15886,1900],{},[1933,15888,1955],{},[1929,15890,1931],{},[2060,15892,15893],{"encoding":2062},"p_1^0 = 1",[1865,15895,15897,15963],{"className":15896,"ariaHidden":1901},[2067],[1865,15898,15900,15903,15954,15957,15960],{"className":15899},[2071],[1865,15901],{"className":15902,"style":8554},[2075],[1865,15904,15906,15909],{"className":15905},[2080],[1865,15907,1798],{"className":15908},[2080,2154],[1865,15910,15912],{"className":15911},[2158],[1865,15913,15915,15946],{"className":15914},[2091,2092],[1865,15916,15918,15943],{"className":15917},[2096],[1865,15919,15921,15932],{"className":15920,"style":8573},[2100],[1865,15922,15923,15926],{"style":8576},[1865,15924],{"className":15925,"style":2175},[2108],[1865,15927,15929],{"className":15928},[2179,2180,2181,2182],[1865,15930,1931],{"className":15931},[2080,2182],[1865,15933,15934,15937],{"style":7519},[1865,15935],{"className":15936,"style":2175},[2108],[1865,15938,15940],{"className":15939},[2179,2180,2181,2182],[1865,15941,1900],{"className":15942},[2080,2182],[1865,15944,2190],{"className":15945},[2189],[1865,15947,15949],{"className":15948},[2096],[1865,15950,15952],{"className":15951,"style":8606},[2100],[1865,15953],{},[1865,15955],{"className":15956,"style":2693},[2246],[1865,15958,1955],{"className":15959},[2697],[1865,15961],{"className":15962,"style":2693},[2246],[1865,15964,15966,15969],{"className":15965},[2071],[1865,15967],{"className":15968,"style":7553},[2075],[1865,15970,1931],{"className":15971},[2080],"): ",[1865,15974,15976,16015],{"className":15975},[1872],[1865,15977,15979],{"className":15978},[1876],[1878,15980,15981],{"xmlns":1880},[1883,15982,15983,16012],{},[1903,15984,15985,15993,15995,15997,15999,16007,16009],{},[8534,15986,15987,15989,15991],{},[1911,15988,1927],{},[1929,15990,1931],{},[1929,15992,1900],{},[1933,15994,1955],{},[1929,15996,1931],{},[1933,15998,2784],{"separator":1901},[8534,16000,16001,16003,16005],{},[1911,16002,1927],{},[1929,16004,1984],{},[1929,16006,1900],{},[1933,16008,1955],{},[1929,16010,16011],{},"19",[2060,16013,16014],{"encoding":2062},"x_1^0 = 1, x_2^0 = 19",[1865,16016,16018,16084,16159],{"className":16017,"ariaHidden":1901},[2067],[1865,16019,16021,16024,16075,16078,16081],{"className":16020},[2071],[1865,16022],{"className":16023,"style":8554},[2075],[1865,16025,16027,16030],{"className":16026},[2080],[1865,16028,1927],{"className":16029},[2080,2154],[1865,16031,16033],{"className":16032},[2158],[1865,16034,16036,16067],{"className":16035},[2091,2092],[1865,16037,16039,16064],{"className":16038},[2096],[1865,16040,16042,16053],{"className":16041,"style":8573},[2100],[1865,16043,16044,16047],{"style":8576},[1865,16045],{"className":16046,"style":2175},[2108],[1865,16048,16050],{"className":16049},[2179,2180,2181,2182],[1865,16051,1931],{"className":16052},[2080,2182],[1865,16054,16055,16058],{"style":7519},[1865,16056],{"className":16057,"style":2175},[2108],[1865,16059,16061],{"className":16060},[2179,2180,2181,2182],[1865,16062,1900],{"className":16063},[2080,2182],[1865,16065,2190],{"className":16066},[2189],[1865,16068,16070],{"className":16069},[2096],[1865,16071,16073],{"className":16072,"style":8606},[2100],[1865,16074],{},[1865,16076],{"className":16077,"style":2693},[2246],[1865,16079,1955],{"className":16080},[2697],[1865,16082],{"className":16083,"style":2693},[2246],[1865,16085,16087,16090,16093,16096,16099,16150,16153,16156],{"className":16086},[2071],[1865,16088],{"className":16089,"style":8554},[2075],[1865,16091,1931],{"className":16092},[2080],[1865,16094,2784],{"className":16095},[2851],[1865,16097],{"className":16098,"style":2855},[2246],[1865,16100,16102,16105],{"className":16101},[2080],[1865,16103,1927],{"className":16104},[2080,2154],[1865,16106,16108],{"className":16107},[2158],[1865,16109,16111,16142],{"className":16110},[2091,2092],[1865,16112,16114,16139],{"className":16113},[2096],[1865,16115,16117,16128],{"className":16116,"style":8573},[2100],[1865,16118,16119,16122],{"style":8576},[1865,16120],{"className":16121,"style":2175},[2108],[1865,16123,16125],{"className":16124},[2179,2180,2181,2182],[1865,16126,1984],{"className":16127},[2080,2182],[1865,16129,16130,16133],{"style":7519},[1865,16131],{"className":16132,"style":2175},[2108],[1865,16134,16136],{"className":16135},[2179,2180,2181,2182],[1865,16137,1900],{"className":16138},[2080,2182],[1865,16140,2190],{"className":16141},[2189],[1865,16143,16145],{"className":16144},[2096],[1865,16146,16148],{"className":16147,"style":8606},[2100],[1865,16149],{},[1865,16151],{"className":16152,"style":2693},[2246],[1865,16154,1955],{"className":16155},[2697],[1865,16157],{"className":16158,"style":2693},[2246],[1865,16160,16162,16165],{"className":16161},[2071],[1865,16163],{"className":16164,"style":7553},[2075],[1865,16166,16011],{"className":16167},[2080],", ",[1865,16170,16172,16209],{"className":16171},[1872],[1865,16173,16175],{"className":16174},[1876],[1878,16176,16177],{"xmlns":1880},[1883,16178,16179,16206],{},[1903,16180,16181,16187,16189,16191,16193,16195,16197,16199,16201,16203],{},[6885,16182,16183,16185],{},[1911,16184,3508],{},[1929,16186,1900],{},[1933,16188,1955],{},[1929,16190,1984],{},[1933,16192,4942],{"stretchy":3501},[1929,16194,1931],{},[1933,16196,4963],{"stretchy":3501},[1933,16198,2029],{},[1929,16200,16011],{},[1933,16202,1955],{},[1929,16204,16205],{},"21",[2060,16207,16208],{"encoding":2062},"u^0 = 2(1) + 19 = 21",[1865,16210,16212,16256,16283,16301],{"className":16211,"ariaHidden":1901},[2067],[1865,16213,16215,16218,16247,16250,16253],{"className":16214},[2071],[1865,16216],{"className":16217,"style":8573},[2075],[1865,16219,16221,16224],{"className":16220},[2080],[1865,16222,3508],{"className":16223},[2080,2154],[1865,16225,16227],{"className":16226},[2158],[1865,16228,16230],{"className":16229},[2091],[1865,16231,16233],{"className":16232},[2096],[1865,16234,16236],{"className":16235,"style":8573},[2100],[1865,16237,16238,16241],{"style":7519},[1865,16239],{"className":16240,"style":2175},[2108],[1865,16242,16244],{"className":16243},[2179,2180,2181,2182],[1865,16245,1900],{"className":16246},[2080,2182],[1865,16248],{"className":16249,"style":2693},[2246],[1865,16251,1955],{"className":16252},[2697],[1865,16254],{"className":16255,"style":2693},[2246],[1865,16257,16259,16262,16265,16268,16271,16274,16277,16280],{"className":16258},[2071],[1865,16260],{"className":16261,"style":5030},[2075],[1865,16263,1984],{"className":16264},[2080],[1865,16266,4942],{"className":16267},[2119],[1865,16269,1931],{"className":16270},[2080],[1865,16272,4963],{"className":16273},[2242],[1865,16275],{"className":16276,"style":2247},[2246],[1865,16278,2029],{"className":16279},[2251],[1865,16281],{"className":16282,"style":2247},[2246],[1865,16284,16286,16289,16292,16295,16298],{"className":16285},[2071],[1865,16287],{"className":16288,"style":7553},[2075],[1865,16290,16011],{"className":16291},[2080],[1865,16293],{"className":16294,"style":2693},[2246],[1865,16296,1955],{"className":16297},[2697],[1865,16299],{"className":16300,"style":2693},[2246],[1865,16302,16304,16307],{"className":16303},[2071],[1865,16305],{"className":16306,"style":7553},[2075],[1865,16308,16205],{"className":16309},[2080],[1808,16311,16312,16313,15972,16417,16168,16619],{},"最终 (",[1865,16314,16316,16339],{"className":16315},[1872],[1865,16317,16319],{"className":16318},[1876],[1878,16320,16321],{"xmlns":1880},[1883,16322,16323,16337],{},[1903,16324,16325,16333,16335],{},[8534,16326,16327,16329,16331],{},[1911,16328,1798],{},[1929,16330,1931],{},[1929,16332,1931],{},[1933,16334,1955],{},[1929,16336,13355],{},[2060,16338,13358],{"encoding":2062},[1865,16340,16342,16408],{"className":16341,"ariaHidden":1901},[2067],[1865,16343,16345,16348,16399,16402,16405],{"className":16344},[2071],[1865,16346],{"className":16347,"style":8554},[2075],[1865,16349,16351,16354],{"className":16350},[2080],[1865,16352,1798],{"className":16353},[2080,2154],[1865,16355,16357],{"className":16356},[2158],[1865,16358,16360,16391],{"className":16359},[2091,2092],[1865,16361,16363,16388],{"className":16362},[2096],[1865,16364,16366,16377],{"className":16365,"style":8573},[2100],[1865,16367,16368,16371],{"style":8576},[1865,16369],{"className":16370,"style":2175},[2108],[1865,16372,16374],{"className":16373},[2179,2180,2181,2182],[1865,16375,1931],{"className":16376},[2080,2182],[1865,16378,16379,16382],{"style":7519},[1865,16380],{"className":16381,"style":2175},[2108],[1865,16383,16385],{"className":16384},[2179,2180,2181,2182],[1865,16386,1931],{"className":16387},[2080,2182],[1865,16389,2190],{"className":16390},[2189],[1865,16392,16394],{"className":16393},[2096],[1865,16395,16397],{"className":16396,"style":8606},[2100],[1865,16398],{},[1865,16400],{"className":16401,"style":2693},[2246],[1865,16403,1955],{"className":16404},[2697],[1865,16406],{"className":16407,"style":2693},[2246],[1865,16409,16411,16414],{"className":16410},[2071],[1865,16412],{"className":16413,"style":7553},[2075],[1865,16415,13355],{"className":16416},[2080],[1865,16418,16420,16465],{"className":16419},[1872],[1865,16421,16423],{"className":16422},[1876],[1878,16424,16425],{"xmlns":1880},[1883,16426,16427,16462],{},[1903,16428,16429,16437,16439,16441,16444,16447,16449,16457,16459],{},[8534,16430,16431,16433,16435],{},[1911,16432,1927],{},[1929,16434,1931],{},[1929,16436,1931],{},[1933,16438,1955],{},[1929,16440,1931],{},[1911,16442,16443],{"mathvariant":1913},"\u002F",[1929,16445,16446],{},"16",[1933,16448,2784],{"separator":1901},[8534,16450,16451,16453,16455],{},[1911,16452,1927],{},[1929,16454,1984],{},[1929,16456,1931],{},[1933,16458,1955],{},[1929,16460,16461],{},"19.75",[2060,16463,16464],{"encoding":2062},"x_1^1 = 1\u002F16, x_2^1 = 19.75",[1865,16466,16468,16534,16610],{"className":16467,"ariaHidden":1901},[2067],[1865,16469,16471,16474,16525,16528,16531],{"className":16470},[2071],[1865,16472],{"className":16473,"style":8554},[2075],[1865,16475,16477,16480],{"className":16476},[2080],[1865,16478,1927],{"className":16479},[2080,2154],[1865,16481,16483],{"className":16482},[2158],[1865,16484,16486,16517],{"className":16485},[2091,2092],[1865,16487,16489,16514],{"className":16488},[2096],[1865,16490,16492,16503],{"className":16491,"style":8573},[2100],[1865,16493,16494,16497],{"style":8576},[1865,16495],{"className":16496,"style":2175},[2108],[1865,16498,16500],{"className":16499},[2179,2180,2181,2182],[1865,16501,1931],{"className":16502},[2080,2182],[1865,16504,16505,16508],{"style":7519},[1865,16506],{"className":16507,"style":2175},[2108],[1865,16509,16511],{"className":16510},[2179,2180,2181,2182],[1865,16512,1931],{"className":16513},[2080,2182],[1865,16515,2190],{"className":16516},[2189],[1865,16518,16520],{"className":16519},[2096],[1865,16521,16523],{"className":16522,"style":8606},[2100],[1865,16524],{},[1865,16526],{"className":16527,"style":2693},[2246],[1865,16529,1955],{"className":16530},[2697],[1865,16532],{"className":16533,"style":2693},[2246],[1865,16535,16537,16540,16544,16547,16550,16601,16604,16607],{"className":16536},[2071],[1865,16538],{"className":16539,"style":9243},[2075],[1865,16541,16543],{"className":16542},[2080],"1\u002F16",[1865,16545,2784],{"className":16546},[2851],[1865,16548],{"className":16549,"style":2855},[2246],[1865,16551,16553,16556],{"className":16552},[2080],[1865,16554,1927],{"className":16555},[2080,2154],[1865,16557,16559],{"className":16558},[2158],[1865,16560,16562,16593],{"className":16561},[2091,2092],[1865,16563,16565,16590],{"className":16564},[2096],[1865,16566,16568,16579],{"className":16567,"style":8573},[2100],[1865,16569,16570,16573],{"style":8576},[1865,16571],{"className":16572,"style":2175},[2108],[1865,16574,16576],{"className":16575},[2179,2180,2181,2182],[1865,16577,1984],{"className":16578},[2080,2182],[1865,16580,16581,16584],{"style":7519},[1865,16582],{"className":16583,"style":2175},[2108],[1865,16585,16587],{"className":16586},[2179,2180,2181,2182],[1865,16588,1931],{"className":16589},[2080,2182],[1865,16591,2190],{"className":16592},[2189],[1865,16594,16596],{"className":16595},[2096],[1865,16597,16599],{"className":16598,"style":8606},[2100],[1865,16600],{},[1865,16602],{"className":16603,"style":2693},[2246],[1865,16605,1955],{"className":16606},[2697],[1865,16608],{"className":16609,"style":2693},[2246],[1865,16611,16613,16616],{"className":16612},[2071],[1865,16614],{"className":16615,"style":7553},[2075],[1865,16617,16461],{"className":16618},[2080],[1865,16620,16622,16663],{"className":16621},[1872],[1865,16623,16625],{"className":16624},[1876],[1878,16626,16627],{"xmlns":1880},[1883,16628,16629,16660],{},[1903,16630,16631,16637,16639,16641,16643,16645,16647,16649,16651,16653,16655,16657],{},[6885,16632,16633,16635],{},[1911,16634,3508],{},[1929,16636,1931],{},[1933,16638,1955],{},[1929,16640,1984],{},[1933,16642,4942],{"stretchy":3501},[1929,16644,1931],{},[1911,16646,16443],{"mathvariant":1913},[1929,16648,13355],{},[1933,16650,4963],{"stretchy":3501},[1933,16652,2029],{},[1929,16654,16461],{},[1933,16656,1955],{},[1929,16658,16659],{},"20.25",[2060,16661,16662],{"encoding":2062},"u^1 = 2(1\u002F4) + 19.75 = 20.25",[1865,16664,16666,16710,16738,16756],{"className":16665,"ariaHidden":1901},[2067],[1865,16667,16669,16672,16701,16704,16707],{"className":16668},[2071],[1865,16670],{"className":16671,"style":8573},[2075],[1865,16673,16675,16678],{"className":16674},[2080],[1865,16676,3508],{"className":16677},[2080,2154],[1865,16679,16681],{"className":16680},[2158],[1865,16682,16684],{"className":16683},[2091],[1865,16685,16687],{"className":16686},[2096],[1865,16688,16690],{"className":16689,"style":8573},[2100],[1865,16691,16692,16695],{"style":7519},[1865,16693],{"className":16694,"style":2175},[2108],[1865,16696,16698],{"className":16697},[2179,2180,2181,2182],[1865,16699,1931],{"className":16700},[2080,2182],[1865,16702],{"className":16703,"style":2693},[2246],[1865,16705,1955],{"className":16706},[2697],[1865,16708],{"className":16709,"style":2693},[2246],[1865,16711,16713,16716,16719,16722,16726,16729,16732,16735],{"className":16712},[2071],[1865,16714],{"className":16715,"style":5030},[2075],[1865,16717,1984],{"className":16718},[2080],[1865,16720,4942],{"className":16721},[2119],[1865,16723,16725],{"className":16724},[2080],"1\u002F4",[1865,16727,4963],{"className":16728},[2242],[1865,16730],{"className":16731,"style":2247},[2246],[1865,16733,2029],{"className":16734},[2251],[1865,16736],{"className":16737,"style":2247},[2246],[1865,16739,16741,16744,16747,16750,16753],{"className":16740},[2071],[1865,16742],{"className":16743,"style":7553},[2075],[1865,16745,16461],{"className":16746},[2080],[1865,16748],{"className":16749,"style":2693},[2246],[1865,16751,1955],{"className":16752},[2697],[1865,16754],{"className":16755,"style":2693},[2246],[1865,16757,16759,16762],{"className":16758},[2071],[1865,16760],{"className":16761,"style":7553},[2075],[1865,16763,16659],{"className":16764},[2080],[1798,16766,16767],{},[3048,16768,16769],{},"(3) 计算CV",[1798,16771,16772],{},"需要求支出函数。对于拟线性效用，EMP为：",[1865,16774,16776],{"className":16775},[1868],[1865,16777,16779,16855],{"className":16778},[1872],[1865,16780,16782],{"className":16781},[1876],[1878,16783,16784],{"xmlns":1880,"display":1881},[1883,16785,16786,16852],{},[1903,16787,16788,16791,16794,16800,16806,16808,16814,16816,16819,16822,16825,16827,16829,16831,16839,16841,16847,16850],{},[1911,16789,16790],{},"min",[1933,16792,16793],{},"⁡",[1923,16795,16796,16798],{},[1911,16797,1798],{},[1929,16799,1931],{},[1923,16801,16802,16804],{},[1911,16803,1927],{},[1929,16805,1931],{},[1933,16807,2029],{},[1923,16809,16810,16812],{},[1911,16811,1927],{},[1929,16813,1984],{},[2246,16815],{"width":15373},[1911,16817,16818],{},"s",[1911,16820,16821],{"mathvariant":1913},".",[1911,16823,16824],{},"t",[1911,16826,16821],{"mathvariant":1913},[2246,16828],{"width":15373},[1929,16830,1984],{},[12729,16832,16833],{},[1923,16834,16835,16837],{},[1911,16836,1927],{},[1929,16838,1931],{},[1933,16840,2029],{},[1923,16842,16843,16845],{},[1911,16844,1927],{},[1929,16846,1984],{},[1933,16848,16849],{},"≥",[1911,16851,3508],{},[2060,16853,16854],{"encoding":2062},"\\min p_1 x_1 + x_2 \\quad s.t. \\quad 2\\sqrt{x_1} + x_2 \\ge u",[1865,16856,16858,16960,17120,17176],{"className":16857,"ariaHidden":1901},[2067],[1865,16859,16861,16865,16868,16871,16911,16951,16954,16957],{"className":16860},[2071],[1865,16862],{"className":16863,"style":16864},[2075],"height:0.8623em;vertical-align:-0.1944em;",[1865,16866,16790],{"className":16867},[11465],[1865,16869],{"className":16870,"style":2855},[2246],[1865,16872,16874,16877],{"className":16873},[2080],[1865,16875,1798],{"className":16876},[2080,2154],[1865,16878,16880],{"className":16879},[2158],[1865,16881,16883,16903],{"className":16882},[2091,2092],[1865,16884,16886,16900],{"className":16885},[2096],[1865,16887,16889],{"className":16888,"style":2168},[2100],[1865,16890,16891,16894],{"style":2171},[1865,16892],{"className":16893,"style":2175},[2108],[1865,16895,16897],{"className":16896},[2179,2180,2181,2182],[1865,16898,1931],{"className":16899},[2080,2182],[1865,16901,2190],{"className":16902},[2189],[1865,16904,16906],{"className":16905},[2096],[1865,16907,16909],{"className":16908,"style":2197},[2100],[1865,16910],{},[1865,16912,16914,16917],{"className":16913},[2080],[1865,16915,1927],{"className":16916},[2080,2154],[1865,16918,16920],{"className":16919},[2158],[1865,16921,16923,16943],{"className":16922},[2091,2092],[1865,16924,16926,16940],{"className":16925},[2096],[1865,16927,16929],{"className":16928,"style":2168},[2100],[1865,16930,16931,16934],{"style":2171},[1865,16932],{"className":16933,"style":2175},[2108],[1865,16935,16937],{"className":16936},[2179,2180,2181,2182],[1865,16938,1931],{"className":16939},[2080,2182],[1865,16941,2190],{"className":16942},[2189],[1865,16944,16946],{"className":16945},[2096],[1865,16947,16949],{"className":16948,"style":2197},[2100],[1865,16950],{},[1865,16952],{"className":16953,"style":2247},[2246],[1865,16955,2029],{"className":16956},[2251],[1865,16958],{"className":16959,"style":2247},[2246],[1865,16961,16963,16966,17006,17009,17012,17015,17018,17021,17024,17027,17111,17114,17117],{"className":16962},[2071],[1865,16964],{"className":16965,"style":13593},[2075],[1865,16967,16969,16972],{"className":16968},[2080],[1865,16970,1927],{"className":16971},[2080,2154],[1865,16973,16975],{"className":16974},[2158],[1865,16976,16978,16998],{"className":16977},[2091,2092],[1865,16979,16981,16995],{"className":16980},[2096],[1865,16982,16984],{"className":16983,"style":2168},[2100],[1865,16985,16986,16989],{"style":2171},[1865,16987],{"className":16988,"style":2175},[2108],[1865,16990,16992],{"className":16991},[2179,2180,2181,2182],[1865,16993,1984],{"className":16994},[2080,2182],[1865,16996,2190],{"className":16997},[2189],[1865,16999,17001],{"className":17000},[2096],[1865,17002,17004],{"className":17003,"style":2197},[2100],[1865,17005],{},[1865,17007],{"className":17008,"style":15635},[2246],[1865,17010,16818],{"className":17011},[2080,2154],[1865,17013,16821],{"className":17014},[2080],[1865,17016,16824],{"className":17017},[2080,2154],[1865,17019,16821],{"className":17020},[2080],[1865,17022],{"className":17023,"style":15635},[2246],[1865,17025,1984],{"className":17026},[2080],[1865,17028,17030],{"className":17029},[2080,12874],[1865,17031,17033,17103],{"className":17032},[2091,2092],[1865,17034,17036,17100],{"className":17035},[2096],[1865,17037,17039,17088],{"className":17038,"style":13609},[2100],[1865,17040,17042,17045],{"className":17041,"style":12889},[12888],[1865,17043],{"className":17044,"style":2140},[2108],[1865,17046,17048],{"className":17047,"style":12896},[2080],[1865,17049,17051,17054],{"className":17050},[2080],[1865,17052,1927],{"className":17053},[2080,2154],[1865,17055,17057],{"className":17056},[2158],[1865,17058,17060,17080],{"className":17059},[2091,2092],[1865,17061,17063,17077],{"className":17062},[2096],[1865,17064,17066],{"className":17065,"style":2168},[2100],[1865,17067,17068,17071],{"style":2171},[1865,17069],{"className":17070,"style":2175},[2108],[1865,17072,17074],{"className":17073},[2179,2180,2181,2182],[1865,17075,1931],{"className":17076},[2080,2182],[1865,17078,2190],{"className":17079},[2189],[1865,17081,17083],{"className":17082},[2096],[1865,17084,17086],{"className":17085,"style":2197},[2100],[1865,17087],{},[1865,17089,17090,17093],{"style":13661},[1865,17091],{"className":17092,"style":2140},[2108],[1865,17094,17096],{"className":17095,"style":12947},[12946],[3893,17097,17098],{"xmlns":3895,"width":12950,"height":12951,"viewBox":12952,"preserveAspectRatio":12953},[3899,17099],{"d":12956},[1865,17101,2190],{"className":17102},[2189],[1865,17104,17106],{"className":17105},[2096],[1865,17107,17109],{"className":17108,"style":13681},[2100],[1865,17110],{},[1865,17112],{"className":17113,"style":2247},[2246],[1865,17115,2029],{"className":17116},[2251],[1865,17118],{"className":17119,"style":2247},[2246],[1865,17121,17123,17127,17167,17170,17173],{"className":17122},[2071],[1865,17124],{"className":17125,"style":17126},[2075],"height:0.786em;vertical-align:-0.15em;",[1865,17128,17130,17133],{"className":17129},[2080],[1865,17131,1927],{"className":17132},[2080,2154],[1865,17134,17136],{"className":17135},[2158],[1865,17137,17139,17159],{"className":17138},[2091,2092],[1865,17140,17142,17156],{"className":17141},[2096],[1865,17143,17145],{"className":17144,"style":2168},[2100],[1865,17146,17147,17150],{"style":2171},[1865,17148],{"className":17149,"style":2175},[2108],[1865,17151,17153],{"className":17152},[2179,2180,2181,2182],[1865,17154,1984],{"className":17155},[2080,2182],[1865,17157,2190],{"className":17158},[2189],[1865,17160,17162],{"className":17161},[2096],[1865,17163,17165],{"className":17164,"style":2197},[2100],[1865,17166],{},[1865,17168],{"className":17169,"style":2693},[2246],[1865,17171,16849],{"className":17172},[2697],[1865,17174],{"className":17175,"style":2693},[2246],[1865,17177,17179,17182],{"className":17178},[2071],[1865,17180],{"className":17181,"style":6852},[2075],[1865,17183,3508],{"className":17184},[2080,2154],[1798,17186,17187,17188,17342],{},"一阶条件给出：",[1865,17189,17191,17223],{"className":17190},[1872],[1865,17192,17194],{"className":17193},[1876],[1878,17195,17196],{"xmlns":1880},[1883,17197,17198,17220],{},[1903,17199,17200,17206,17208,17210,17212],{},[1923,17201,17202,17204],{},[1911,17203,1927],{},[1929,17205,1931],{},[1933,17207,1955],{},[1929,17209,1931],{},[1911,17211,16443],{"mathvariant":1913},[8534,17213,17214,17216,17218],{},[1911,17215,1798],{},[1929,17217,1931],{},[1929,17219,1984],{},[2060,17221,17222],{"encoding":2062},"x_1 = 1\u002Fp_1^2",[1865,17224,17226,17281],{"className":17225,"ariaHidden":1901},[2067],[1865,17227,17229,17232,17272,17275,17278],{"className":17228},[2071],[1865,17230],{"className":17231,"style":12589},[2075],[1865,17233,17235,17238],{"className":17234},[2080],[1865,17236,1927],{"className":17237},[2080,2154],[1865,17239,17241],{"className":17240},[2158],[1865,17242,17244,17264],{"className":17243},[2091,2092],[1865,17245,17247,17261],{"className":17246},[2096],[1865,17248,17250],{"className":17249,"style":2168},[2100],[1865,17251,17252,17255],{"style":2171},[1865,17253],{"className":17254,"style":2175},[2108],[1865,17256,17258],{"className":17257},[2179,2180,2181,2182],[1865,17259,1931],{"className":17260},[2080,2182],[1865,17262,2190],{"className":17263},[2189],[1865,17265,17267],{"className":17266},[2096],[1865,17268,17270],{"className":17269,"style":2197},[2100],[1865,17271],{},[1865,17273],{"className":17274,"style":2693},[2246],[1865,17276,1955],{"className":17277},[2697],[1865,17279],{"className":17280,"style":2693},[2246],[1865,17282,17284,17287,17291],{"className":17283},[2071],[1865,17285],{"className":17286,"style":9243},[2075],[1865,17288,17290],{"className":17289},[2080],"1\u002F",[1865,17292,17294,17297],{"className":17293},[2080],[1865,17295,1798],{"className":17296},[2080,2154],[1865,17298,17300],{"className":17299},[2158],[1865,17301,17303,17334],{"className":17302},[2091,2092],[1865,17304,17306,17331],{"className":17305},[2096],[1865,17307,17309,17320],{"className":17308,"style":8573},[2100],[1865,17310,17311,17314],{"style":8576},[1865,17312],{"className":17313,"style":2175},[2108],[1865,17315,17317],{"className":17316},[2179,2180,2181,2182],[1865,17318,1931],{"className":17319},[2080,2182],[1865,17321,17322,17325],{"style":7519},[1865,17323],{"className":17324,"style":2175},[2108],[1865,17326,17328],{"className":17327},[2179,2180,2181,2182],[1865,17329,1984],{"className":17330},[2080,2182],[1865,17332,2190],{"className":17333},[2189],[1865,17335,17337],{"className":17336},[2096],[1865,17338,17340],{"className":17339,"style":8606},[2100],[1865,17341],{},"（与价格有关，与效用无关！）",[1798,17344,17345,17346],{},"代入约束：",[1865,17347,17349,17383],{"className":17348},[1872],[1865,17350,17352],{"className":17351},[1876],[1878,17353,17354],{"xmlns":1880},[1883,17355,17356,17380],{},[1903,17357,17358,17364,17366,17368,17370,17372,17374],{},[1923,17359,17360,17362],{},[1911,17361,1927],{},[1929,17363,1984],{},[1933,17365,1955],{},[1911,17367,3508],{},[1933,17369,1935],{},[1929,17371,1984],{},[1911,17373,16443],{"mathvariant":1913},[1923,17375,17376,17378],{},[1911,17377,1798],{},[1929,17379,1931],{},[2060,17381,17382],{"encoding":2062},"x_2 = u - 2\u002Fp_1",[1865,17384,17386,17441,17459],{"className":17385,"ariaHidden":1901},[2067],[1865,17387,17389,17392,17432,17435,17438],{"className":17388},[2071],[1865,17390],{"className":17391,"style":12589},[2075],[1865,17393,17395,17398],{"className":17394},[2080],[1865,17396,1927],{"className":17397},[2080,2154],[1865,17399,17401],{"className":17400},[2158],[1865,17402,17404,17424],{"className":17403},[2091,2092],[1865,17405,17407,17421],{"className":17406},[2096],[1865,17408,17410],{"className":17409,"style":2168},[2100],[1865,17411,17412,17415],{"style":2171},[1865,17413],{"className":17414,"style":2175},[2108],[1865,17416,17418],{"className":17417},[2179,2180,2181,2182],[1865,17419,1984],{"className":17420},[2080,2182],[1865,17422,2190],{"className":17423},[2189],[1865,17425,17427],{"className":17426},[2096],[1865,17428,17430],{"className":17429,"style":2197},[2100],[1865,17431],{},[1865,17433],{"className":17434,"style":2693},[2246],[1865,17436,1955],{"className":17437},[2697],[1865,17439],{"className":17440,"style":2693},[2246],[1865,17442,17444,17447,17450,17453,17456],{"className":17443},[2071],[1865,17445],{"className":17446,"style":10638},[2075],[1865,17448,3508],{"className":17449},[2080,2154],[1865,17451],{"className":17452,"style":2247},[2246],[1865,17454,1935],{"className":17455},[2251],[1865,17457],{"className":17458,"style":2247},[2246],[1865,17460,17462,17465,17469],{"className":17461},[2071],[1865,17463],{"className":17464,"style":5030},[2075],[1865,17466,17468],{"className":17467},[2080],"2\u002F",[1865,17470,17472,17475],{"className":17471},[2080],[1865,17473,1798],{"className":17474},[2080,2154],[1865,17476,17478],{"className":17477},[2158],[1865,17479,17481,17501],{"className":17480},[2091,2092],[1865,17482,17484,17498],{"className":17483},[2096],[1865,17485,17487],{"className":17486,"style":2168},[2100],[1865,17488,17489,17492],{"style":2171},[1865,17490],{"className":17491,"style":2175},[2108],[1865,17493,17495],{"className":17494},[2179,2180,2181,2182],[1865,17496,1931],{"className":17497},[2080,2182],[1865,17499,2190],{"className":17500},[2189],[1865,17502,17504],{"className":17503},[2096],[1865,17505,17507],{"className":17506,"style":2197},[2100],[1865,17508],{},[1798,17510,17511],{},"支出函数：",[1865,17513,17515],{"className":17514},[1868],[1865,17516,17518,17600],{"className":17517},[1872],[1865,17519,17521],{"className":17520},[1876],[1878,17522,17523],{"xmlns":1880,"display":1881},[1883,17524,17525,17597],{},[1903,17526,17527,17529,17531,17537,17539,17541,17543,17545,17551,17553,17565,17567,17569,17571,17581,17583,17585,17587],{},[1911,17528,8742],{},[1933,17530,4942],{"stretchy":3501},[1923,17532,17533,17535],{},[1911,17534,1798],{},[1929,17536,1931],{},[1933,17538,2784],{"separator":1901},[1911,17540,3508],{},[1933,17542,4963],{"stretchy":3501},[1933,17544,1955],{},[1923,17546,17547,17549],{},[1911,17548,1798],{},[1929,17550,1931],{},[1933,17552,5600],{},[1906,17554,17555,17557],{},[1929,17556,1931],{},[8534,17558,17559,17561,17563],{},[1911,17560,1798],{},[1929,17562,1931],{},[1929,17564,1984],{},[1933,17566,2029],{},[1911,17568,3508],{},[1933,17570,1935],{},[1906,17572,17573,17575],{},[1929,17574,1984],{},[1923,17576,17577,17579],{},[1911,17578,1798],{},[1929,17580,1931],{},[1933,17582,1955],{},[1911,17584,3508],{},[1933,17586,1935],{},[1906,17588,17589,17591],{},[1929,17590,1931],{},[1923,17592,17593,17595],{},[1911,17594,1798],{},[1929,17596,1931],{},[2060,17598,17599],{"encoding":2062},"e(p_1, u) = p_1 \\cdot \\frac{1}{p_1^2} + u - \\frac{2}{p_1} = u - \\frac{1}{p_1}",[1865,17601,17603,17676,17731,17856,17874,17988,18006],{"className":17602,"ariaHidden":1901},[2067],[1865,17604,17606,17609,17612,17615,17655,17658,17661,17664,17667,17670,17673],{"className":17605},[2071],[1865,17607],{"className":17608,"style":5030},[2075],[1865,17610,8742],{"className":17611},[2080,2154],[1865,17613,4942],{"className":17614},[2119],[1865,17616,17618,17621],{"className":17617},[2080],[1865,17619,1798],{"className":17620},[2080,2154],[1865,17622,17624],{"className":17623},[2158],[1865,17625,17627,17647],{"className":17626},[2091,2092],[1865,17628,17630,17644],{"className":17629},[2096],[1865,17631,17633],{"className":17632,"style":2168},[2100],[1865,17634,17635,17638],{"style":2171},[1865,17636],{"className":17637,"style":2175},[2108],[1865,17639,17641],{"className":17640},[2179,2180,2181,2182],[1865,17642,1931],{"className":17643},[2080,2182],[1865,17645,2190],{"className":17646},[2189],[1865,17648,17650],{"className":17649},[2096],[1865,17651,17653],{"className":17652,"style":2197},[2100],[1865,17654],{},[1865,17656,2784],{"className":17657},[2851],[1865,17659],{"className":17660,"style":2855},[2246],[1865,17662,3508],{"className":17663},[2080,2154],[1865,17665,4963],{"className":17666},[2242],[1865,17668],{"className":17669,"style":2693},[2246],[1865,17671,1955],{"className":17672},[2697],[1865,17674],{"className":17675,"style":2693},[2246],[1865,17677,17679,17682,17722,17725,17728],{"className":17678},[2071],[1865,17680],{"className":17681,"style":15022},[2075],[1865,17683,17685,17688],{"className":17684},[2080],[1865,17686,1798],{"className":17687},[2080,2154],[1865,17689,17691],{"className":17690},[2158],[1865,17692,17694,17714],{"className":17693},[2091,2092],[1865,17695,17697,17711],{"className":17696},[2096],[1865,17698,17700],{"className":17699,"style":2168},[2100],[1865,17701,17702,17705],{"style":2171},[1865,17703],{"className":17704,"style":2175},[2108],[1865,17706,17708],{"className":17707},[2179,2180,2181,2182],[1865,17709,1931],{"className":17710},[2080,2182],[1865,17712,2190],{"className":17713},[2189],[1865,17715,17717],{"className":17716},[2096],[1865,17718,17720],{"className":17719,"style":2197},[2100],[1865,17721],{},[1865,17723],{"className":17724,"style":2247},[2246],[1865,17726,5600],{"className":17727},[2251],[1865,17729],{"className":17730,"style":2247},[2246],[1865,17732,17734,17737,17847,17850,17853],{"className":17733},[2071],[1865,17735],{"className":17736,"style":14754},[2075],[1865,17738,17740,17743,17844],{"className":17739},[2080],[1865,17741],{"className":17742},[2119,2120],[1865,17744,17746],{"className":17745},[1906],[1865,17747,17749,17836],{"className":17748},[2091,2092],[1865,17750,17752,17833],{"className":17751},[2096],[1865,17753,17755,17814,17822],{"className":17754,"style":6666},[2100],[1865,17756,17757,17760],{"style":2136},[1865,17758],{"className":17759,"style":2140},[2108],[1865,17761,17763],{"className":17762},[2080],[1865,17764,17766,17769],{"className":17765},[2080],[1865,17767,1798],{"className":17768},[2080,2154],[1865,17770,17772],{"className":17771},[2158],[1865,17773,17775,17806],{"className":17774},[2091,2092],[1865,17776,17778,17803],{"className":17777},[2096],[1865,17779,17781,17792],{"className":17780,"style":14799},[2100],[1865,17782,17783,17786],{"style":14802},[1865,17784],{"className":17785,"style":2175},[2108],[1865,17787,17789],{"className":17788},[2179,2180,2181,2182],[1865,17790,1931],{"className":17791},[2080,2182],[1865,17793,17794,17797],{"style":14814},[1865,17795],{"className":17796,"style":2175},[2108],[1865,17798,17800],{"className":17799},[2179,2180,2181,2182],[1865,17801,1984],{"className":17802},[2080,2182],[1865,17804,2190],{"className":17805},[2189],[1865,17807,17809],{"className":17808},[2096],[1865,17810,17812],{"className":17811,"style":14833},[2100],[1865,17813],{},[1865,17815,17816,17819],{"style":2202},[1865,17817],{"className":17818,"style":2140},[2108],[1865,17820],{"className":17821,"style":2210},[2209],[1865,17823,17824,17827],{"style":2213},[1865,17825],{"className":17826,"style":2140},[2108],[1865,17828,17830],{"className":17829},[2080],[1865,17831,1931],{"className":17832},[2080],[1865,17834,2190],{"className":17835},[2189],[1865,17837,17839],{"className":17838},[2096],[1865,17840,17842],{"className":17841,"style":14864},[2100],[1865,17843],{},[1865,17845],{"className":17846},[2242,2120],[1865,17848],{"className":17849,"style":2247},[2246],[1865,17851,2029],{"className":17852},[2251],[1865,17854],{"className":17855,"style":2247},[2246],[1865,17857,17859,17862,17865,17868,17871],{"className":17858},[2071],[1865,17860],{"className":17861,"style":10638},[2075],[1865,17863,3508],{"className":17864},[2080,2154],[1865,17866],{"className":17867,"style":2247},[2246],[1865,17869,1935],{"className":17870},[2251],[1865,17872],{"className":17873,"style":2247},[2246],[1865,17875,17877,17880,17979,17982,17985],{"className":17876},[2071],[1865,17878],{"className":17879,"style":15221},[2075],[1865,17881,17883,17886,17976],{"className":17882},[2080],[1865,17884],{"className":17885},[2119,2120],[1865,17887,17889],{"className":17888},[1906],[1865,17890,17892,17968],{"className":17891},[2091,2092],[1865,17893,17895,17965],{"className":17894},[2096],[1865,17896,17898,17946,17954],{"className":17897,"style":6666},[2100],[1865,17899,17900,17903],{"style":2136},[1865,17901],{"className":17902,"style":2140},[2108],[1865,17904,17906],{"className":17905},[2080],[1865,17907,17909,17912],{"className":17908},[2080],[1865,17910,1798],{"className":17911},[2080,2154],[1865,17913,17915],{"className":17914},[2158],[1865,17916,17918,17938],{"className":17917},[2091,2092],[1865,17919,17921,17935],{"className":17920},[2096],[1865,17922,17924],{"className":17923,"style":2168},[2100],[1865,17925,17926,17929],{"style":2171},[1865,17927],{"className":17928,"style":2175},[2108],[1865,17930,17932],{"className":17931},[2179,2180,2181,2182],[1865,17933,1931],{"className":17934},[2080,2182],[1865,17936,2190],{"className":17937},[2189],[1865,17939,17941],{"className":17940},[2096],[1865,17942,17944],{"className":17943,"style":2197},[2100],[1865,17945],{},[1865,17947,17948,17951],{"style":2202},[1865,17949],{"className":17950,"style":2140},[2108],[1865,17952],{"className":17953,"style":2210},[2209],[1865,17955,17956,17959],{"style":2213},[1865,17957],{"className":17958,"style":2140},[2108],[1865,17960,17962],{"className":17961},[2080],[1865,17963,1984],{"className":17964},[2080],[1865,17966,2190],{"className":17967},[2189],[1865,17969,17971],{"className":17970},[2096],[1865,17972,17974],{"className":17973,"style":3396},[2100],[1865,17975],{},[1865,17977],{"className":17978},[2242,2120],[1865,17980],{"className":17981,"style":2693},[2246],[1865,17983,1955],{"className":17984},[2697],[1865,17986],{"className":17987,"style":2693},[2246],[1865,17989,17991,17994,17997,18000,18003],{"className":17990},[2071],[1865,17992],{"className":17993,"style":10638},[2075],[1865,17995,3508],{"className":17996},[2080,2154],[1865,17998],{"className":17999,"style":2247},[2246],[1865,18001,1935],{"className":18002},[2251],[1865,18004],{"className":18005,"style":2247},[2246],[1865,18007,18009,18012],{"className":18008},[2071],[1865,18010],{"className":18011,"style":15221},[2075],[1865,18013,18015,18018,18108],{"className":18014},[2080],[1865,18016],{"className":18017},[2119,2120],[1865,18019,18021],{"className":18020},[1906],[1865,18022,18024,18100],{"className":18023},[2091,2092],[1865,18025,18027,18097],{"className":18026},[2096],[1865,18028,18030,18078,18086],{"className":18029,"style":6666},[2100],[1865,18031,18032,18035],{"style":2136},[1865,18033],{"className":18034,"style":2140},[2108],[1865,18036,18038],{"className":18037},[2080],[1865,18039,18041,18044],{"className":18040},[2080],[1865,18042,1798],{"className":18043},[2080,2154],[1865,18045,18047],{"className":18046},[2158],[1865,18048,18050,18070],{"className":18049},[2091,2092],[1865,18051,18053,18067],{"className":18052},[2096],[1865,18054,18056],{"className":18055,"style":2168},[2100],[1865,18057,18058,18061],{"style":2171},[1865,18059],{"className":18060,"style":2175},[2108],[1865,18062,18064],{"className":18063},[2179,2180,2181,2182],[1865,18065,1931],{"className":18066},[2080,2182],[1865,18068,2190],{"className":18069},[2189],[1865,18071,18073],{"className":18072},[2096],[1865,18074,18076],{"className":18075,"style":2197},[2100],[1865,18077],{},[1865,18079,18080,18083],{"style":2202},[1865,18081],{"className":18082,"style":2140},[2108],[1865,18084],{"className":18085,"style":2210},[2209],[1865,18087,18088,18091],{"style":2213},[1865,18089],{"className":18090,"style":2140},[2108],[1865,18092,18094],{"className":18093},[2080],[1865,18095,1931],{"className":18096},[2080],[1865,18098,2190],{"className":18099},[2189],[1865,18101,18103],{"className":18102},[2096],[1865,18104,18106],{"className":18105,"style":3396},[2100],[1865,18107],{},[1865,18109],{"className":18110},[2242,2120],[1798,18112,18113],{},"因此：",[1865,18115,18117],{"className":18116},[1868],[1865,18118,18120,18278],{"className":18119},[1872],[1865,18121,18123],{"className":18122},[1876],[1878,18124,18125],{"xmlns":1880,"display":1881},[1883,18126,18127,18275],{},[1886,18128,18129,18197,18245],{"rowspacing":1888,"columnalign":1889,"columnspacing":1890},[1892,18130,18131,18141],{},[1895,18132,18133],{},[1898,18134,18135],{"scriptlevel":1900,"displaystyle":1901},[1903,18136,18137,18139],{},[1911,18138,8734],{},[1911,18140,8737],{},[1895,18142,18143],{},[1898,18144,18145],{"scriptlevel":1900,"displaystyle":1901},[1903,18146,18147,18149,18151,18153,18155,18163,18165,18171,18173,18175,18177,18179,18187,18189,18195],{},[1903,18148],{},[1933,18150,1955],{},[1911,18152,8742],{},[1933,18154,4942],{"stretchy":3501},[8534,18156,18157,18159,18161],{},[1911,18158,1798],{},[1929,18160,1931],{},[1929,18162,1931],{},[1933,18164,2784],{"separator":1901},[6885,18166,18167,18169],{},[1911,18168,3508],{},[1929,18170,1900],{},[1933,18172,4963],{"stretchy":3501},[1933,18174,1935],{},[1911,18176,8742],{},[1933,18178,4942],{"stretchy":3501},[8534,18180,18181,18183,18185],{},[1911,18182,1798],{},[1929,18184,1931],{},[1929,18186,1900],{},[1933,18188,2784],{"separator":1901},[6885,18190,18191,18193],{},[1911,18192,3508],{},[1929,18194,1900],{},[1933,18196,4963],{"stretchy":3501},[1892,18198,18199,18205],{},[1895,18200,18201],{},[1898,18202,18203],{"scriptlevel":1900,"displaystyle":1901},[1903,18204],{},[1895,18206,18207],{},[1898,18208,18209],{"scriptlevel":1900,"displaystyle":1901},[1903,18210,18211,18213,18215,18231,18233],{},[1903,18212],{},[1933,18214,1955],{},[1903,18216,18217,18219,18221,18223,18229],{},[1933,18218,4942],{"fence":1901},[1929,18220,16205],{},[1933,18222,1935],{},[1906,18224,18225,18227],{},[1929,18226,1931],{},[1929,18228,13355],{},[1933,18230,4963],{"fence":1901},[1933,18232,1935],{},[1903,18234,18235,18237,18239,18241,18243],{},[1933,18236,4942],{"fence":1901},[1929,18238,16205],{},[1933,18240,1935],{},[1929,18242,1931],{},[1933,18244,4963],{"fence":1901},[1892,18246,18247,18253],{},[1895,18248,18249],{},[1898,18250,18251],{"scriptlevel":1900,"displaystyle":1901},[1903,18252],{},[1895,18254,18255],{},[1898,18256,18257],{"scriptlevel":1900,"displaystyle":1901},[1903,18258,18259,18261,18263,18266,18268,18270,18272],{},[1903,18260],{},[1933,18262,1955],{},[1929,18264,18265],{},"20.75",[1933,18267,1935],{},[1929,18269,13226],{},[1933,18271,1955],{},[1929,18273,18274],{},"0.75",[2060,18276,18277],{"encoding":2062},"\\begin{align*}\nCV &= e(p_1^1, u^0) - e(p_1^0, u^0) \\\\\n&= \\left(21 - \\frac{1}{4}\\right) - \\left(21 - 1\\right) \\\\\n&= 20.75 - 20 = 0.75\n\\end{align*}",[1865,18279,18281],{"className":18280,"ariaHidden":1901},[2067],[1865,18282,18284,18288],{"className":18283},[2071],[1865,18285],{"className":18286,"style":18287},[2075],"height:5.4241em;vertical-align:-2.4621em;",[1865,18289,18291],{"className":18290},[2080],[1865,18292,18294,18353],{"className":18293},[1886],[1865,18295,18297],{"className":18296},[2087],[1865,18298,18300,18344],{"className":18299},[2091,2092],[1865,18301,18303,18341],{"className":18302},[2096],[1865,18304,18307,18323,18332],{"className":18305,"style":18306},[2100],"height:2.9621em;",[1865,18308,18310,18314],{"style":18309},"top:-5.548em;",[1865,18311],{"className":18312,"style":18313},[2108],"height:3.45em;",[1865,18315,18317,18320],{"className":18316},[2080],[1865,18318,8734],{"className":18319,"style":8819},[2080,2154],[1865,18321,8737],{"className":18322,"style":2247},[2080,2154],[1865,18324,18326,18329],{"style":18325},"top:-3.438em;",[1865,18327],{"className":18328,"style":18313},[2108],[1865,18330],{"className":18331},[2080],[1865,18333,18335,18338],{"style":18334},"top:-1.3479em;",[1865,18336],{"className":18337,"style":18313},[2108],[1865,18339],{"className":18340},[2080],[1865,18342,2190],{"className":18343},[2189],[1865,18345,18347],{"className":18346},[2096],[1865,18348,18351],{"className":18349,"style":18350},[2100],"height:2.4621em;",[1865,18352],{},[1865,18354,18356],{"className":18355},[2669],[1865,18357,18359,18779],{"className":18358},[2091,2092],[1865,18360,18362,18776],{"className":18361},[2096],[1865,18363,18365,18584,18729],{"className":18364,"style":18306},[2100],[1865,18366,18367,18370],{"style":18309},[1865,18368],{"className":18369,"style":18313},[2108],[1865,18371,18373,18376,18379,18382,18385,18388,18391,18442,18445,18448,18477,18480,18483,18486,18489,18492,18495,18546,18549,18552,18581],{"className":18372},[2080],[1865,18374],{"className":18375},[2080],[1865,18377],{"className":18378,"style":2693},[2246],[1865,18380,1955],{"className":18381},[2697],[1865,18383],{"className":18384,"style":2693},[2246],[1865,18386,8742],{"className":18387},[2080,2154],[1865,18389,4942],{"className":18390},[2119],[1865,18392,18394,18397],{"className":18393},[2080],[1865,18395,1798],{"className":18396},[2080,2154],[1865,18398,18400],{"className":18399},[2158],[1865,18401,18403,18434],{"className":18402},[2091,2092],[1865,18404,18406,18431],{"className":18405},[2096],[1865,18407,18409,18420],{"className":18408,"style":8863},[2100],[1865,18410,18411,18414],{"style":8866},[1865,18412],{"className":18413,"style":2175},[2108],[1865,18415,18417],{"className":18416},[2179,2180,2181,2182],[1865,18418,1931],{"className":18419},[2080,2182],[1865,18421,18422,18425],{"style":7181},[1865,18423],{"className":18424,"style":2175},[2108],[1865,18426,18428],{"className":18427},[2179,2180,2181,2182],[1865,18429,1931],{"className":18430},[2080,2182],[1865,18432,2190],{"className":18433},[2189],[1865,18435,18437],{"className":18436},[2096],[1865,18438,18440],{"className":18439,"style":8896},[2100],[1865,18441],{},[1865,18443,2784],{"className":18444},[2851],[1865,18446],{"className":18447,"style":2855},[2246],[1865,18449,18451,18454],{"className":18450},[2080],[1865,18452,3508],{"className":18453},[2080,2154],[1865,18455,18457],{"className":18456},[2158],[1865,18458,18460],{"className":18459},[2091],[1865,18461,18463],{"className":18462},[2096],[1865,18464,18466],{"className":18465,"style":8863},[2100],[1865,18467,18468,18471],{"style":7181},[1865,18469],{"className":18470,"style":2175},[2108],[1865,18472,18474],{"className":18473},[2179,2180,2181,2182],[1865,18475,1900],{"className":18476},[2080,2182],[1865,18478,4963],{"className":18479},[2242],[1865,18481],{"className":18482,"style":2247},[2246],[1865,18484,1935],{"className":18485},[2251],[1865,18487],{"className":18488,"style":2247},[2246],[1865,18490,8742],{"className":18491},[2080,2154],[1865,18493,4942],{"className":18494},[2119],[1865,18496,18498,18501],{"className":18497},[2080],[1865,18499,1798],{"className":18500},[2080,2154],[1865,18502,18504],{"className":18503},[2158],[1865,18505,18507,18538],{"className":18506},[2091,2092],[1865,18508,18510,18535],{"className":18509},[2096],[1865,18511,18513,18524],{"className":18512,"style":8863},[2100],[1865,18514,18515,18518],{"style":8866},[1865,18516],{"className":18517,"style":2175},[2108],[1865,18519,18521],{"className":18520},[2179,2180,2181,2182],[1865,18522,1931],{"className":18523},[2080,2182],[1865,18525,18526,18529],{"style":7181},[1865,18527],{"className":18528,"style":2175},[2108],[1865,18530,18532],{"className":18531},[2179,2180,2181,2182],[1865,18533,1900],{"className":18534},[2080,2182],[1865,18536,2190],{"className":18537},[2189],[1865,18539,18541],{"className":18540},[2096],[1865,18542,18544],{"className":18543,"style":8896},[2100],[1865,18545],{},[1865,18547,2784],{"className":18548},[2851],[1865,18550],{"className":18551,"style":2855},[2246],[1865,18553,18555,18558],{"className":18554},[2080],[1865,18556,3508],{"className":18557},[2080,2154],[1865,18559,18561],{"className":18560},[2158],[1865,18562,18564],{"className":18563},[2091],[1865,18565,18567],{"className":18566},[2096],[1865,18568,18570],{"className":18569,"style":8863},[2100],[1865,18571,18572,18575],{"style":7181},[1865,18573],{"className":18574,"style":2175},[2108],[1865,18576,18578],{"className":18577},[2179,2180,2181,2182],[1865,18579,1900],{"className":18580},[2080,2182],[1865,18582,4963],{"className":18583},[2242],[1865,18585,18586,18589],{"style":18325},[1865,18587],{"className":18588,"style":18313},[2108],[1865,18590,18592,18595,18598,18601,18604,18696,18699,18702,18705],{"className":18591},[2080],[1865,18593],{"className":18594},[2080],[1865,18596],{"className":18597,"style":2693},[2246],[1865,18599,1955],{"className":18600},[2697],[1865,18602],{"className":18603,"style":2693},[2246],[1865,18605,18608,18616,18619,18622,18625,18628,18690],{"className":18606},[18607],"minner",[1865,18609,18613],{"className":18610,"style":18612},[2119,18611],"delimcenter","top:0em;",[1865,18614,4942],{"className":18615},[3870,2181],[1865,18617,16205],{"className":18618},[2080],[1865,18620],{"className":18621,"style":2247},[2246],[1865,18623,1935],{"className":18624},[2251],[1865,18626],{"className":18627,"style":2247},[2246],[1865,18629,18631,18634,18687],{"className":18630},[2080],[1865,18632],{"className":18633},[2119,2120],[1865,18635,18637],{"className":18636},[1906],[1865,18638,18640,18679],{"className":18639},[2091,2092],[1865,18641,18643,18676],{"className":18642},[2096],[1865,18644,18646,18657,18665],{"className":18645,"style":6666},[2100],[1865,18647,18648,18651],{"style":2136},[1865,18649],{"className":18650,"style":2140},[2108],[1865,18652,18654],{"className":18653},[2080],[1865,18655,13355],{"className":18656},[2080],[1865,18658,18659,18662],{"style":2202},[1865,18660],{"className":18661,"style":2140},[2108],[1865,18663],{"className":18664,"style":2210},[2209],[1865,18666,18667,18670],{"style":2213},[1865,18668],{"className":18669,"style":2140},[2108],[1865,18671,18673],{"className":18672},[2080],[1865,18674,1931],{"className":18675},[2080],[1865,18677,2190],{"className":18678},[2189],[1865,18680,18682],{"className":18681},[2096],[1865,18683,18685],{"className":18684,"style":4149},[2100],[1865,18686],{},[1865,18688],{"className":18689},[2242,2120],[1865,18691,18693],{"className":18692,"style":18612},[2242,18611],[1865,18694,4963],{"className":18695},[3870,2181],[1865,18697],{"className":18698,"style":2247},[2246],[1865,18700,1935],{"className":18701},[2251],[1865,18703],{"className":18704,"style":2247},[2246],[1865,18706,18708,18711,18714,18717,18720,18723,18726],{"className":18707},[18607],[1865,18709,4942],{"className":18710,"style":18612},[2119,18611],[1865,18712,16205],{"className":18713},[2080],[1865,18715],{"className":18716,"style":2247},[2246],[1865,18718,1935],{"className":18719},[2251],[1865,18721],{"className":18722,"style":2247},[2246],[1865,18724,1931],{"className":18725},[2080],[1865,18727,4963],{"className":18728,"style":18612},[2242,18611],[1865,18730,18731,18734],{"style":18334},[1865,18732],{"className":18733,"style":18313},[2108],[1865,18735,18737,18740,18743,18746,18749,18752,18755,18758,18761,18764,18767,18770,18773],{"className":18736},[2080],[1865,18738],{"className":18739},[2080],[1865,18741],{"className":18742,"style":2693},[2246],[1865,18744,1955],{"className":18745},[2697],[1865,18747],{"className":18748,"style":2693},[2246],[1865,18750,18265],{"className":18751},[2080],[1865,18753],{"className":18754,"style":2247},[2246],[1865,18756,1935],{"className":18757},[2251],[1865,18759],{"className":18760,"style":2247},[2246],[1865,18762,13226],{"className":18763},[2080],[1865,18765],{"className":18766,"style":2693},[2246],[1865,18768,1955],{"className":18769},[2697],[1865,18771],{"className":18772,"style":2693},[2246],[1865,18774,18274],{"className":18775},[2080],[1865,18777,2190],{"className":18778},[2189],[1865,18780,18782],{"className":18781},[2096],[1865,18783,18785],{"className":18784,"style":18350},[2100],[1865,18786],{},[1798,18788,18789],{},[3048,18790,18791],{},"(4) 计算EV",[1865,18793,18795],{"className":18794},[1868],[1865,18796,18798,18949],{"className":18797},[1872],[1865,18799,18801],{"className":18800},[1876],[1878,18802,18803],{"xmlns":1880,"display":1881},[1883,18804,18805,18946],{},[1886,18806,18807,18875,18915],{"rowspacing":1888,"columnalign":1889,"columnspacing":1890},[1892,18808,18809,18819],{},[1895,18810,18811],{},[1898,18812,18813],{"scriptlevel":1900,"displaystyle":1901},[1903,18814,18815,18817],{},[1911,18816,9930],{},[1911,18818,8737],{},[1895,18820,18821],{},[1898,18822,18823],{"scriptlevel":1900,"displaystyle":1901},[1903,18824,18825,18827,18829,18831,18833,18841,18843,18849,18851,18853,18855,18857,18865,18867,18873],{},[1903,18826],{},[1933,18828,1955],{},[1911,18830,8742],{},[1933,18832,4942],{"stretchy":3501},[8534,18834,18835,18837,18839],{},[1911,18836,1798],{},[1929,18838,1931],{},[1929,18840,1900],{},[1933,18842,2784],{"separator":1901},[6885,18844,18845,18847],{},[1911,18846,3508],{},[1929,18848,1931],{},[1933,18850,4963],{"stretchy":3501},[1933,18852,1935],{},[1911,18854,8742],{},[1933,18856,4942],{"stretchy":3501},[8534,18858,18859,18861,18863],{},[1911,18860,1798],{},[1929,18862,1931],{},[1929,18864,1900],{},[1933,18866,2784],{"separator":1901},[6885,18868,18869,18871],{},[1911,18870,3508],{},[1929,18872,1900],{},[1933,18874,4963],{"stretchy":3501},[1892,18876,18877,18883],{},[1895,18878,18879],{},[1898,18880,18881],{"scriptlevel":1900,"displaystyle":1901},[1903,18882],{},[1895,18884,18885],{},[1898,18886,18887],{"scriptlevel":1900,"displaystyle":1901},[1903,18888,18889,18891,18893,18895,18897,18899,18901,18903,18905,18907,18909,18911,18913],{},[1903,18890],{},[1933,18892,1955],{},[1933,18894,4942],{"stretchy":3501},[1929,18896,16659],{},[1933,18898,1935],{},[1929,18900,1931],{},[1933,18902,4963],{"stretchy":3501},[1933,18904,1935],{},[1933,18906,4942],{"stretchy":3501},[1929,18908,16205],{},[1933,18910,1935],{},[1929,18912,1931],{},[1933,18914,4963],{"stretchy":3501},[1892,18916,18917,18923],{},[1895,18918,18919],{},[1898,18920,18921],{"scriptlevel":1900,"displaystyle":1901},[1903,18922],{},[1895,18924,18925],{},[1898,18926,18927],{"scriptlevel":1900,"displaystyle":1901},[1903,18928,18929,18931,18933,18936,18938,18940,18942,18944],{},[1903,18930],{},[1933,18932,1955],{},[1929,18934,18935],{},"19.25",[1933,18937,1935],{},[1929,18939,13226],{},[1933,18941,1955],{},[1933,18943,1935],{},[1929,18945,18274],{},[2060,18947,18948],{"encoding":2062},"\\begin{align*}\nEV &= e(p_1^0, u^1) - e(p_1^0, u^0) \\\\\n&= (20.25 - 1) - (21 - 1) \\\\\n&= 19.25 - 20 = -0.75\n\\end{align*}",[1865,18950,18952],{"className":18951,"ariaHidden":1901},[2067],[1865,18953,18955,18959],{"className":18954},[2071],[1865,18956],{"className":18957,"style":18958},[2075],"height:4.2241em;vertical-align:-1.8621em;",[1865,18960,18962],{"className":18961},[2080],[1865,18963,18965,19023],{"className":18964},[1886],[1865,18966,18968],{"className":18967},[2087],[1865,18969,18971,19014],{"className":18970},[2091,2092],[1865,18972,18974,19011],{"className":18973},[2096],[1865,18975,18978,18993,19002],{"className":18976,"style":18977},[2100],"height:2.3621em;",[1865,18979,18981,18984],{"style":18980},"top:-4.4979em;",[1865,18982],{"className":18983,"style":2140},[2108],[1865,18985,18987,18990],{"className":18986},[2080],[1865,18988,9930],{"className":18989,"style":7058},[2080,2154],[1865,18991,8737],{"className":18992,"style":2247},[2080,2154],[1865,18994,18996,18999],{"style":18995},"top:-2.9979em;",[1865,18997],{"className":18998,"style":2140},[2108],[1865,19000],{"className":19001},[2080],[1865,19003,19005,19008],{"style":19004},"top:-1.4979em;",[1865,19006],{"className":19007,"style":2140},[2108],[1865,19009],{"className":19010},[2080],[1865,19012,2190],{"className":19013},[2189],[1865,19015,19017],{"className":19016},[2096],[1865,19018,19021],{"className":19019,"style":19020},[2100],"height:1.8621em;",[1865,19022],{},[1865,19024,19026],{"className":19025},[2669],[1865,19027,19029,19378],{"className":19028},[2091,2092],[1865,19030,19032,19375],{"className":19031},[2096],[1865,19033,19035,19254,19325],{"className":19034,"style":18977},[2100],[1865,19036,19037,19040],{"style":18980},[1865,19038],{"className":19039,"style":2140},[2108],[1865,19041,19043,19046,19049,19052,19055,19058,19061,19112,19115,19118,19147,19150,19153,19156,19159,19162,19165,19216,19219,19222,19251],{"className":19042},[2080],[1865,19044],{"className":19045},[2080],[1865,19047],{"className":19048,"style":2693},[2246],[1865,19050,1955],{"className":19051},[2697],[1865,19053],{"className":19054,"style":2693},[2246],[1865,19056,8742],{"className":19057},[2080,2154],[1865,19059,4942],{"className":19060},[2119],[1865,19062,19064,19067],{"className":19063},[2080],[1865,19065,1798],{"className":19066},[2080,2154],[1865,19068,19070],{"className":19069},[2158],[1865,19071,19073,19104],{"className":19072},[2091,2092],[1865,19074,19076,19101],{"className":19075},[2096],[1865,19077,19079,19090],{"className":19078,"style":8863},[2100],[1865,19080,19081,19084],{"style":8866},[1865,19082],{"className":19083,"style":2175},[2108],[1865,19085,19087],{"className":19086},[2179,2180,2181,2182],[1865,19088,1931],{"className":19089},[2080,2182],[1865,19091,19092,19095],{"style":7181},[1865,19093],{"className":19094,"style":2175},[2108],[1865,19096,19098],{"className":19097},[2179,2180,2181,2182],[1865,19099,1900],{"className":19100},[2080,2182],[1865,19102,2190],{"className":19103},[2189],[1865,19105,19107],{"className":19106},[2096],[1865,19108,19110],{"className":19109,"style":8896},[2100],[1865,19111],{},[1865,19113,2784],{"className":19114},[2851],[1865,19116],{"className":19117,"style":2855},[2246],[1865,19119,19121,19124],{"className":19120},[2080],[1865,19122,3508],{"className":19123},[2080,2154],[1865,19125,19127],{"className":19126},[2158],[1865,19128,19130],{"className":19129},[2091],[1865,19131,19133],{"className":19132},[2096],[1865,19134,19136],{"className":19135,"style":8863},[2100],[1865,19137,19138,19141],{"style":7181},[1865,19139],{"className":19140,"style":2175},[2108],[1865,19142,19144],{"className":19143},[2179,2180,2181,2182],[1865,19145,1931],{"className":19146},[2080,2182],[1865,19148,4963],{"className":19149},[2242],[1865,19151],{"className":19152,"style":2247},[2246],[1865,19154,1935],{"className":19155},[2251],[1865,19157],{"className":19158,"style":2247},[2246],[1865,19160,8742],{"className":19161},[2080,2154],[1865,19163,4942],{"className":19164},[2119],[1865,19166,19168,19171],{"className":19167},[2080],[1865,19169,1798],{"className":19170},[2080,2154],[1865,19172,19174],{"className":19173},[2158],[1865,19175,19177,19208],{"className":19176},[2091,2092],[1865,19178,19180,19205],{"className":19179},[2096],[1865,19181,19183,19194],{"className":19182,"style":8863},[2100],[1865,19184,19185,19188],{"style":8866},[1865,19186],{"className":19187,"style":2175},[2108],[1865,19189,19191],{"className":19190},[2179,2180,2181,2182],[1865,19192,1931],{"className":19193},[2080,2182],[1865,19195,19196,19199],{"style":7181},[1865,19197],{"className":19198,"style":2175},[2108],[1865,19200,19202],{"className":19201},[2179,2180,2181,2182],[1865,19203,1900],{"className":19204},[2080,2182],[1865,19206,2190],{"className":19207},[2189],[1865,19209,19211],{"className":19210},[2096],[1865,19212,19214],{"className":19213,"style":8896},[2100],[1865,19215],{},[1865,19217,2784],{"className":19218},[2851],[1865,19220],{"className":19221,"style":2855},[2246],[1865,19223,19225,19228],{"className":19224},[2080],[1865,19226,3508],{"className":19227},[2080,2154],[1865,19229,19231],{"className":19230},[2158],[1865,19232,19234],{"className":19233},[2091],[1865,19235,19237],{"className":19236},[2096],[1865,19238,19240],{"className":19239,"style":8863},[2100],[1865,19241,19242,19245],{"style":7181},[1865,19243],{"className":19244,"style":2175},[2108],[1865,19246,19248],{"className":19247},[2179,2180,2181,2182],[1865,19249,1900],{"className":19250},[2080,2182],[1865,19252,4963],{"className":19253},[2242],[1865,19255,19256,19259],{"style":18995},[1865,19257],{"className":19258,"style":2140},[2108],[1865,19260,19262,19265,19268,19271,19274,19277,19280,19283,19286,19289,19292,19295,19298,19301,19304,19307,19310,19313,19316,19319,19322],{"className":19261},[2080],[1865,19263],{"className":19264},[2080],[1865,19266],{"className":19267,"style":2693},[2246],[1865,19269,1955],{"className":19270},[2697],[1865,19272],{"className":19273,"style":2693},[2246],[1865,19275,4942],{"className":19276},[2119],[1865,19278,16659],{"className":19279},[2080],[1865,19281],{"className":19282,"style":2247},[2246],[1865,19284,1935],{"className":19285},[2251],[1865,19287],{"className":19288,"style":2247},[2246],[1865,19290,1931],{"className":19291},[2080],[1865,19293,4963],{"className":19294},[2242],[1865,19296],{"className":19297,"style":2247},[2246],[1865,19299,1935],{"className":19300},[2251],[1865,19302],{"className":19303,"style":2247},[2246],[1865,19305,4942],{"className":19306},[2119],[1865,19308,16205],{"className":19309},[2080],[1865,19311],{"className":19312,"style":2247},[2246],[1865,19314,1935],{"className":19315},[2251],[1865,19317],{"className":19318,"style":2247},[2246],[1865,19320,1931],{"className":19321},[2080],[1865,19323,4963],{"className":19324},[2242],[1865,19326,19327,19330],{"style":19004},[1865,19328],{"className":19329,"style":2140},[2108],[1865,19331,19333,19336,19339,19342,19345,19348,19351,19354,19357,19360,19363,19366,19369,19372],{"className":19332},[2080],[1865,19334],{"className":19335},[2080],[1865,19337],{"className":19338,"style":2693},[2246],[1865,19340,1955],{"className":19341},[2697],[1865,19343],{"className":19344,"style":2693},[2246],[1865,19346,18935],{"className":19347},[2080],[1865,19349],{"className":19350,"style":2247},[2246],[1865,19352,1935],{"className":19353},[2251],[1865,19355],{"className":19356,"style":2247},[2246],[1865,19358,13226],{"className":19359},[2080],[1865,19361],{"className":19362,"style":2693},[2246],[1865,19364,1955],{"className":19365},[2697],[1865,19367],{"className":19368,"style":2693},[2246],[1865,19370,1935],{"className":19371},[2080],[1865,19373,18274],{"className":19374},[2080],[1865,19376,2190],{"className":19377},[2189],[1865,19379,19381],{"className":19380},[2096],[1865,19382,19384],{"className":19383,"style":19020},[2100],[1865,19385],{},[1798,19387,19388],{},"等等，这里符号有问题。让我们重新定义：价格上涨使效用下降，所以：",[1805,19390,19391,19515],{},[1808,19392,19393,19427,19428,19486,19487],{},[1865,19394,19396,19412],{"className":19395},[1872],[1865,19397,19399],{"className":19398},[1876],[1878,19400,19401],{"xmlns":1880},[1883,19402,19403,19409],{},[1903,19404,19405,19407],{},[1911,19406,8734],{},[1911,19408,8737],{},[2060,19410,19411],{"encoding":2062},"CV",[1865,19413,19415],{"className":19414,"ariaHidden":1901},[2067],[1865,19416,19418,19421,19424],{"className":19417},[2071],[1865,19419],{"className":19420,"style":8815},[2075],[1865,19422,8734],{"className":19423,"style":8819},[2080,2154],[1865,19425,8737],{"className":19426,"style":2247},[2080,2154],": 在新价格下恢复到",[1865,19429,19431,19448],{"className":19430},[1872],[1865,19432,19434],{"className":19433},[1876],[1878,19435,19436],{"xmlns":1880},[1883,19437,19438,19446],{},[1903,19439,19440],{},[6885,19441,19442,19444],{},[1911,19443,3508],{},[1929,19445,1900],{},[2060,19447,10857],{"encoding":2062},[1865,19449,19451],{"className":19450,"ariaHidden":1901},[2067],[1865,19452,19454,19457],{"className":19453},[2071],[1865,19455],{"className":19456,"style":8573},[2075],[1865,19458,19460,19463],{"className":19459},[2080],[1865,19461,3508],{"className":19462},[2080,2154],[1865,19464,19466],{"className":19465},[2158],[1865,19467,19469],{"className":19468},[2091],[1865,19470,19472],{"className":19471},[2096],[1865,19473,19475],{"className":19474,"style":8573},[2100],[1865,19476,19477,19480],{"style":7519},[1865,19478],{"className":19479,"style":2175},[2108],[1865,19481,19483],{"className":19482},[2179,2180,2181,2182],[1865,19484,1900],{"className":19485},[2080,2182],"需要的补偿 = ",[1865,19488,19490,19503],{"className":19489},[1872],[1865,19491,19493],{"className":19492},[1876],[1878,19494,19495],{"xmlns":1880},[1883,19496,19497,19501],{},[1903,19498,19499],{},[1929,19500,18274],{},[2060,19502,18274],{"encoding":2062},[1865,19504,19506],{"className":19505,"ariaHidden":1901},[2067],[1865,19507,19509,19512],{"className":19508},[2071],[1865,19510],{"className":19511,"style":7553},[2075],[1865,19513,18274],{"className":19514},[2080],[1808,19516,19517,19551,19552,19610,19611],{},[1865,19518,19520,19536],{"className":19519},[1872],[1865,19521,19523],{"className":19522},[1876],[1878,19524,19525],{"xmlns":1880},[1883,19526,19527,19533],{},[1903,19528,19529,19531],{},[1911,19530,9930],{},[1911,19532,8737],{},[2060,19534,19535],{"encoding":2062},"EV",[1865,19537,19539],{"className":19538,"ariaHidden":1901},[2067],[1865,19540,19542,19545,19548],{"className":19541},[2071],[1865,19543],{"className":19544,"style":8815},[2075],[1865,19546,9930],{"className":19547,"style":7058},[2080,2154],[1865,19549,8737],{"className":19550,"style":2247},[2080,2154],": 在旧价格下达到",[1865,19553,19555,19572],{"className":19554},[1872],[1865,19556,19558],{"className":19557},[1876],[1878,19559,19560],{"xmlns":1880},[1883,19561,19562,19570],{},[1903,19563,19564],{},[6885,19565,19566,19568],{},[1911,19567,3508],{},[1929,19569,1931],{},[2060,19571,10919],{"encoding":2062},[1865,19573,19575],{"className":19574,"ariaHidden":1901},[2067],[1865,19576,19578,19581],{"className":19577},[2071],[1865,19579],{"className":19580,"style":8573},[2075],[1865,19582,19584,19587],{"className":19583},[2080],[1865,19585,3508],{"className":19586},[2080,2154],[1865,19588,19590],{"className":19589},[2158],[1865,19591,19593],{"className":19592},[2091],[1865,19594,19596],{"className":19595},[2096],[1865,19597,19599],{"className":19598,"style":8573},[2100],[1865,19600,19601,19604],{"style":7519},[1865,19602],{"className":19603,"style":2175},[2108],[1865,19605,19607],{"className":19606},[2179,2180,2181,2182],[1865,19608,1931],{"className":19609},[2080,2182],"相当于损失的收入 = ",[1865,19612,19614,19627],{"className":19613},[1872],[1865,19615,19617],{"className":19616},[1876],[1878,19618,19619],{"xmlns":1880},[1883,19620,19621,19625],{},[1903,19622,19623],{},[1929,19624,18274],{},[2060,19626,18274],{"encoding":2062},[1865,19628,19630],{"className":19629,"ariaHidden":1901},[2067],[1865,19631,19633,19636],{"className":19632},[2071],[1865,19634],{"className":19635,"style":7553},[2075],[1865,19637,18274],{"className":19638},[2080],[1798,19640,19641,19644,19645,19705],{},[3048,19642,19643],{},"重要发现",": 对于拟线性效用，",[1865,19646,19648,19669],{"className":19647},[1872],[1865,19649,19651],{"className":19650},[1876],[1878,19652,19653],{"xmlns":1880},[1883,19654,19655,19667],{},[1903,19656,19657,19659,19661,19663,19665],{},[1911,19658,8734],{},[1911,19660,8737],{},[1933,19662,1955],{},[1911,19664,9930],{},[1911,19666,8737],{},[2060,19668,11227],{"encoding":2062},[1865,19670,19672,19693],{"className":19671,"ariaHidden":1901},[2067],[1865,19673,19675,19678,19681,19684,19687,19690],{"className":19674},[2071],[1865,19676],{"className":19677,"style":8815},[2075],[1865,19679,8734],{"className":19680,"style":8819},[2080,2154],[1865,19682,8737],{"className":19683,"style":2247},[2080,2154],[1865,19685],{"className":19686,"style":2693},[2246],[1865,19688,1955],{"className":19689},[2697],[1865,19691],{"className":19692,"style":2693},[2246],[1865,19694,19696,19699,19702],{"className":19695},[2071],[1865,19697],{"className":19698,"style":8815},[2075],[1865,19700,9930],{"className":19701,"style":7058},[2080,2154],[1865,19703,8737],{"className":19704,"style":2247},[2080,2154],"！",[1798,19707,19708],{},[3048,19709,19710,19711],{},"(5) 计算",[1865,19712,19714,19731],{"className":19713},[1872],[1865,19715,19717],{"className":19716},[1876],[1878,19718,19719],{"xmlns":1880},[1883,19720,19721,19729],{},[1903,19722,19723,19725,19727],{},[1911,19724,11793],{"mathvariant":1913},[1911,19726,8734],{},[1911,19728,6896],{},[2060,19730,13458],{"encoding":2062},[1865,19732,19734],{"className":19733,"ariaHidden":1901},[2067],[1865,19735,19737,19740,19743,19746],{"className":19736},[2071],[1865,19738],{"className":19739,"style":8815},[2075],[1865,19741,11793],{"className":19742},[2080],[1865,19744,8734],{"className":19745,"style":8819},[2080,2154],[1865,19747,6896],{"className":19748,"style":7058},[2080,2154],[1798,19750,19751,19752,19904,19905],{},"反需求函数：从",[1865,19753,19755,19786],{"className":19754},[1872],[1865,19756,19758],{"className":19757},[1876],[1878,19759,19760],{"xmlns":1880},[1883,19761,19762,19784],{},[1903,19763,19764,19770,19772,19774,19776],{},[1923,19765,19766,19768],{},[1911,19767,1927],{},[1929,19769,1931],{},[1933,19771,1955],{},[1929,19773,1931],{},[1911,19775,16443],{"mathvariant":1913},[8534,19777,19778,19780,19782],{},[1911,19779,1798],{},[1929,19781,1931],{},[1929,19783,1984],{},[2060,19785,17222],{"encoding":2062},[1865,19787,19789,19844],{"className":19788,"ariaHidden":1901},[2067],[1865,19790,19792,19795,19835,19838,19841],{"className":19791},[2071],[1865,19793],{"className":19794,"style":12589},[2075],[1865,19796,19798,19801],{"className":19797},[2080],[1865,19799,1927],{"className":19800},[2080,2154],[1865,19802,19804],{"className":19803},[2158],[1865,19805,19807,19827],{"className":19806},[2091,2092],[1865,19808,19810,19824],{"className":19809},[2096],[1865,19811,19813],{"className":19812,"style":2168},[2100],[1865,19814,19815,19818],{"style":2171},[1865,19816],{"className":19817,"style":2175},[2108],[1865,19819,19821],{"className":19820},[2179,2180,2181,2182],[1865,19822,1931],{"className":19823},[2080,2182],[1865,19825,2190],{"className":19826},[2189],[1865,19828,19830],{"className":19829},[2096],[1865,19831,19833],{"className":19832,"style":2197},[2100],[1865,19834],{},[1865,19836],{"className":19837,"style":2693},[2246],[1865,19839,1955],{"className":19840},[2697],[1865,19842],{"className":19843,"style":2693},[2246],[1865,19845,19847,19850,19853],{"className":19846},[2071],[1865,19848],{"className":19849,"style":9243},[2075],[1865,19851,17290],{"className":19852},[2080],[1865,19854,19856,19859],{"className":19855},[2080],[1865,19857,1798],{"className":19858},[2080,2154],[1865,19860,19862],{"className":19861},[2158],[1865,19863,19865,19896],{"className":19864},[2091,2092],[1865,19866,19868,19893],{"className":19867},[2096],[1865,19869,19871,19882],{"className":19870,"style":8573},[2100],[1865,19872,19873,19876],{"style":8576},[1865,19874],{"className":19875,"style":2175},[2108],[1865,19877,19879],{"className":19878},[2179,2180,2181,2182],[1865,19880,1931],{"className":19881},[2080,2182],[1865,19883,19884,19887],{"style":7519},[1865,19885],{"className":19886,"style":2175},[2108],[1865,19888,19890],{"className":19889},[2179,2180,2181,2182],[1865,19891,1984],{"className":19892},[2080,2182],[1865,19894,2190],{"className":19895},[2189],[1865,19897,19899],{"className":19898},[2096],[1865,19900,19902],{"className":19901,"style":8606},[2100],[1865,19903],{},"得",[1865,19906,19908,19940],{"className":19907},[1872],[1865,19909,19911],{"className":19910},[1876],[1878,19912,19913],{"xmlns":1880},[1883,19914,19915,19937],{},[1903,19916,19917,19923,19925,19927,19929],{},[1923,19918,19919,19921],{},[1911,19920,1798],{},[1929,19922,1931],{},[1933,19924,1955],{},[1929,19926,1931],{},[1911,19928,16443],{"mathvariant":1913},[12729,19930,19931],{},[1923,19932,19933,19935],{},[1911,19934,1927],{},[1929,19936,1931],{},[2060,19938,19939],{"encoding":2062},"p_1 = 1\u002F\\sqrt{x_1}",[1865,19941,19943,19998],{"className":19942,"ariaHidden":1901},[2067],[1865,19944,19946,19949,19989,19992,19995],{"className":19945},[2071],[1865,19947],{"className":19948,"style":2948},[2075],[1865,19950,19952,19955],{"className":19951},[2080],[1865,19953,1798],{"className":19954},[2080,2154],[1865,19956,19958],{"className":19957},[2158],[1865,19959,19961,19981],{"className":19960},[2091,2092],[1865,19962,19964,19978],{"className":19963},[2096],[1865,19965,19967],{"className":19966,"style":2168},[2100],[1865,19968,19969,19972],{"style":2171},[1865,19970],{"className":19971,"style":2175},[2108],[1865,19973,19975],{"className":19974},[2179,2180,2181,2182],[1865,19976,1931],{"className":19977},[2080,2182],[1865,19979,2190],{"className":19980},[2189],[1865,19982,19984],{"className":19983},[2096],[1865,19985,19987],{"className":19986,"style":2197},[2100],[1865,19988],{},[1865,19990],{"className":19991,"style":2693},[2246],[1865,19993,1955],{"className":19994},[2697],[1865,19996],{"className":19997,"style":2693},[2246],[1865,19999,20001,20005,20008],{"className":20000},[2071],[1865,20002],{"className":20003,"style":20004},[2075],"height:1.0647em;vertical-align:-0.3147em;",[1865,20006,17290],{"className":20007},[2080],[1865,20009,20011],{"className":20010},[2080,12874],[1865,20012,20014,20084],{"className":20013},[2091,2092],[1865,20015,20017,20081],{"className":20016},[2096],[1865,20018,20020,20069],{"className":20019,"style":12884},[2100],[1865,20021,20023,20026],{"className":20022,"style":12889},[12888],[1865,20024],{"className":20025,"style":2140},[2108],[1865,20027,20029],{"className":20028,"style":12896},[2080],[1865,20030,20032,20035],{"className":20031},[2080],[1865,20033,1927],{"className":20034},[2080,2154],[1865,20036,20038],{"className":20037},[2158],[1865,20039,20041,20061],{"className":20040},[2091,2092],[1865,20042,20044,20058],{"className":20043},[2096],[1865,20045,20047],{"className":20046,"style":2168},[2100],[1865,20048,20049,20052],{"style":2171},[1865,20050],{"className":20051,"style":2175},[2108],[1865,20053,20055],{"className":20054},[2179,2180,2181,2182],[1865,20056,1931],{"className":20057},[2080,2182],[1865,20059,2190],{"className":20060},[2189],[1865,20062,20064],{"className":20063},[2096],[1865,20065,20067],{"className":20066,"style":2197},[2100],[1865,20068],{},[1865,20070,20071,20074],{"style":12939},[1865,20072],{"className":20073,"style":2140},[2108],[1865,20075,20077],{"className":20076,"style":12947},[12946],[3893,20078,20079],{"xmlns":3895,"width":12950,"height":12951,"viewBox":12952,"preserveAspectRatio":12953},[3899,20080],{"d":12956},[1865,20082,2190],{"className":20083},[2189],[1865,20085,20087],{"className":20086},[2096],[1865,20088,20090],{"className":20089,"style":12966},[2100],[1865,20091],{},[1865,20093,20095],{"className":20094},[1868],[1865,20096,20098,20300],{"className":20097},[1872],[1865,20099,20101],{"className":20100},[1876],[1878,20102,20103],{"xmlns":1880,"display":1881},[1883,20104,20105,20297],{},[1886,20106,20107,20169,20215,20259],{"rowspacing":1888,"columnalign":1889,"columnspacing":1890},[1892,20108,20109,20121],{},[1895,20110,20111],{},[1898,20112,20113],{"scriptlevel":1900,"displaystyle":1901},[1903,20114,20115,20117,20119],{},[1911,20116,11793],{"mathvariant":1913},[1911,20118,8734],{},[1911,20120,6896],{},[1895,20122,20123],{},[1898,20124,20125],{"scriptlevel":1900,"displaystyle":1901},[1903,20126,20127,20129,20131,20133,20153,20159,20161,20163,20165,20167],{},[1903,20128],{},[1933,20130,1955],{},[1933,20132,1935],{},[8534,20134,20135,20137,20145],{},[1933,20136,11392],{},[8534,20138,20139,20141,20143],{},[1911,20140,1927],{},[1929,20142,1931],{},[1929,20144,1931],{},[8534,20146,20147,20149,20151],{},[1911,20148,1927],{},[1929,20150,1931],{},[1929,20152,1900],{},[1923,20154,20155,20157],{},[1911,20156,1798],{},[1929,20158,1931],{},[1933,20160,4942],{"stretchy":3501},[1911,20162,1927],{},[1933,20164,4963],{"stretchy":3501},[1911,20166,3144],{},[1911,20168,1927],{},[1892,20170,20171,20177],{},[1895,20172,20173],{},[1898,20174,20175],{"scriptlevel":1900,"displaystyle":1901},[1903,20176],{},[1895,20178,20179],{},[1898,20180,20181],{"scriptlevel":1900,"displaystyle":1901},[1903,20182,20183,20185,20187,20189,20203,20211,20213],{},[1903,20184],{},[1933,20186,1955],{},[1933,20188,1935],{},[8534,20190,20191,20193,20201],{},[1933,20192,11392],{},[1903,20194,20195,20197,20199],{},[1929,20196,1931],{},[1911,20198,16443],{"mathvariant":1913},[1929,20200,16446],{},[1929,20202,1931],{},[1906,20204,20205,20207],{},[1929,20206,1931],{},[12729,20208,20209],{},[1911,20210,1927],{},[1911,20212,3144],{},[1911,20214,1927],{},[1892,20216,20217,20223],{},[1895,20218,20219],{},[1898,20220,20221],{"scriptlevel":1900,"displaystyle":1901},[1903,20222],{},[1895,20224,20225],{},[1898,20226,20227],{"scriptlevel":1900,"displaystyle":1901},[1903,20228,20229,20231,20233,20235,20238,20240,20244],{},[1903,20230],{},[1933,20232,1955],{},[1933,20234,1935],{},[1933,20236,20237],{"stretchy":3501},"[",[1929,20239,1984],{},[12729,20241,20242],{},[1911,20243,1927],{},[8534,20245,20246,20249,20257],{},[1933,20247,20248],{"stretchy":3501},"]",[1903,20250,20251,20253,20255],{},[1929,20252,1931],{},[1911,20254,16443],{"mathvariant":1913},[1929,20256,16446],{},[1929,20258,1931],{},[1892,20260,20261,20267],{},[1895,20262,20263],{},[1898,20264,20265],{"scriptlevel":1900,"displaystyle":1901},[1903,20266],{},[1895,20268,20269],{},[1898,20270,20271],{"scriptlevel":1900,"displaystyle":1901},[1903,20272,20273,20275,20277,20279,20281,20283,20285,20288,20290,20292,20294],{},[1903,20274],{},[1933,20276,1955],{},[1933,20278,1935],{},[1933,20280,4942],{"stretchy":3501},[1929,20282,1984],{},[1933,20284,1935],{},[1929,20286,20287],{},"0.5",[1933,20289,4963],{"stretchy":3501},[1933,20291,1955],{},[1933,20293,1935],{},[1929,20295,20296],{},"1.5",[2060,20298,20299],{"encoding":2062},"\\begin{align*}\n\\Delta CS &= -\\int_{x_1^1}^{x_1^0} p_1(x)dx \\\\\n&= -\\int_{1\u002F16}^{1} \\frac{1}{\\sqrt{x}}dx \\\\\n&= -[2\\sqrt{x}]_{1\u002F16}^{1} \\\\\n&= -(2 - 0.5) = -1.5\n\\end{align*}",[1865,20301,20303],{"className":20302,"ariaHidden":1901},[2067],[1865,20304,20306,20310],{"className":20305},[2071],[1865,20307],{"className":20308,"style":20309},[2075],"height:8.9289em;vertical-align:-4.2144em;",[1865,20311,20313],{"className":20312},[2080],[1865,20314,20316,20387],{"className":20315},[1886],[1865,20317,20319],{"className":20318},[2087],[1865,20320,20322,20378],{"className":20321},[2091,2092],[1865,20323,20325,20375],{"className":20324},[2096],[1865,20326,20329,20348,20357,20366],{"className":20327,"style":20328},[2100],"height:4.7144em;",[1865,20330,20332,20336],{"style":20331},"top:-6.7144em;",[1865,20333],{"className":20334,"style":20335},[2108],"height:3.7368em;",[1865,20337,20339,20342,20345],{"className":20338},[2080],[1865,20340,11793],{"className":20341},[2080],[1865,20343,8734],{"className":20344,"style":8819},[2080,2154],[1865,20346,6896],{"className":20347,"style":7058},[2080,2154],[1865,20349,20351,20354],{"style":20350},"top:-3.7204em;",[1865,20352],{"className":20353,"style":20335},[2108],[1865,20355],{"className":20356},[2080],[1865,20358,20360,20363],{"style":20359},"top:-1.4694em;",[1865,20361],{"className":20362,"style":20335},[2108],[1865,20364],{"className":20365},[2080],[1865,20367,20369,20372],{"style":20368},"top:0.1176em;",[1865,20370],{"className":20371,"style":20335},[2108],[1865,20373],{"className":20374},[2080],[1865,20376,2190],{"className":20377},[2189],[1865,20379,20381],{"className":20380},[2096],[1865,20382,20385],{"className":20383,"style":20384},[2100],"height:4.2144em;",[1865,20386],{},[1865,20388,20390],{"className":20389},[2669],[1865,20391,20393,21048],{"className":20392},[2091,2092],[1865,20394,20396,21045],{"className":20395},[2096],[1865,20397,20399,20643,20848,20986],{"className":20398,"style":20328},[2100],[1865,20400,20401,20404],{"style":20331},[1865,20402],{"className":20403,"style":20335},[2108],[1865,20405,20407,20410,20413,20416,20419,20422,20425,20585,20588,20628,20631,20634,20637,20640],{"className":20406},[2080],[1865,20408],{"className":20409},[2080],[1865,20411],{"className":20412,"style":2693},[2246],[1865,20414,1955],{"className":20415},[2697],[1865,20417],{"className":20418,"style":2693},[2246],[1865,20420,1935],{"className":20421},[2080],[1865,20423],{"className":20424,"style":2855},[2246],[1865,20426,20428,20431],{"className":20427},[11465],[1865,20429,11392],{"className":20430,"style":11471},[11465,11469,11470],[1865,20432,20434],{"className":20433},[2158],[1865,20435,20437,20576],{"className":20436},[2091,2092],[1865,20438,20440,20573],{"className":20439},[2096],[1865,20441,20443,20509],{"className":20442,"style":11889},[2100],[1865,20444,20445,20448],{"style":11487},[1865,20446],{"className":20447,"style":2175},[2108],[1865,20449,20451],{"className":20450},[2179,2180,2181,2182],[1865,20452,20454],{"className":20453},[2080,2182],[1865,20455,20457,20460],{"className":20456},[2080,2182],[1865,20458,1927],{"className":20459},[2080,2154,2182],[1865,20461,20463],{"className":20462},[2158],[1865,20464,20466,20500],{"className":20465},[2091,2092],[1865,20467,20469,20497],{"className":20468},[2096],[1865,20470,20473,20485],{"className":20471,"style":20472},[2100],"height:0.8051em;",[1865,20474,20476,20479],{"style":20475},"top:-2.1885em;margin-left:0em;margin-right:0.0714em;",[1865,20477],{"className":20478,"style":4268},[2108],[1865,20480,20482],{"className":20481},[2179,4272,4273,2182],[1865,20483,1931],{"className":20484},[2080,2182],[1865,20486,20488,20491],{"style":20487},"top:-2.8448em;margin-right:0.0714em;",[1865,20489],{"className":20490,"style":4268},[2108],[1865,20492,20494],{"className":20493},[2179,4272,4273,2182],[1865,20495,1931],{"className":20496},[2080,2182],[1865,20498,2190],{"className":20499},[2189],[1865,20501,20503],{"className":20502},[2096],[1865,20504,20507],{"className":20505,"style":20506},[2100],"height:0.3115em;",[1865,20508],{},[1865,20510,20511,20514],{"style":11499},[1865,20512],{"className":20513,"style":2175},[2108],[1865,20515,20517],{"className":20516},[2179,2180,2181,2182],[1865,20518,20520],{"className":20519},[2080,2182],[1865,20521,20523,20526],{"className":20522},[2080,2182],[1865,20524,1927],{"className":20525},[2080,2154,2182],[1865,20527,20529],{"className":20528},[2158],[1865,20530,20532,20564],{"className":20531},[2091,2092],[1865,20533,20535,20561],{"className":20534},[2096],[1865,20536,20538,20550],{"className":20537,"style":11961},[2100],[1865,20539,20541,20544],{"style":20540},"top:-2.214em;margin-left:0em;margin-right:0.0714em;",[1865,20542],{"className":20543,"style":4268},[2108],[1865,20545,20547],{"className":20546},[2179,4272,4273,2182],[1865,20548,1931],{"className":20549},[2080,2182],[1865,20551,20552,20555],{"style":11530},[1865,20553],{"className":20554,"style":4268},[2108],[1865,20556,20558],{"className":20557},[2179,4272,4273,2182],[1865,20559,1900],{"className":20560},[2080,2182],[1865,20562,2190],{"className":20563},[2189],[1865,20565,20567],{"className":20566},[2096],[1865,20568,20571],{"className":20569,"style":20570},[2100],"height:0.286em;",[1865,20572],{},[1865,20574,2190],{"className":20575},[2189],[1865,20577,20579],{"className":20578},[2096],[1865,20580,20583],{"className":20581,"style":20582},[2100],"height:1.13em;",[1865,20584],{},[1865,20586],{"className":20587,"style":2855},[2246],[1865,20589,20591,20594],{"className":20590},[2080],[1865,20592,1798],{"className":20593},[2080,2154],[1865,20595,20597],{"className":20596},[2158],[1865,20598,20600,20620],{"className":20599},[2091,2092],[1865,20601,20603,20617],{"className":20602},[2096],[1865,20604,20606],{"className":20605,"style":2168},[2100],[1865,20607,20608,20611],{"style":2171},[1865,20609],{"className":20610,"style":2175},[2108],[1865,20612,20614],{"className":20613},[2179,2180,2181,2182],[1865,20615,1931],{"className":20616},[2080,2182],[1865,20618,2190],{"className":20619},[2189],[1865,20621,20623],{"className":20622},[2096],[1865,20624,20626],{"className":20625,"style":2197},[2100],[1865,20627],{},[1865,20629,4942],{"className":20630},[2119],[1865,20632,1927],{"className":20633},[2080,2154],[1865,20635,4963],{"className":20636},[2242],[1865,20638,3144],{"className":20639},[2080,2154],[1865,20641,1927],{"className":20642},[2080,2154],[1865,20644,20645,20648],{"style":20350},[1865,20646],{"className":20647,"style":20335},[2108],[1865,20649,20651,20654,20657,20660,20663,20666,20669,20728,20731,20842,20845],{"className":20650},[2080],[1865,20652],{"className":20653},[2080],[1865,20655],{"className":20656,"style":2693},[2246],[1865,20658,1955],{"className":20659},[2697],[1865,20661],{"className":20662,"style":2693},[2246],[1865,20664,1935],{"className":20665},[2080],[1865,20667],{"className":20668,"style":2855},[2246],[1865,20670,20672,20675],{"className":20671},[11465],[1865,20673,11392],{"className":20674,"style":11471},[11465,11469,11470],[1865,20676,20678],{"className":20677},[2158],[1865,20679,20681,20719],{"className":20680},[2091,2092],[1865,20682,20684,20716],{"className":20683},[2096],[1865,20685,20688,20702],{"className":20686,"style":20687},[2100],"height:1.564em;",[1865,20689,20690,20693],{"style":11487},[1865,20691],{"className":20692,"style":2175},[2108],[1865,20694,20696],{"className":20695},[2179,2180,2181,2182],[1865,20697,20699],{"className":20698},[2080,2182],[1865,20700,16543],{"className":20701},[2080,2182],[1865,20703,20704,20707],{"style":11499},[1865,20705],{"className":20706,"style":2175},[2108],[1865,20708,20710],{"className":20709},[2179,2180,2181,2182],[1865,20711,20713],{"className":20712},[2080,2182],[1865,20714,1931],{"className":20715},[2080,2182],[1865,20717,2190],{"className":20718},[2189],[1865,20720,20722],{"className":20721},[2096],[1865,20723,20726],{"className":20724,"style":20725},[2100],"height:1.0869em;",[1865,20727],{},[1865,20729],{"className":20730,"style":2855},[2246],[1865,20732,20734,20737,20839],{"className":20733},[2080],[1865,20735],{"className":20736},[2119,2120],[1865,20738,20740],{"className":20739},[1906],[1865,20741,20743,20830],{"className":20742},[2091,2092],[1865,20744,20746,20827],{"className":20745},[2096],[1865,20747,20749,20808,20816],{"className":20748,"style":6666},[2100],[1865,20750,20752,20755],{"style":20751},"top:-2.3097em;",[1865,20753],{"className":20754,"style":2140},[2108],[1865,20756,20758],{"className":20757},[2080],[1865,20759,20761],{"className":20760},[2080,12874],[1865,20762,20764,20799],{"className":20763},[2091,2092],[1865,20765,20767,20796],{"className":20766},[2096],[1865,20768,20771,20783],{"className":20769,"style":20770},[2100],"height:0.8003em;",[1865,20772,20774,20777],{"className":20773,"style":12889},[12888],[1865,20775],{"className":20776,"style":2140},[2108],[1865,20778,20780],{"className":20779,"style":12896},[2080],[1865,20781,1927],{"className":20782},[2080,2154],[1865,20784,20786,20789],{"style":20785},"top:-2.7603em;",[1865,20787],{"className":20788,"style":2140},[2108],[1865,20790,20792],{"className":20791,"style":12947},[12946],[3893,20793,20794],{"xmlns":3895,"width":12950,"height":12951,"viewBox":12952,"preserveAspectRatio":12953},[3899,20795],{"d":12956},[1865,20797,2190],{"className":20798},[2189],[1865,20800,20802],{"className":20801},[2096],[1865,20803,20806],{"className":20804,"style":20805},[2100],"height:0.2397em;",[1865,20807],{},[1865,20809,20810,20813],{"style":2202},[1865,20811],{"className":20812,"style":2140},[2108],[1865,20814],{"className":20815,"style":2210},[2209],[1865,20817,20818,20821],{"style":2213},[1865,20819],{"className":20820,"style":2140},[2108],[1865,20822,20824],{"className":20823},[2080],[1865,20825,1931],{"className":20826},[2080],[1865,20828,2190],{"className":20829},[2189],[1865,20831,20833],{"className":20832},[2096],[1865,20834,20837],{"className":20835,"style":20836},[2100],"height:0.93em;",[1865,20838],{},[1865,20840],{"className":20841},[2242,2120],[1865,20843,3144],{"className":20844},[2080,2154],[1865,20846,1927],{"className":20847},[2080,2154],[1865,20849,20850,20853],{"style":20359},[1865,20851],{"className":20852,"style":20335},[2108],[1865,20854,20856,20859,20862,20865,20868,20871,20874,20877,20927],{"className":20855},[2080],[1865,20857],{"className":20858},[2080],[1865,20860],{"className":20861,"style":2693},[2246],[1865,20863,1955],{"className":20864},[2697],[1865,20866],{"className":20867,"style":2693},[2246],[1865,20869,1935],{"className":20870},[2080],[1865,20872,20237],{"className":20873},[2119],[1865,20875,1984],{"className":20876},[2080],[1865,20878,20880],{"className":20879},[2080,12874],[1865,20881,20883,20918],{"className":20882},[2091,2092],[1865,20884,20886,20915],{"className":20885},[2096],[1865,20887,20890,20902],{"className":20888,"style":20889},[2100],"height:0.8492em;",[1865,20891,20893,20896],{"className":20892,"style":12889},[12888],[1865,20894],{"className":20895,"style":2140},[2108],[1865,20897,20899],{"className":20898,"style":12896},[2080],[1865,20900,1927],{"className":20901},[2080,2154],[1865,20903,20905,20908],{"style":20904},"top:-2.8092em;",[1865,20906],{"className":20907,"style":2140},[2108],[1865,20909,20911],{"className":20910,"style":12947},[12946],[3893,20912,20913],{"xmlns":3895,"width":12950,"height":12951,"viewBox":12952,"preserveAspectRatio":12953},[3899,20914],{"d":12956},[1865,20916,2190],{"className":20917},[2189],[1865,20919,20921],{"className":20920},[2096],[1865,20922,20925],{"className":20923,"style":20924},[2100],"height:0.1908em;",[1865,20926],{},[1865,20928,20930,20933],{"className":20929},[2242],[1865,20931,20248],{"className":20932},[2242],[1865,20934,20936],{"className":20935},[2158],[1865,20937,20939,20977],{"className":20938},[2091,2092],[1865,20940,20942,20974],{"className":20941},[2096],[1865,20943,20945,20960],{"className":20944,"style":8863},[2100],[1865,20946,20948,20951],{"style":20947},"top:-2.428em;margin-left:0em;margin-right:0.05em;",[1865,20949],{"className":20950,"style":2175},[2108],[1865,20952,20954],{"className":20953},[2179,2180,2181,2182],[1865,20955,20957],{"className":20956},[2080,2182],[1865,20958,16543],{"className":20959},[2080,2182],[1865,20961,20962,20965],{"style":7181},[1865,20963],{"className":20964,"style":2175},[2108],[1865,20966,20968],{"className":20967},[2179,2180,2181,2182],[1865,20969,20971],{"className":20970},[2080,2182],[1865,20972,1931],{"className":20973},[2080,2182],[1865,20975,2190],{"className":20976},[2189],[1865,20978,20980],{"className":20979},[2096],[1865,20981,20984],{"className":20982,"style":20983},[2100],"height:0.447em;",[1865,20985],{},[1865,20987,20988,20991],{"style":20368},[1865,20989],{"className":20990,"style":20335},[2108],[1865,20992,20994,20997,21000,21003,21006,21009,21012,21015,21018,21021,21024,21027,21030,21033,21036,21039,21042],{"className":20993},[2080],[1865,20995],{"className":20996},[2080],[1865,20998],{"className":20999,"style":2693},[2246],[1865,21001,1955],{"className":21002},[2697],[1865,21004],{"className":21005,"style":2693},[2246],[1865,21007,1935],{"className":21008},[2080],[1865,21010,4942],{"className":21011},[2119],[1865,21013,1984],{"className":21014},[2080],[1865,21016],{"className":21017,"style":2247},[2246],[1865,21019,1935],{"className":21020},[2251],[1865,21022],{"className":21023,"style":2247},[2246],[1865,21025,20287],{"className":21026},[2080],[1865,21028,4963],{"className":21029},[2242],[1865,21031],{"className":21032,"style":2693},[2246],[1865,21034,1955],{"className":21035},[2697],[1865,21037],{"className":21038,"style":2693},[2246],[1865,21040,1935],{"className":21041},[2080],[1865,21043,20296],{"className":21044},[2080],[1865,21046,2190],{"className":21047},[2189],[1865,21049,21051],{"className":21050},[2096],[1865,21052,21054],{"className":21053,"style":20384},[2100],[1865,21055],{},[1798,21057,21058],{},"不对，我算错了。让我用另一种方法：",[1865,21060,21062],{"className":21061},[1868],[1865,21063,21065,21185],{"className":21064},[1872],[1865,21066,21068],{"className":21067},[1876],[1878,21069,21070],{"xmlns":1880,"display":1881},[1883,21071,21072,21182],{},[1903,21073,21074,21076,21078,21080,21082,21102,21108,21110,21112,21114,21116,21118,21120,21128,21138,21140,21142,21144,21164,21166,21168,21174,21176,21178,21180],{},[1911,21075,11793],{"mathvariant":1913},[1911,21077,8734],{},[1911,21079,6896],{},[1933,21081,1955],{},[8534,21083,21084,21086,21094],{},[1933,21085,11392],{},[8534,21087,21088,21090,21092],{},[1911,21089,1798],{},[1929,21091,1931],{},[1929,21093,1900],{},[8534,21095,21096,21098,21100],{},[1911,21097,1798],{},[1929,21099,1931],{},[1929,21101,1931],{},[1923,21103,21104,21106],{},[1911,21105,1927],{},[1929,21107,1931],{},[1933,21109,4942],{"stretchy":3501},[1911,21111,1798],{},[1933,21113,4963],{"stretchy":3501},[1911,21115,3144],{},[1911,21117,1798],{},[1933,21119,1955],{},[8534,21121,21122,21124,21126],{},[1933,21123,11392],{},[1929,21125,1931],{},[1929,21127,13355],{},[1906,21129,21130,21132],{},[1929,21131,1931],{},[6885,21133,21134,21136],{},[1911,21135,1798],{},[1929,21137,1984],{},[1911,21139,3144],{},[1911,21141,1798],{},[1933,21143,1955],{},[8534,21145,21146,21160,21162],{},[1903,21147,21148,21150,21152,21158],{},[1933,21149,20237],{"fence":1901},[1933,21151,1935],{},[1906,21153,21154,21156],{},[1929,21155,1931],{},[1911,21157,1798],{},[1933,21159,20248],{"fence":1901},[1929,21161,1931],{},[1929,21163,13355],{},[1933,21165,1955],{},[1933,21167,1935],{},[1906,21169,21170,21172],{},[1929,21171,1931],{},[1929,21173,13355],{},[1933,21175,2029],{},[1929,21177,1931],{},[1933,21179,1955],{},[1929,21181,18274],{},[2060,21183,21184],{"encoding":2062},"\\Delta CS = \\int_{p_1^0}^{p_1^1} x_1(p)dp = \\int_1^4 \\frac{1}{p^2}dp = \\left[-\\frac{1}{p}\\right]_1^4 = -\\frac{1}{4} + 1 = 0.75",[1865,21186,21188,21212,21439,21604,21750,21831,21849],{"className":21187,"ariaHidden":1901},[2067],[1865,21189,21191,21194,21197,21200,21203,21206,21209],{"className":21190},[2071],[1865,21192],{"className":21193,"style":8815},[2075],[1865,21195,11793],{"className":21196},[2080],[1865,21198,8734],{"className":21199,"style":8819},[2080,2154],[1865,21201,6896],{"className":21202,"style":7058},[2080,2154],[1865,21204],{"className":21205,"style":2693},[2246],[1865,21207,1955],{"className":21208},[2697],[1865,21210],{"className":21211,"style":2693},[2246],[1865,21213,21215,21219,21372,21375,21415,21418,21421,21424,21427,21430,21433,21436],{"className":21214},[2071],[1865,21216],{"className":21217,"style":21218},[2075],"height:2.8668em;vertical-align:-1.13em;",[1865,21220,21222,21225],{"className":21221},[11465],[1865,21223,11392],{"className":21224,"style":11471},[11465,11469,11470],[1865,21226,21228],{"className":21227},[2158],[1865,21229,21231,21364],{"className":21230},[2091,2092],[1865,21232,21234,21361],{"className":21233},[2096],[1865,21235,21237,21299],{"className":21236,"style":11889},[2100],[1865,21238,21239,21242],{"style":11487},[1865,21240],{"className":21241,"style":2175},[2108],[1865,21243,21245],{"className":21244},[2179,2180,2181,2182],[1865,21246,21248],{"className":21247},[2080,2182],[1865,21249,21251,21254],{"className":21250},[2080,2182],[1865,21252,1798],{"className":21253},[2080,2154,2182],[1865,21255,21257],{"className":21256},[2158],[1865,21258,21260,21291],{"className":21259},[2091,2092],[1865,21261,21263,21288],{"className":21262},[2096],[1865,21264,21266,21277],{"className":21265,"style":20472},[2100],[1865,21267,21268,21271],{"style":20475},[1865,21269],{"className":21270,"style":4268},[2108],[1865,21272,21274],{"className":21273},[2179,4272,4273,2182],[1865,21275,1931],{"className":21276},[2080,2182],[1865,21278,21279,21282],{"style":20487},[1865,21280],{"className":21281,"style":4268},[2108],[1865,21283,21285],{"className":21284},[2179,4272,4273,2182],[1865,21286,1900],{"className":21287},[2080,2182],[1865,21289,2190],{"className":21290},[2189],[1865,21292,21294],{"className":21293},[2096],[1865,21295,21297],{"className":21296,"style":20506},[2100],[1865,21298],{},[1865,21300,21301,21304],{"style":11499},[1865,21302],{"className":21303,"style":2175},[2108],[1865,21305,21307],{"className":21306},[2179,2180,2181,2182],[1865,21308,21310],{"className":21309},[2080,2182],[1865,21311,21313,21316],{"className":21312},[2080,2182],[1865,21314,1798],{"className":21315},[2080,2154,2182],[1865,21317,21319],{"className":21318},[2158],[1865,21320,21322,21353],{"className":21321},[2091,2092],[1865,21323,21325,21350],{"className":21324},[2096],[1865,21326,21328,21339],{"className":21327,"style":11961},[2100],[1865,21329,21330,21333],{"style":20540},[1865,21331],{"className":21332,"style":4268},[2108],[1865,21334,21336],{"className":21335},[2179,4272,4273,2182],[1865,21337,1931],{"className":21338},[2080,2182],[1865,21340,21341,21344],{"style":11530},[1865,21342],{"className":21343,"style":4268},[2108],[1865,21345,21347],{"className":21346},[2179,4272,4273,2182],[1865,21348,1931],{"className":21349},[2080,2182],[1865,21351,2190],{"className":21352},[2189],[1865,21354,21356],{"className":21355},[2096],[1865,21357,21359],{"className":21358,"style":20570},[2100],[1865,21360],{},[1865,21362,2190],{"className":21363},[2189],[1865,21365,21367],{"className":21366},[2096],[1865,21368,21370],{"className":21369,"style":20582},[2100],[1865,21371],{},[1865,21373],{"className":21374,"style":2855},[2246],[1865,21376,21378,21381],{"className":21377},[2080],[1865,21379,1927],{"className":21380},[2080,2154],[1865,21382,21384],{"className":21383},[2158],[1865,21385,21387,21407],{"className":21386},[2091,2092],[1865,21388,21390,21404],{"className":21389},[2096],[1865,21391,21393],{"className":21392,"style":2168},[2100],[1865,21394,21395,21398],{"style":2171},[1865,21396],{"className":21397,"style":2175},[2108],[1865,21399,21401],{"className":21400},[2179,2180,2181,2182],[1865,21402,1931],{"className":21403},[2080,2182],[1865,21405,2190],{"className":21406},[2189],[1865,21408,21410],{"className":21409},[2096],[1865,21411,21413],{"className":21412,"style":2197},[2100],[1865,21414],{},[1865,21416,4942],{"className":21417},[2119],[1865,21419,1798],{"className":21420},[2080,2154],[1865,21422,4963],{"className":21423},[2242],[1865,21425,3144],{"className":21426},[2080,2154],[1865,21428,1798],{"className":21429},[2080,2154],[1865,21431],{"className":21432,"style":2693},[2246],[1865,21434,1955],{"className":21435},[2697],[1865,21437],{"className":21438,"style":2693},[2246],[1865,21440,21442,21446,21497,21500,21589,21592,21595,21598,21601],{"className":21441},[2071],[1865,21443],{"className":21444,"style":21445},[2075],"height:2.476em;vertical-align:-0.9119em;",[1865,21447,21449,21452],{"className":21448},[11465],[1865,21450,11392],{"className":21451,"style":11471},[11465,11469,11470],[1865,21453,21455],{"className":21454},[2158],[1865,21456,21458,21489],{"className":21457},[2091,2092],[1865,21459,21461,21486],{"className":21460},[2096],[1865,21462,21464,21475],{"className":21463,"style":20687},[2100],[1865,21465,21466,21469],{"style":11487},[1865,21467],{"className":21468,"style":2175},[2108],[1865,21470,21472],{"className":21471},[2179,2180,2181,2182],[1865,21473,1931],{"className":21474},[2080,2182],[1865,21476,21477,21480],{"style":11499},[1865,21478],{"className":21479,"style":2175},[2108],[1865,21481,21483],{"className":21482},[2179,2180,2181,2182],[1865,21484,13355],{"className":21485},[2080,2182],[1865,21487,2190],{"className":21488},[2189],[1865,21490,21492],{"className":21491},[2096],[1865,21493,21495],{"className":21494,"style":11549},[2100],[1865,21496],{},[1865,21498],{"className":21499,"style":2855},[2246],[1865,21501,21503,21506,21586],{"className":21502},[2080],[1865,21504],{"className":21505},[2119,2120],[1865,21507,21509],{"className":21508},[1906],[1865,21510,21512,21578],{"className":21511},[2091,2092],[1865,21513,21515,21575],{"className":21514},[2096],[1865,21516,21518,21556,21564],{"className":21517,"style":6666},[2100],[1865,21519,21520,21523],{"style":2136},[1865,21521],{"className":21522,"style":2140},[2108],[1865,21524,21526],{"className":21525},[2080],[1865,21527,21529,21532],{"className":21528},[2080],[1865,21530,1798],{"className":21531},[2080,2154],[1865,21533,21535],{"className":21534},[2158],[1865,21536,21538],{"className":21537},[2091],[1865,21539,21541],{"className":21540},[2096],[1865,21542,21545],{"className":21543,"style":21544},[2100],"height:0.7401em;",[1865,21546,21547,21550],{"style":6991},[1865,21548],{"className":21549,"style":2175},[2108],[1865,21551,21553],{"className":21552},[2179,2180,2181,2182],[1865,21554,1984],{"className":21555},[2080,2182],[1865,21557,21558,21561],{"style":2202},[1865,21559],{"className":21560,"style":2140},[2108],[1865,21562],{"className":21563,"style":2210},[2209],[1865,21565,21566,21569],{"style":2213},[1865,21567],{"className":21568,"style":2140},[2108],[1865,21570,21572],{"className":21571},[2080],[1865,21573,1931],{"className":21574},[2080],[1865,21576,2190],{"className":21577},[2189],[1865,21579,21581],{"className":21580},[2096],[1865,21582,21584],{"className":21583,"style":3396},[2100],[1865,21585],{},[1865,21587],{"className":21588},[2242,2120],[1865,21590,3144],{"className":21591},[2080,2154],[1865,21593,1798],{"className":21594},[2080,2154],[1865,21596],{"className":21597,"style":2693},[2246],[1865,21599,1955],{"className":21600},[2697],[1865,21602],{"className":21603,"style":2693},[2246],[1865,21605,21607,21611,21741,21744,21747],{"className":21606},[2071],[1865,21608],{"className":21609,"style":21610},[2075],"height:2.6537em;vertical-align:-0.9997em;",[1865,21612,21614,21694],{"className":21613},[18607],[1865,21615,21617,21623,21626,21688],{"className":21616},[18607],[1865,21618,21620],{"className":21619,"style":18612},[2119,18611],[1865,21621,20237],{"className":21622},[3870,2181],[1865,21624,1935],{"className":21625},[2080],[1865,21627,21629,21632,21685],{"className":21628},[2080],[1865,21630],{"className":21631},[2119,2120],[1865,21633,21635],{"className":21634},[1906],[1865,21636,21638,21677],{"className":21637},[2091,2092],[1865,21639,21641,21674],{"className":21640},[2096],[1865,21642,21644,21655,21663],{"className":21643,"style":6666},[2100],[1865,21645,21646,21649],{"style":2136},[1865,21647],{"className":21648,"style":2140},[2108],[1865,21650,21652],{"className":21651},[2080],[1865,21653,1798],{"className":21654},[2080,2154],[1865,21656,21657,21660],{"style":2202},[1865,21658],{"className":21659,"style":2140},[2108],[1865,21661],{"className":21662,"style":2210},[2209],[1865,21664,21665,21668],{"style":2213},[1865,21666],{"className":21667,"style":2140},[2108],[1865,21669,21671],{"className":21670},[2080],[1865,21672,1931],{"className":21673},[2080],[1865,21675,2190],{"className":21676},[2189],[1865,21678,21680],{"className":21679},[2096],[1865,21681,21683],{"className":21682,"style":3396},[2100],[1865,21684],{},[1865,21686],{"className":21687},[2242,2120],[1865,21689,21691],{"className":21690,"style":18612},[2242,18611],[1865,21692,20248],{"className":21693},[3870,2181],[1865,21695,21697],{"className":21696},[2158],[1865,21698,21700,21733],{"className":21699},[2091,2092],[1865,21701,21703,21730],{"className":21702},[2096],[1865,21704,21707,21718],{"className":21705,"style":21706},[2100],"height:1.654em;",[1865,21708,21709,21712],{"style":3929},[1865,21710],{"className":21711,"style":2175},[2108],[1865,21713,21715],{"className":21714},[2179,2180,2181,2182],[1865,21716,1931],{"className":21717},[2080,2182],[1865,21719,21721,21724],{"style":21720},"top:-3.9029em;margin-right:0.05em;",[1865,21722],{"className":21723,"style":2175},[2108],[1865,21725,21727],{"className":21726},[2179,2180,2181,2182],[1865,21728,13355],{"className":21729},[2080,2182],[1865,21731,2190],{"className":21732},[2189],[1865,21734,21736],{"className":21735},[2096],[1865,21737,21739],{"className":21738,"style":3990},[2100],[1865,21740],{},[1865,21742],{"className":21743,"style":2693},[2246],[1865,21745,1955],{"className":21746},[2697],[1865,21748],{"className":21749,"style":2693},[2246],[1865,21751,21753,21757,21760,21822,21825,21828],{"className":21752},[2071],[1865,21754],{"className":21755,"style":21756},[2075],"height:2.0074em;vertical-align:-0.686em;",[1865,21758,1935],{"className":21759},[2080],[1865,21761,21763,21766,21819],{"className":21762},[2080],[1865,21764],{"className":21765},[2119,2120],[1865,21767,21769],{"className":21768},[1906],[1865,21770,21772,21811],{"className":21771},[2091,2092],[1865,21773,21775,21808],{"className":21774},[2096],[1865,21776,21778,21789,21797],{"className":21777,"style":6666},[2100],[1865,21779,21780,21783],{"style":2136},[1865,21781],{"className":21782,"style":2140},[2108],[1865,21784,21786],{"className":21785},[2080],[1865,21787,13355],{"className":21788},[2080],[1865,21790,21791,21794],{"style":2202},[1865,21792],{"className":21793,"style":2140},[2108],[1865,21795],{"className":21796,"style":2210},[2209],[1865,21798,21799,21802],{"style":2213},[1865,21800],{"className":21801,"style":2140},[2108],[1865,21803,21805],{"className":21804},[2080],[1865,21806,1931],{"className":21807},[2080],[1865,21809,2190],{"className":21810},[2189],[1865,21812,21814],{"className":21813},[2096],[1865,21815,21817],{"className":21816,"style":4149},[2100],[1865,21818],{},[1865,21820],{"className":21821},[2242,2120],[1865,21823],{"className":21824,"style":2247},[2246],[1865,21826,2029],{"className":21827},[2251],[1865,21829],{"className":21830,"style":2247},[2246],[1865,21832,21834,21837,21840,21843,21846],{"className":21833},[2071],[1865,21835],{"className":21836,"style":7553},[2075],[1865,21838,1931],{"className":21839},[2080],[1865,21841],{"className":21842,"style":2693},[2246],[1865,21844,1955],{"className":21845},[2697],[1865,21847],{"className":21848,"style":2693},[2246],[1865,21850,21852,21855],{"className":21851},[2071],[1865,21853],{"className":21854,"style":7553},[2075],[1865,21856,18274],{"className":21857},[2080],[1798,21859,21860,7266,21863,21974],{},[3048,21861,21862],{},"结论",[1865,21864,21866,21896],{"className":21865},[1872],[1865,21867,21869],{"className":21868},[1876],[1878,21870,21871],{"xmlns":1880},[1883,21872,21873,21893],{},[1903,21874,21875,21877,21879,21881,21883,21885,21887,21889,21891],{},[1911,21876,8734],{},[1911,21878,8737],{},[1933,21880,1955],{},[1911,21882,9930],{},[1911,21884,8737],{},[1933,21886,1955],{},[11827,21888,12032],{},[1933,21890,1955],{},[1929,21892,18274],{},[2060,21894,21895],{"encoding":2062},"CV = EV = \\text{CS 损失} = 0.75",[1865,21897,21899,21920,21941,21965],{"className":21898,"ariaHidden":1901},[2067],[1865,21900,21902,21905,21908,21911,21914,21917],{"className":21901},[2071],[1865,21903],{"className":21904,"style":8815},[2075],[1865,21906,8734],{"className":21907,"style":8819},[2080,2154],[1865,21909,8737],{"className":21910,"style":2247},[2080,2154],[1865,21912],{"className":21913,"style":2693},[2246],[1865,21915,1955],{"className":21916},[2697],[1865,21918],{"className":21919,"style":2693},[2246],[1865,21921,21923,21926,21929,21932,21935,21938],{"className":21922},[2071],[1865,21924],{"className":21925,"style":8815},[2075],[1865,21927,9930],{"className":21928,"style":7058},[2080,2154],[1865,21930,8737],{"className":21931,"style":2247},[2080,2154],[1865,21933],{"className":21934,"style":2693},[2246],[1865,21936,1955],{"className":21937},[2697],[1865,21939],{"className":21940,"style":2693},[2246],[1865,21942,21944,21947,21956,21959,21962],{"className":21943},[2071],[1865,21945],{"className":21946,"style":8815},[2075],[1865,21948,21950,21953],{"className":21949},[2080,11278],[1865,21951,12083],{"className":21952},[2080],[1865,21954,12088],{"className":21955},[2080,12087],[1865,21957],{"className":21958,"style":2693},[2246],[1865,21960,1955],{"className":21961},[2697],[1865,21963],{"className":21964,"style":2693},[2246],[1865,21966,21968,21971],{"className":21967},[2071],[1865,21969],{"className":21970,"style":7553},[2075],[1865,21972,18274],{"className":21973},[2080],"（拟线性效用的特殊性质）",[1854,21976,21978],{"id":21977},"例题-2-斯勒茨基分解的数值计算","例题 2: 斯勒茨基分解的数值计算",[1798,21980,21981,21983,21984,7457,22154,22358,22359,22428],{},[3048,21982,12690],{},": 柯布-道格拉斯效用 ",[1865,21985,21987,22019],{"className":21986},[1872],[1865,21988,21990],{"className":21989},[1876],[1878,21991,21992],{"xmlns":1880},[1883,21993,21994,22016],{},[1903,21995,21996,21998,22000,22008],{},[1911,21997,1917],{},[1933,21999,1955],{},[8534,22001,22002,22004,22006],{},[1911,22003,1927],{},[1929,22005,1931],{},[1929,22007,20287],{},[8534,22009,22010,22012,22014],{},[1911,22011,1927],{},[1929,22013,1984],{},[1929,22015,20287],{},[2060,22017,22018],{"encoding":2062},"U = x_1^{0.5} x_2^{0.5}",[1865,22020,22022,22040],{"className":22021,"ariaHidden":1901},[2067],[1865,22023,22025,22028,22031,22034,22037],{"className":22024},[2071],[1865,22026],{"className":22027,"style":8815},[2075],[1865,22029,1917],{"className":22030,"style":2226},[2080,2154],[1865,22032],{"className":22033,"style":2693},[2246],[1865,22035,1955],{"className":22036},[2697],[1865,22038],{"className":22039,"style":2693},[2246],[1865,22041,22043,22046,22100],{"className":22042},[2071],[1865,22044],{"className":22045,"style":8554},[2075],[1865,22047,22049,22052],{"className":22048},[2080],[1865,22050,1927],{"className":22051},[2080,2154],[1865,22053,22055],{"className":22054},[2158],[1865,22056,22058,22092],{"className":22057},[2091,2092],[1865,22059,22061,22089],{"className":22060},[2096],[1865,22062,22064,22075],{"className":22063,"style":8573},[2100],[1865,22065,22066,22069],{"style":8576},[1865,22067],{"className":22068,"style":2175},[2108],[1865,22070,22072],{"className":22071},[2179,2180,2181,2182],[1865,22073,1931],{"className":22074},[2080,2182],[1865,22076,22077,22080],{"style":7519},[1865,22078],{"className":22079,"style":2175},[2108],[1865,22081,22083],{"className":22082},[2179,2180,2181,2182],[1865,22084,22086],{"className":22085},[2080,2182],[1865,22087,20287],{"className":22088},[2080,2182],[1865,22090,2190],{"className":22091},[2189],[1865,22093,22095],{"className":22094},[2096],[1865,22096,22098],{"className":22097,"style":8606},[2100],[1865,22099],{},[1865,22101,22103,22106],{"className":22102},[2080],[1865,22104,1927],{"className":22105},[2080,2154],[1865,22107,22109],{"className":22108},[2158],[1865,22110,22112,22146],{"className":22111},[2091,2092],[1865,22113,22115,22143],{"className":22114},[2096],[1865,22116,22118,22129],{"className":22117,"style":8573},[2100],[1865,22119,22120,22123],{"style":8576},[1865,22121],{"className":22122,"style":2175},[2108],[1865,22124,22126],{"className":22125},[2179,2180,2181,2182],[1865,22127,1984],{"className":22128},[2080,2182],[1865,22130,22131,22134],{"style":7519},[1865,22132],{"className":22133,"style":2175},[2108],[1865,22135,22137],{"className":22136},[2179,2180,2181,2182],[1865,22138,22140],{"className":22139},[2080,2182],[1865,22141,20287],{"className":22142},[2080,2182],[1865,22144,2190],{"className":22145},[2189],[1865,22147,22149],{"className":22148},[2096],[1865,22150,22152],{"className":22151,"style":8606},[2100],[1865,22153],{},[1865,22155,22157,22200],{"className":22156},[1872],[1865,22158,22160],{"className":22159},[1876],[1878,22161,22162],{"xmlns":1880},[1883,22163,22164,22197],{},[1903,22165,22166,22172,22174,22176,22178,22184,22186,22188,22190,22192,22194],{},[1923,22167,22168,22170],{},[1911,22169,1798],{},[1929,22171,1931],{},[1933,22173,1955],{},[1929,22175,1984],{},[1933,22177,2784],{"separator":1901},[1923,22179,22180,22182],{},[1911,22181,1798],{},[1929,22183,1984],{},[1933,22185,1955],{},[1929,22187,1931],{},[1933,22189,2784],{"separator":1901},[1911,22191,2046],{},[1933,22193,1955],{},[1929,22195,22196],{},"100",[2060,22198,22199],{"encoding":2062},"p_1 = 2, p_2 = 1, m = 100",[1865,22201,22203,22258,22322,22349],{"className":22202,"ariaHidden":1901},[2067],[1865,22204,22206,22209,22249,22252,22255],{"className":22205},[2071],[1865,22207],{"className":22208,"style":2948},[2075],[1865,22210,22212,22215],{"className":22211},[2080],[1865,22213,1798],{"className":22214},[2080,2154],[1865,22216,22218],{"className":22217},[2158],[1865,22219,22221,22241],{"className":22220},[2091,2092],[1865,22222,22224,22238],{"className":22223},[2096],[1865,22225,22227],{"className":22226,"style":2168},[2100],[1865,22228,22229,22232],{"style":2171},[1865,22230],{"className":22231,"style":2175},[2108],[1865,22233,22235],{"className":22234},[2179,2180,2181,2182],[1865,22236,1931],{"className":22237},[2080,2182],[1865,22239,2190],{"className":22240},[2189],[1865,22242,22244],{"className":22243},[2096],[1865,22245,22247],{"className":22246,"style":2197},[2100],[1865,22248],{},[1865,22250],{"className":22251,"style":2693},[2246],[1865,22253,1955],{"className":22254},[2697],[1865,22256],{"className":22257,"style":2693},[2246],[1865,22259,22261,22264,22267,22270,22273,22313,22316,22319],{"className":22260},[2071],[1865,22262],{"className":22263,"style":13139},[2075],[1865,22265,1984],{"className":22266},[2080],[1865,22268,2784],{"className":22269},[2851],[1865,22271],{"className":22272,"style":2855},[2246],[1865,22274,22276,22279],{"className":22275},[2080],[1865,22277,1798],{"className":22278},[2080,2154],[1865,22280,22282],{"className":22281},[2158],[1865,22283,22285,22305],{"className":22284},[2091,2092],[1865,22286,22288,22302],{"className":22287},[2096],[1865,22289,22291],{"className":22290,"style":2168},[2100],[1865,22292,22293,22296],{"style":2171},[1865,22294],{"className":22295,"style":2175},[2108],[1865,22297,22299],{"className":22298},[2179,2180,2181,2182],[1865,22300,1984],{"className":22301},[2080,2182],[1865,22303,2190],{"className":22304},[2189],[1865,22306,22308],{"className":22307},[2096],[1865,22309,22311],{"className":22310,"style":2197},[2100],[1865,22312],{},[1865,22314],{"className":22315,"style":2693},[2246],[1865,22317,1955],{"className":22318},[2697],[1865,22320],{"className":22321,"style":2693},[2246],[1865,22323,22325,22328,22331,22334,22337,22340,22343,22346],{"className":22324},[2071],[1865,22326],{"className":22327,"style":13139},[2075],[1865,22329,1931],{"className":22330},[2080],[1865,22332,2784],{"className":22333},[2851],[1865,22335],{"className":22336,"style":2855},[2246],[1865,22338,2046],{"className":22339},[2080,2154],[1865,22341],{"className":22342,"style":2693},[2246],[1865,22344,1955],{"className":22345},[2697],[1865,22347],{"className":22348,"style":2693},[2246],[1865,22350,22352,22355],{"className":22351},[2071],[1865,22353],{"className":22354,"style":7553},[2075],[1865,22356,22196],{"className":22357},[2080],"。若",[1865,22360,22362,22379],{"className":22361},[1872],[1865,22363,22365],{"className":22364},[1876],[1878,22366,22367],{"xmlns":1880},[1883,22368,22369,22377],{},[1903,22370,22371],{},[1923,22372,22373,22375],{},[1911,22374,1798],{},[1929,22376,1931],{},[2060,22378,3079],{"encoding":2062},[1865,22380,22382],{"className":22381,"ariaHidden":1901},[2067],[1865,22383,22385,22388],{"className":22384},[2071],[1865,22386],{"className":22387,"style":2948},[2075],[1865,22389,22391,22394],{"className":22390},[2080],[1865,22392,1798],{"className":22393},[2080,2154],[1865,22395,22397],{"className":22396},[2158],[1865,22398,22400,22420],{"className":22399},[2091,2092],[1865,22401,22403,22417],{"className":22402},[2096],[1865,22404,22406],{"className":22405,"style":2168},[2100],[1865,22407,22408,22411],{"style":2171},[1865,22409],{"className":22410,"style":2175},[2108],[1865,22412,22414],{"className":22413},[2179,2180,2181,2182],[1865,22415,1931],{"className":22416},[2080,2182],[1865,22418,2190],{"className":22419},[2189],[1865,22421,22423],{"className":22422},[2096],[1865,22424,22426],{"className":22425,"style":2197},[2100],[1865,22427],{},"涨到3，分解需求变化为替代效应和收入效应。",[1798,22430,22431,4915],{},[3048,22432,13482],{},[1798,22434,15323,22435],{},[1865,22436,22438,22485],{"className":22437},[1872],[1865,22439,22441],{"className":22440},[1876],[1878,22442,22443],{"xmlns":1880},[1883,22444,22445,22482],{},[1903,22446,22447,22453,22455,22469,22471],{},[1923,22448,22449,22451],{},[1911,22450,1927],{},[1929,22452,1931],{},[1933,22454,1955],{},[1906,22456,22457,22463],{},[1903,22458,22459,22461],{},[1929,22460,20287],{},[1911,22462,2046],{},[1923,22464,22465,22467],{},[1911,22466,1798],{},[1929,22468,1931],{},[1933,22470,1955],{},[1906,22472,22473,22476],{},[1929,22474,22475],{},"50",[1923,22477,22478,22480],{},[1911,22479,1798],{},[1929,22481,1931],{},[2060,22483,22484],{"encoding":2062},"x_1 = \\frac{0.5m}{p_1} = \\frac{50}{p_1}",[1865,22486,22488,22543,22670],{"className":22487,"ariaHidden":1901},[2067],[1865,22489,22491,22494,22534,22537,22540],{"className":22490},[2071],[1865,22492],{"className":22493,"style":12589},[2075],[1865,22495,22497,22500],{"className":22496},[2080],[1865,22498,1927],{"className":22499},[2080,2154],[1865,22501,22503],{"className":22502},[2158],[1865,22504,22506,22526],{"className":22505},[2091,2092],[1865,22507,22509,22523],{"className":22508},[2096],[1865,22510,22512],{"className":22511,"style":2168},[2100],[1865,22513,22514,22517],{"style":2171},[1865,22515],{"className":22516,"style":2175},[2108],[1865,22518,22520],{"className":22519},[2179,2180,2181,2182],[1865,22521,1931],{"className":22522},[2080,2182],[1865,22524,2190],{"className":22525},[2189],[1865,22527,22529],{"className":22528},[2096],[1865,22530,22532],{"className":22531,"style":2197},[2100],[1865,22533],{},[1865,22535],{"className":22536,"style":2693},[2246],[1865,22538,1955],{"className":22539},[2697],[1865,22541],{"className":22542,"style":2693},[2246],[1865,22544,22546,22550,22661,22664,22667],{"className":22545},[2071],[1865,22547],{"className":22548,"style":22549},[2075],"height:1.3262em;vertical-align:-0.4811em;",[1865,22551,22553,22556,22658],{"className":22552},[2080],[1865,22554],{"className":22555},[2119,2120],[1865,22557,22559],{"className":22558},[1906],[1865,22560,22562,22650],{"className":22561},[2091,2092],[1865,22563,22565,22647],{"className":22564},[2096],[1865,22566,22569,22621,22629],{"className":22567,"style":22568},[2100],"height:0.8451em;",[1865,22570,22571,22574],{"style":4230},[1865,22572],{"className":22573,"style":2140},[2108],[1865,22575,22577],{"className":22576},[2179,2180,2181,2182],[1865,22578,22580],{"className":22579},[2080,2182],[1865,22581,22583,22586],{"className":22582},[2080,2182],[1865,22584,1798],{"className":22585},[2080,2154,2182],[1865,22587,22589],{"className":22588},[2158],[1865,22590,22592,22613],{"className":22591},[2091,2092],[1865,22593,22595,22610],{"className":22594},[2096],[1865,22596,22599],{"className":22597,"style":22598},[2100],"height:0.3173em;",[1865,22600,22601,22604],{"style":4264},[1865,22602],{"className":22603,"style":4268},[2108],[1865,22605,22607],{"className":22606},[2179,4272,4273,2182],[1865,22608,1931],{"className":22609},[2080,2182],[1865,22611,2190],{"className":22612},[2189],[1865,22614,22616],{"className":22615},[2096],[1865,22617,22619],{"className":22618,"style":4350},[2100],[1865,22620],{},[1865,22622,22623,22626],{"style":2202},[1865,22624],{"className":22625,"style":2140},[2108],[1865,22627],{"className":22628,"style":2210},[2209],[1865,22630,22632,22635],{"style":22631},"top:-3.394em;",[1865,22633],{"className":22634,"style":2140},[2108],[1865,22636,22638],{"className":22637},[2179,2180,2181,2182],[1865,22639,22641,22644],{"className":22640},[2080,2182],[1865,22642,20287],{"className":22643},[2080,2182],[1865,22645,2046],{"className":22646},[2080,2154,2182],[1865,22648,2190],{"className":22649},[2189],[1865,22651,22653],{"className":22652},[2096],[1865,22654,22656],{"className":22655,"style":8258},[2100],[1865,22657],{},[1865,22659],{"className":22660},[2242,2120],[1865,22662],{"className":22663,"style":2693},[2246],[1865,22665,1955],{"className":22666},[2697],[1865,22668],{"className":22669,"style":2693},[2246],[1865,22671,22673,22676],{"className":22672},[2071],[1865,22674],{"className":22675,"style":22549},[2075],[1865,22677,22679,22682,22778],{"className":22678},[2080],[1865,22680],{"className":22681},[2119,2120],[1865,22683,22685],{"className":22684},[1906],[1865,22686,22688,22770],{"className":22687},[2091,2092],[1865,22689,22691,22767],{"className":22690},[2096],[1865,22692,22694,22745,22753],{"className":22693,"style":22568},[2100],[1865,22695,22696,22699],{"style":4230},[1865,22697],{"className":22698,"style":2140},[2108],[1865,22700,22702],{"className":22701},[2179,2180,2181,2182],[1865,22703,22705],{"className":22704},[2080,2182],[1865,22706,22708,22711],{"className":22707},[2080,2182],[1865,22709,1798],{"className":22710},[2080,2154,2182],[1865,22712,22714],{"className":22713},[2158],[1865,22715,22717,22737],{"className":22716},[2091,2092],[1865,22718,22720,22734],{"className":22719},[2096],[1865,22721,22723],{"className":22722,"style":22598},[2100],[1865,22724,22725,22728],{"style":4264},[1865,22726],{"className":22727,"style":4268},[2108],[1865,22729,22731],{"className":22730},[2179,4272,4273,2182],[1865,22732,1931],{"className":22733},[2080,2182],[1865,22735,2190],{"className":22736},[2189],[1865,22738,22740],{"className":22739},[2096],[1865,22741,22743],{"className":22742,"style":4350},[2100],[1865,22744],{},[1865,22746,22747,22750],{"style":2202},[1865,22748],{"className":22749,"style":2140},[2108],[1865,22751],{"className":22752,"style":2210},[2209],[1865,22754,22755,22758],{"style":22631},[1865,22756],{"className":22757,"style":2140},[2108],[1865,22759,22761],{"className":22760},[2179,2180,2181,2182],[1865,22762,22764],{"className":22763},[2080,2182],[1865,22765,22475],{"className":22766},[2080,2182],[1865,22768,2190],{"className":22769},[2189],[1865,22771,22773],{"className":22772},[2096],[1865,22774,22776],{"className":22775,"style":8258},[2100],[1865,22777],{},[1865,22779],{"className":22780},[2242,2120],[1805,22782,22783,22892,23001],{},[1808,22784,22785,22786],{},"初始: ",[1865,22787,22789,22814],{"className":22788},[1872],[1865,22790,22792],{"className":22791},[1876],[1878,22793,22794],{"xmlns":1880},[1883,22795,22796,22811],{},[1903,22797,22798,22806,22808],{},[8534,22799,22800,22802,22804],{},[1911,22801,1927],{},[1929,22803,1931],{},[1929,22805,1900],{},[1933,22807,1955],{},[1929,22809,22810],{},"25",[2060,22812,22813],{"encoding":2062},"x_1^0 = 25",[1865,22815,22817,22883],{"className":22816,"ariaHidden":1901},[2067],[1865,22818,22820,22823,22874,22877,22880],{"className":22819},[2071],[1865,22821],{"className":22822,"style":8554},[2075],[1865,22824,22826,22829],{"className":22825},[2080],[1865,22827,1927],{"className":22828},[2080,2154],[1865,22830,22832],{"className":22831},[2158],[1865,22833,22835,22866],{"className":22834},[2091,2092],[1865,22836,22838,22863],{"className":22837},[2096],[1865,22839,22841,22852],{"className":22840,"style":8573},[2100],[1865,22842,22843,22846],{"style":8576},[1865,22844],{"className":22845,"style":2175},[2108],[1865,22847,22849],{"className":22848},[2179,2180,2181,2182],[1865,22850,1931],{"className":22851},[2080,2182],[1865,22853,22854,22857],{"style":7519},[1865,22855],{"className":22856,"style":2175},[2108],[1865,22858,22860],{"className":22859},[2179,2180,2181,2182],[1865,22861,1900],{"className":22862},[2080,2182],[1865,22864,2190],{"className":22865},[2189],[1865,22867,22869],{"className":22868},[2096],[1865,22870,22872],{"className":22871,"style":8606},[2100],[1865,22873],{},[1865,22875],{"className":22876,"style":2693},[2246],[1865,22878,1955],{"className":22879},[2697],[1865,22881],{"className":22882,"style":2693},[2246],[1865,22884,22886,22889],{"className":22885},[2071],[1865,22887],{"className":22888,"style":7553},[2075],[1865,22890,22810],{"className":22891},[2080],[1808,22893,22894,22895],{},"最终: ",[1865,22896,22898,22923],{"className":22897},[1872],[1865,22899,22901],{"className":22900},[1876],[1878,22902,22903],{"xmlns":1880},[1883,22904,22905,22920],{},[1903,22906,22907,22915,22917],{},[8534,22908,22909,22911,22913],{},[1911,22910,1927],{},[1929,22912,1931],{},[1929,22914,1931],{},[1933,22916,1955],{},[1929,22918,22919],{},"16.67",[2060,22921,22922],{"encoding":2062},"x_1^1 = 16.67",[1865,22924,22926,22992],{"className":22925,"ariaHidden":1901},[2067],[1865,22927,22929,22932,22983,22986,22989],{"className":22928},[2071],[1865,22930],{"className":22931,"style":8554},[2075],[1865,22933,22935,22938],{"className":22934},[2080],[1865,22936,1927],{"className":22937},[2080,2154],[1865,22939,22941],{"className":22940},[2158],[1865,22942,22944,22975],{"className":22943},[2091,2092],[1865,22945,22947,22972],{"className":22946},[2096],[1865,22948,22950,22961],{"className":22949,"style":8573},[2100],[1865,22951,22952,22955],{"style":8576},[1865,22953],{"className":22954,"style":2175},[2108],[1865,22956,22958],{"className":22957},[2179,2180,2181,2182],[1865,22959,1931],{"className":22960},[2080,2182],[1865,22962,22963,22966],{"style":7519},[1865,22964],{"className":22965,"style":2175},[2108],[1865,22967,22969],{"className":22968},[2179,2180,2181,2182],[1865,22970,1931],{"className":22971},[2080,2182],[1865,22973,2190],{"className":22974},[2189],[1865,22976,22978],{"className":22977},[2096],[1865,22979,22981],{"className":22980,"style":8606},[2100],[1865,22982],{},[1865,22984],{"className":22985,"style":2693},[2246],[1865,22987,1955],{"className":22988},[2697],[1865,22990],{"className":22991,"style":2693},[2246],[1865,22993,22995,22998],{"className":22994},[2071],[1865,22996],{"className":22997,"style":7553},[2075],[1865,22999,22919],{"className":23000},[2080],[1808,23002,23003,23004],{},"总效应: ",[1865,23005,23007,23034],{"className":23006},[1872],[1865,23008,23010],{"className":23009},[1876],[1878,23011,23012],{"xmlns":1880},[1883,23013,23014,23031],{},[1903,23015,23016,23018,23024,23026,23028],{},[1911,23017,11793],{"mathvariant":1913},[1923,23019,23020,23022],{},[1911,23021,1927],{},[1929,23023,1931],{},[1933,23025,1955],{},[1933,23027,1935],{},[1929,23029,23030],{},"8.33",[2060,23032,23033],{"encoding":2062},"\\Delta x_1 = -8.33",[1865,23035,23037,23096],{"className":23036,"ariaHidden":1901},[2067],[1865,23038,23040,23044,23047,23087,23090,23093],{"className":23039},[2071],[1865,23041],{"className":23042,"style":23043},[2075],"height:0.8333em;vertical-align:-0.15em;",[1865,23045,11793],{"className":23046},[2080],[1865,23048,23050,23053],{"className":23049},[2080],[1865,23051,1927],{"className":23052},[2080,2154],[1865,23054,23056],{"className":23055},[2158],[1865,23057,23059,23079],{"className":23058},[2091,2092],[1865,23060,23062,23076],{"className":23061},[2096],[1865,23063,23065],{"className":23064,"style":2168},[2100],[1865,23066,23067,23070],{"style":2171},[1865,23068],{"className":23069,"style":2175},[2108],[1865,23071,23073],{"className":23072},[2179,2180,2181,2182],[1865,23074,1931],{"className":23075},[2080,2182],[1865,23077,2190],{"className":23078},[2189],[1865,23080,23082],{"className":23081},[2096],[1865,23083,23085],{"className":23084,"style":2197},[2100],[1865,23086],{},[1865,23088],{"className":23089,"style":2693},[2246],[1865,23091,1955],{"className":23092},[2697],[1865,23094],{"className":23095,"style":2693},[2246],[1865,23097,23099,23102,23105],{"className":23098},[2071],[1865,23100],{"className":23101,"style":15003},[2075],[1865,23103,1935],{"className":23104},[2080],[1865,23106,23030],{"className":23107},[2080],[1798,23109,23110],{},"计算替代效应（需要希克斯需求）：",[1798,23112,23113,23114],{},"初始效用: ",[1865,23115,23117,23156],{"className":23116},[1872],[1865,23118,23120],{"className":23119},[1876],[1878,23121,23122],{"xmlns":1880},[1883,23123,23124,23153],{},[1903,23125,23126,23132,23134,23140,23142,23148,23150],{},[6885,23127,23128,23130],{},[1911,23129,3508],{},[1929,23131,1900],{},[1933,23133,1955],{},[6885,23135,23136,23138],{},[1929,23137,22810],{},[1929,23139,20287],{},[1933,23141,5600],{},[6885,23143,23144,23146],{},[1929,23145,22475],{},[1929,23147,20287],{},[1933,23149,1955],{},[1929,23151,23152],{},"35.36",[2060,23154,23155],{"encoding":2062},"u^0 = 25^{0.5} \\cdot 50^{0.5} = 35.36",[1865,23157,23159,23203,23254,23304],{"className":23158,"ariaHidden":1901},[2067],[1865,23160,23162,23165,23194,23197,23200],{"className":23161},[2071],[1865,23163],{"className":23164,"style":8573},[2075],[1865,23166,23168,23171],{"className":23167},[2080],[1865,23169,3508],{"className":23170},[2080,2154],[1865,23172,23174],{"className":23173},[2158],[1865,23175,23177],{"className":23176},[2091],[1865,23178,23180],{"className":23179},[2096],[1865,23181,23183],{"className":23182,"style":8573},[2100],[1865,23184,23185,23188],{"style":7519},[1865,23186],{"className":23187,"style":2175},[2108],[1865,23189,23191],{"className":23190},[2179,2180,2181,2182],[1865,23192,1900],{"className":23193},[2080,2182],[1865,23195],{"className":23196,"style":2693},[2246],[1865,23198,1955],{"className":23199},[2697],[1865,23201],{"className":23202,"style":2693},[2246],[1865,23204,23206,23209,23212,23245,23248,23251],{"className":23205},[2071],[1865,23207],{"className":23208,"style":8573},[2075],[1865,23210,1984],{"className":23211},[2080],[1865,23213,23215,23219],{"className":23214},[2080],[1865,23216,23218],{"className":23217},[2080],"5",[1865,23220,23222],{"className":23221},[2158],[1865,23223,23225],{"className":23224},[2091],[1865,23226,23228],{"className":23227},[2096],[1865,23229,23231],{"className":23230,"style":8573},[2100],[1865,23232,23233,23236],{"style":7519},[1865,23234],{"className":23235,"style":2175},[2108],[1865,23237,23239],{"className":23238},[2179,2180,2181,2182],[1865,23240,23242],{"className":23241},[2080,2182],[1865,23243,20287],{"className":23244},[2080,2182],[1865,23246],{"className":23247,"style":2247},[2246],[1865,23249,5600],{"className":23250},[2251],[1865,23252],{"className":23253,"style":2247},[2246],[1865,23255,23257,23260,23263,23295,23298,23301],{"className":23256},[2071],[1865,23258],{"className":23259,"style":8573},[2075],[1865,23261,23218],{"className":23262},[2080],[1865,23264,23266,23269],{"className":23265},[2080],[1865,23267,1900],{"className":23268},[2080],[1865,23270,23272],{"className":23271},[2158],[1865,23273,23275],{"className":23274},[2091],[1865,23276,23278],{"className":23277},[2096],[1865,23279,23281],{"className":23280,"style":8573},[2100],[1865,23282,23283,23286],{"style":7519},[1865,23284],{"className":23285,"style":2175},[2108],[1865,23287,23289],{"className":23288},[2179,2180,2181,2182],[1865,23290,23292],{"className":23291},[2080,2182],[1865,23293,20287],{"className":23294},[2080,2182],[1865,23296],{"className":23297,"style":2693},[2246],[1865,23299,1955],{"className":23300},[2697],[1865,23302],{"className":23303,"style":2693},[2246],[1865,23305,23307,23310],{"className":23306},[2071],[1865,23308],{"className":23309,"style":7553},[2075],[1865,23311,23152],{"className":23312},[2080],[1798,23314,23315,23316,23374],{},"在新价格下维持",[1865,23317,23319,23336],{"className":23318},[1872],[1865,23320,23322],{"className":23321},[1876],[1878,23323,23324],{"xmlns":1880},[1883,23325,23326,23334],{},[1903,23327,23328],{},[6885,23329,23330,23332],{},[1911,23331,3508],{},[1929,23333,1900],{},[2060,23335,10857],{"encoding":2062},[1865,23337,23339],{"className":23338,"ariaHidden":1901},[2067],[1865,23340,23342,23345],{"className":23341},[2071],[1865,23343],{"className":23344,"style":8573},[2075],[1865,23346,23348,23351],{"className":23347},[2080],[1865,23349,3508],{"className":23350},[2080,2154],[1865,23352,23354],{"className":23353},[2158],[1865,23355,23357],{"className":23356},[2091],[1865,23358,23360],{"className":23359},[2096],[1865,23361,23363],{"className":23362,"style":8573},[2100],[1865,23364,23365,23368],{"style":7519},[1865,23366],{"className":23367,"style":2175},[2108],[1865,23369,23371],{"className":23370},[2179,2180,2181,2182],[1865,23372,1900],{"className":23373},[2080,2182],"的支出：",[1865,23376,23378],{"className":23377},[1868],[1865,23379,23381,23459],{"className":23380},[1872],[1865,23382,23384],{"className":23383},[1876],[1878,23385,23386],{"xmlns":1880,"display":1881},[1883,23387,23388,23456],{},[1903,23389,23390,23392,23394,23397,23399,23401,23403,23409,23411,23413,23415,23417,23423,23425,23431,23433,23439,23441,23443,23447,23449,23451,23453],{},[1911,23391,8742],{},[1933,23393,4942],{"stretchy":3501},[1929,23395,23396],{},"3",[1933,23398,2784],{"separator":1901},[1929,23400,1931],{},[1933,23402,2784],{"separator":1901},[6885,23404,23405,23407],{},[1911,23406,3508],{},[1929,23408,1900],{},[1933,23410,4963],{"stretchy":3501},[1933,23412,1955],{},[1929,23414,1984],{},[1933,23416,5600],{},[6885,23418,23419,23421],{},[1929,23420,23396],{},[1929,23422,20287],{},[1933,23424,5600],{},[6885,23426,23427,23429],{},[1929,23428,1931],{},[1929,23430,20287],{},[1933,23432,5600],{},[6885,23434,23435,23437],{},[1911,23436,3508],{},[1929,23438,1900],{},[1933,23440,1955],{},[1929,23442,1984],{},[12729,23444,23445],{},[1929,23446,23396],{},[1933,23448,5600],{},[1929,23450,23152],{},[1933,23452,12263],{},[1929,23454,23455],{},"122.47",[2060,23457,23458],{"encoding":2062},"e(3, 1, u^0) = 2 \\cdot 3^{0.5} \\cdot 1^{0.5} \\cdot u^0 = 2\\sqrt{3} \\cdot 35.36 \\approx 122.47",[1865,23460,23462,23533,23551,23598,23645,23689,23758,23776],{"className":23461,"ariaHidden":1901},[2067],[1865,23463,23465,23468,23471,23474,23477,23480,23483,23486,23489,23492,23521,23524,23527,23530],{"className":23464},[2071],[1865,23466],{"className":23467,"style":8838},[2075],[1865,23469,8742],{"className":23470},[2080,2154],[1865,23472,4942],{"className":23473},[2119],[1865,23475,23396],{"className":23476},[2080],[1865,23478,2784],{"className":23479},[2851],[1865,23481],{"className":23482,"style":2855},[2246],[1865,23484,1931],{"className":23485},[2080],[1865,23487,2784],{"className":23488},[2851],[1865,23490],{"className":23491,"style":2855},[2246],[1865,23493,23495,23498],{"className":23494},[2080],[1865,23496,3508],{"className":23497},[2080,2154],[1865,23499,23501],{"className":23500},[2158],[1865,23502,23504],{"className":23503},[2091],[1865,23505,23507],{"className":23506},[2096],[1865,23508,23510],{"className":23509,"style":8863},[2100],[1865,23511,23512,23515],{"style":7181},[1865,23513],{"className":23514,"style":2175},[2108],[1865,23516,23518],{"className":23517},[2179,2180,2181,2182],[1865,23519,1900],{"className":23520},[2080,2182],[1865,23522,4963],{"className":23523},[2242],[1865,23525],{"className":23526,"style":2693},[2246],[1865,23528,1955],{"className":23529},[2697],[1865,23531],{"className":23532,"style":2693},[2246],[1865,23534,23536,23539,23542,23545,23548],{"className":23535},[2071],[1865,23537],{"className":23538,"style":7553},[2075],[1865,23540,1984],{"className":23541},[2080],[1865,23543],{"className":23544,"style":2247},[2246],[1865,23546,5600],{"className":23547},[2251],[1865,23549],{"className":23550,"style":2247},[2246],[1865,23552,23554,23557,23589,23592,23595],{"className":23553},[2071],[1865,23555],{"className":23556,"style":8863},[2075],[1865,23558,23560,23563],{"className":23559},[2080],[1865,23561,23396],{"className":23562},[2080],[1865,23564,23566],{"className":23565},[2158],[1865,23567,23569],{"className":23568},[2091],[1865,23570,23572],{"className":23571},[2096],[1865,23573,23575],{"className":23574,"style":8863},[2100],[1865,23576,23577,23580],{"style":7181},[1865,23578],{"className":23579,"style":2175},[2108],[1865,23581,23583],{"className":23582},[2179,2180,2181,2182],[1865,23584,23586],{"className":23585},[2080,2182],[1865,23587,20287],{"className":23588},[2080,2182],[1865,23590],{"className":23591,"style":2247},[2246],[1865,23593,5600],{"className":23594},[2251],[1865,23596],{"className":23597,"style":2247},[2246],[1865,23599,23601,23604,23636,23639,23642],{"className":23600},[2071],[1865,23602],{"className":23603,"style":8863},[2075],[1865,23605,23607,23610],{"className":23606},[2080],[1865,23608,1931],{"className":23609},[2080],[1865,23611,23613],{"className":23612},[2158],[1865,23614,23616],{"className":23615},[2091],[1865,23617,23619],{"className":23618},[2096],[1865,23620,23622],{"className":23621,"style":8863},[2100],[1865,23623,23624,23627],{"style":7181},[1865,23625],{"className":23626,"style":2175},[2108],[1865,23628,23630],{"className":23629},[2179,2180,2181,2182],[1865,23631,23633],{"className":23632},[2080,2182],[1865,23634,20287],{"className":23635},[2080,2182],[1865,23637],{"className":23638,"style":2247},[2246],[1865,23640,5600],{"className":23641},[2251],[1865,23643],{"className":23644,"style":2247},[2246],[1865,23646,23648,23651,23680,23683,23686],{"className":23647},[2071],[1865,23649],{"className":23650,"style":8863},[2075],[1865,23652,23654,23657],{"className":23653},[2080],[1865,23655,3508],{"className":23656},[2080,2154],[1865,23658,23660],{"className":23659},[2158],[1865,23661,23663],{"className":23662},[2091],[1865,23664,23666],{"className":23665},[2096],[1865,23667,23669],{"className":23668,"style":8863},[2100],[1865,23670,23671,23674],{"style":7181},[1865,23672],{"className":23673,"style":2175},[2108],[1865,23675,23677],{"className":23676},[2179,2180,2181,2182],[1865,23678,1900],{"className":23679},[2080,2182],[1865,23681],{"className":23682,"style":2693},[2246],[1865,23684,1955],{"className":23685},[2697],[1865,23687],{"className":23688,"style":2693},[2246],[1865,23690,23692,23696,23699,23749,23752,23755],{"className":23691},[2071],[1865,23693],{"className":23694,"style":23695},[2075],"height:1.04em;vertical-align:-0.0839em;",[1865,23697,1984],{"className":23698},[2080],[1865,23700,23702],{"className":23701},[2080,12874],[1865,23703,23705,23740],{"className":23704},[2091,2092],[1865,23706,23708,23737],{"className":23707},[2096],[1865,23709,23712,23724],{"className":23710,"style":23711},[2100],"height:0.9561em;",[1865,23713,23715,23718],{"className":23714,"style":12889},[12888],[1865,23716],{"className":23717,"style":2140},[2108],[1865,23719,23721],{"className":23720,"style":12896},[2080],[1865,23722,23396],{"className":23723},[2080],[1865,23725,23727,23730],{"style":23726},"top:-2.9161em;",[1865,23728],{"className":23729,"style":2140},[2108],[1865,23731,23733],{"className":23732,"style":12947},[12946],[3893,23734,23735],{"xmlns":3895,"width":12950,"height":12951,"viewBox":12952,"preserveAspectRatio":12953},[3899,23736],{"d":12956},[1865,23738,2190],{"className":23739},[2189],[1865,23741,23743],{"className":23742},[2096],[1865,23744,23747],{"className":23745,"style":23746},[2100],"height:0.0839em;",[1865,23748],{},[1865,23750],{"className":23751,"style":2247},[2246],[1865,23753,5600],{"className":23754},[2251],[1865,23756],{"className":23757,"style":2247},[2246],[1865,23759,23761,23764,23767,23770,23773],{"className":23760},[2071],[1865,23762],{"className":23763,"style":7553},[2075],[1865,23765,23152],{"className":23766},[2080],[1865,23768],{"className":23769,"style":2693},[2246],[1865,23771,12263],{"className":23772},[2697],[1865,23774],{"className":23775,"style":2693},[2246],[1865,23777,23779,23782],{"className":23778},[2071],[1865,23780],{"className":23781,"style":7553},[2075],[1865,23783,23455],{"className":23784},[2080],[1798,23786,23787],{},"在此支出下的希克斯需求：",[1865,23789,23791],{"className":23790},[1868],[1865,23792,23794,23849],{"className":23793},[1872],[1865,23795,23797],{"className":23796},[1876],[1878,23798,23799],{"xmlns":1880,"display":1881},[1883,23800,23801,23846],{},[1903,23802,23803,23809,23811,23813,23815,23817,23819,23825,23827,23829,23841,23843],{},[1923,23804,23805,23807],{},[1911,23806,3484],{},[1929,23808,1931],{},[1933,23810,4942],{"stretchy":3501},[1929,23812,23396],{},[1933,23814,2784],{"separator":1901},[1929,23816,1931],{},[1933,23818,2784],{"separator":1901},[6885,23820,23821,23823],{},[1911,23822,3508],{},[1929,23824,1900],{},[1933,23826,4963],{"stretchy":3501},[1933,23828,1955],{},[1906,23830,23831,23839],{},[1903,23832,23833,23835,23837],{},[1929,23834,20287],{},[1933,23836,5600],{},[1929,23838,23455],{},[1929,23840,23396],{},[1933,23842,1955],{},[1929,23844,23845],{},"20.41",[2060,23847,23848],{"encoding":2062},"h_1(3, 1, u^0) = \\frac{0.5 \\cdot 122.47}{3} = 20.41",[1865,23850,23852,23960,24049],{"className":23851,"ariaHidden":1901},[2067],[1865,23853,23855,23858,23898,23901,23904,23907,23910,23913,23916,23919,23948,23951,23954,23957],{"className":23854},[2071],[1865,23856],{"className":23857,"style":8838},[2075],[1865,23859,23861,23864],{"className":23860},[2080],[1865,23862,3484],{"className":23863},[2080,2154],[1865,23865,23867],{"className":23866},[2158],[1865,23868,23870,23890],{"className":23869},[2091,2092],[1865,23871,23873,23887],{"className":23872},[2096],[1865,23874,23876],{"className":23875,"style":2168},[2100],[1865,23877,23878,23881],{"style":2171},[1865,23879],{"className":23880,"style":2175},[2108],[1865,23882,23884],{"className":23883},[2179,2180,2181,2182],[1865,23885,1931],{"className":23886},[2080,2182],[1865,23888,2190],{"className":23889},[2189],[1865,23891,23893],{"className":23892},[2096],[1865,23894,23896],{"className":23895,"style":2197},[2100],[1865,23897],{},[1865,23899,4942],{"className":23900},[2119],[1865,23902,23396],{"className":23903},[2080],[1865,23905,2784],{"className":23906},[2851],[1865,23908],{"className":23909,"style":2855},[2246],[1865,23911,1931],{"className":23912},[2080],[1865,23914,2784],{"className":23915},[2851],[1865,23917],{"className":23918,"style":2855},[2246],[1865,23920,23922,23925],{"className":23921},[2080],[1865,23923,3508],{"className":23924},[2080,2154],[1865,23926,23928],{"className":23927},[2158],[1865,23929,23931],{"className":23930},[2091],[1865,23932,23934],{"className":23933},[2096],[1865,23935,23937],{"className":23936,"style":8863},[2100],[1865,23938,23939,23942],{"style":7181},[1865,23940],{"className":23941,"style":2175},[2108],[1865,23943,23945],{"className":23944},[2179,2180,2181,2182],[1865,23946,1900],{"className":23947},[2080,2182],[1865,23949,4963],{"className":23950},[2242],[1865,23952],{"className":23953,"style":2693},[2246],[1865,23955,1955],{"className":23956},[2697],[1865,23958],{"className":23959,"style":2693},[2246],[1865,23961,23963,23966,24040,24043,24046],{"className":23962},[2071],[1865,23964],{"className":23965,"style":21756},[2075],[1865,23967,23969,23972,24037],{"className":23968},[2080],[1865,23970],{"className":23971},[2119,2120],[1865,23973,23975],{"className":23974},[1906],[1865,23976,23978,24029],{"className":23977},[2091,2092],[1865,23979,23981,24026],{"className":23980},[2096],[1865,23982,23984,23995,24003],{"className":23983,"style":6666},[2100],[1865,23985,23986,23989],{"style":2136},[1865,23987],{"className":23988,"style":2140},[2108],[1865,23990,23992],{"className":23991},[2080],[1865,23993,23396],{"className":23994},[2080],[1865,23996,23997,24000],{"style":2202},[1865,23998],{"className":23999,"style":2140},[2108],[1865,24001],{"className":24002,"style":2210},[2209],[1865,24004,24005,24008],{"style":2213},[1865,24006],{"className":24007,"style":2140},[2108],[1865,24009,24011,24014,24017,24020,24023],{"className":24010},[2080],[1865,24012,20287],{"className":24013},[2080],[1865,24015],{"className":24016,"style":2247},[2246],[1865,24018,5600],{"className":24019},[2251],[1865,24021],{"className":24022,"style":2247},[2246],[1865,24024,23455],{"className":24025},[2080],[1865,24027,2190],{"className":24028},[2189],[1865,24030,24032],{"className":24031},[2096],[1865,24033,24035],{"className":24034,"style":4149},[2100],[1865,24036],{},[1865,24038],{"className":24039},[2242,2120],[1865,24041],{"className":24042,"style":2693},[2246],[1865,24044,1955],{"className":24045},[2697],[1865,24047],{"className":24048,"style":2693},[2246],[1865,24050,24052,24055],{"className":24051},[2071],[1865,24053],{"className":24054,"style":7553},[2075],[1865,24056,23845],{"className":24057},[2080],[1805,24059,24060,24283],{},[1808,24061,24062,7266,24064],{},[3048,24063,3412],{},[1865,24065,24067,24110],{"className":24066},[1872],[1865,24068,24070],{"className":24069},[1876],[1878,24071,24072],{"xmlns":1880},[1883,24073,24074,24107],{},[1903,24075,24076,24082,24084,24092,24094,24096,24098,24100,24102,24104],{},[1923,24077,24078,24080],{},[1911,24079,3484],{},[1929,24081,1931],{},[1933,24083,1935],{},[8534,24085,24086,24088,24090],{},[1911,24087,1927],{},[1929,24089,1931],{},[1929,24091,1900],{},[1933,24093,1955],{},[1929,24095,23845],{},[1933,24097,1935],{},[1929,24099,22810],{},[1933,24101,1955],{},[1933,24103,1935],{},[1929,24105,24106],{},"4.59",[2060,24108,24109],{"encoding":2062},"h_1 - x_1^0 = 20.41 - 25 = -4.59",[1865,24111,24113,24169,24235,24253,24271],{"className":24112,"ariaHidden":1901},[2067],[1865,24114,24116,24120,24160,24163,24166],{"className":24115},[2071],[1865,24117],{"className":24118,"style":24119},[2075],"height:0.8444em;vertical-align:-0.15em;",[1865,24121,24123,24126],{"className":24122},[2080],[1865,24124,3484],{"className":24125},[2080,2154],[1865,24127,24129],{"className":24128},[2158],[1865,24130,24132,24152],{"className":24131},[2091,2092],[1865,24133,24135,24149],{"className":24134},[2096],[1865,24136,24138],{"className":24137,"style":2168},[2100],[1865,24139,24140,24143],{"style":2171},[1865,24141],{"className":24142,"style":2175},[2108],[1865,24144,24146],{"className":24145},[2179,2180,2181,2182],[1865,24147,1931],{"className":24148},[2080,2182],[1865,24150,2190],{"className":24151},[2189],[1865,24153,24155],{"className":24154},[2096],[1865,24156,24158],{"className":24157,"style":2197},[2100],[1865,24159],{},[1865,24161],{"className":24162,"style":2247},[2246],[1865,24164,1935],{"className":24165},[2251],[1865,24167],{"className":24168,"style":2247},[2246],[1865,24170,24172,24175,24226,24229,24232],{"className":24171},[2071],[1865,24173],{"className":24174,"style":8554},[2075],[1865,24176,24178,24181],{"className":24177},[2080],[1865,24179,1927],{"className":24180},[2080,2154],[1865,24182,24184],{"className":24183},[2158],[1865,24185,24187,24218],{"className":24186},[2091,2092],[1865,24188,24190,24215],{"className":24189},[2096],[1865,24191,24193,24204],{"className":24192,"style":8573},[2100],[1865,24194,24195,24198],{"style":8576},[1865,24196],{"className":24197,"style":2175},[2108],[1865,24199,24201],{"className":24200},[2179,2180,2181,2182],[1865,24202,1931],{"className":24203},[2080,2182],[1865,24205,24206,24209],{"style":7519},[1865,24207],{"className":24208,"style":2175},[2108],[1865,24210,24212],{"className":24211},[2179,2180,2181,2182],[1865,24213,1900],{"className":24214},[2080,2182],[1865,24216,2190],{"className":24217},[2189],[1865,24219,24221],{"className":24220},[2096],[1865,24222,24224],{"className":24223,"style":8606},[2100],[1865,24225],{},[1865,24227],{"className":24228,"style":2693},[2246],[1865,24230,1955],{"className":24231},[2697],[1865,24233],{"className":24234,"style":2693},[2246],[1865,24236,24238,24241,24244,24247,24250],{"className":24237},[2071],[1865,24239],{"className":24240,"style":15003},[2075],[1865,24242,23845],{"className":24243},[2080],[1865,24245],{"className":24246,"style":2247},[2246],[1865,24248,1935],{"className":24249},[2251],[1865,24251],{"className":24252,"style":2247},[2246],[1865,24254,24256,24259,24262,24265,24268],{"className":24255},[2071],[1865,24257],{"className":24258,"style":7553},[2075],[1865,24260,22810],{"className":24261},[2080],[1865,24263],{"className":24264,"style":2693},[2246],[1865,24266,1955],{"className":24267},[2697],[1865,24269],{"className":24270,"style":2693},[2246],[1865,24272,24274,24277,24280],{"className":24273},[2071],[1865,24275],{"className":24276,"style":15003},[2075],[1865,24278,1935],{"className":24279},[2080],[1865,24281,24106],{"className":24282},[2080],[1808,24284,24285,7266,24287],{},[3048,24286,3418],{},[1865,24288,24290,24333],{"className":24289},[1872],[1865,24291,24293],{"className":24292},[1876],[1878,24294,24295],{"xmlns":1880},[1883,24296,24297,24330],{},[1903,24298,24299,24307,24309,24315,24317,24319,24321,24323,24325,24327],{},[8534,24300,24301,24303,24305],{},[1911,24302,1927],{},[1929,24304,1931],{},[1929,24306,1931],{},[1933,24308,1935],{},[1923,24310,24311,24313],{},[1911,24312,3484],{},[1929,24314,1931],{},[1933,24316,1955],{},[1929,24318,22919],{},[1933,24320,1935],{},[1929,24322,23845],{},[1933,24324,1955],{},[1933,24326,1935],{},[1929,24328,24329],{},"3.74",[2060,24331,24332],{"encoding":2062},"x_1^1 - h_1 = 16.67 - 20.41 = -3.74",[1865,24334,24336,24402,24457,24475,24493],{"className":24335,"ariaHidden":1901},[2067],[1865,24337,24339,24342,24393,24396,24399],{"className":24338},[2071],[1865,24340],{"className":24341,"style":8554},[2075],[1865,24343,24345,24348],{"className":24344},[2080],[1865,24346,1927],{"className":24347},[2080,2154],[1865,24349,24351],{"className":24350},[2158],[1865,24352,24354,24385],{"className":24353},[2091,2092],[1865,24355,24357,24382],{"className":24356},[2096],[1865,24358,24360,24371],{"className":24359,"style":8573},[2100],[1865,24361,24362,24365],{"style":8576},[1865,24363],{"className":24364,"style":2175},[2108],[1865,24366,24368],{"className":24367},[2179,2180,2181,2182],[1865,24369,1931],{"className":24370},[2080,2182],[1865,24372,24373,24376],{"style":7519},[1865,24374],{"className":24375,"style":2175},[2108],[1865,24377,24379],{"className":24378},[2179,2180,2181,2182],[1865,24380,1931],{"className":24381},[2080,2182],[1865,24383,2190],{"className":24384},[2189],[1865,24386,24388],{"className":24387},[2096],[1865,24389,24391],{"className":24390,"style":8606},[2100],[1865,24392],{},[1865,24394],{"className":24395,"style":2247},[2246],[1865,24397,1935],{"className":24398},[2251],[1865,24400],{"className":24401,"style":2247},[2246],[1865,24403,24405,24408,24448,24451,24454],{"className":24404},[2071],[1865,24406],{"className":24407,"style":24119},[2075],[1865,24409,24411,24414],{"className":24410},[2080],[1865,24412,3484],{"className":24413},[2080,2154],[1865,24415,24417],{"className":24416},[2158],[1865,24418,24420,24440],{"className":24419},[2091,2092],[1865,24421,24423,24437],{"className":24422},[2096],[1865,24424,24426],{"className":24425,"style":2168},[2100],[1865,24427,24428,24431],{"style":2171},[1865,24429],{"className":24430,"style":2175},[2108],[1865,24432,24434],{"className":24433},[2179,2180,2181,2182],[1865,24435,1931],{"className":24436},[2080,2182],[1865,24438,2190],{"className":24439},[2189],[1865,24441,24443],{"className":24442},[2096],[1865,24444,24446],{"className":24445,"style":2197},[2100],[1865,24447],{},[1865,24449],{"className":24450,"style":2693},[2246],[1865,24452,1955],{"className":24453},[2697],[1865,24455],{"className":24456,"style":2693},[2246],[1865,24458,24460,24463,24466,24469,24472],{"className":24459},[2071],[1865,24461],{"className":24462,"style":15003},[2075],[1865,24464,22919],{"className":24465},[2080],[1865,24467],{"className":24468,"style":2247},[2246],[1865,24470,1935],{"className":24471},[2251],[1865,24473],{"className":24474,"style":2247},[2246],[1865,24476,24478,24481,24484,24487,24490],{"className":24477},[2071],[1865,24479],{"className":24480,"style":7553},[2075],[1865,24482,23845],{"className":24483},[2080],[1865,24485],{"className":24486,"style":2693},[2246],[1865,24488,1955],{"className":24489},[2697],[1865,24491],{"className":24492,"style":2693},[2246],[1865,24494,24496,24499,24502],{"className":24495},[2071],[1865,24497],{"className":24498,"style":15003},[2075],[1865,24500,1935],{"className":24501},[2080],[1865,24503,24329],{"className":24504},[2080],[1798,24506,24507,24508,24606],{},"验证：",[1865,24509,24511,24543],{"className":24510},[1872],[1865,24512,24514],{"className":24513},[1876],[1878,24515,24516],{"xmlns":1880},[1883,24517,24518,24540],{},[1903,24519,24520,24522,24524,24526,24528,24530,24532,24534,24536,24538],{},[1933,24521,1935],{},[1929,24523,24106],{},[1933,24525,2029],{},[1933,24527,4942],{"stretchy":3501},[1933,24529,1935],{},[1929,24531,24329],{},[1933,24533,4963],{"stretchy":3501},[1933,24535,1955],{},[1933,24537,1935],{},[1929,24539,23030],{},[2060,24541,24542],{"encoding":2062},"-4.59 + (-3.74) = -8.33",[1865,24544,24546,24567,24594],{"className":24545,"ariaHidden":1901},[2067],[1865,24547,24549,24552,24555,24558,24561,24564],{"className":24548},[2071],[1865,24550],{"className":24551,"style":15003},[2075],[1865,24553,1935],{"className":24554},[2080],[1865,24556,24106],{"className":24557},[2080],[1865,24559],{"className":24560,"style":2247},[2246],[1865,24562,2029],{"className":24563},[2251],[1865,24565],{"className":24566,"style":2247},[2246],[1865,24568,24570,24573,24576,24579,24582,24585,24588,24591],{"className":24569},[2071],[1865,24571],{"className":24572,"style":5030},[2075],[1865,24574,4942],{"className":24575},[2119],[1865,24577,1935],{"className":24578},[2080],[1865,24580,24329],{"className":24581},[2080],[1865,24583,4963],{"className":24584},[2242],[1865,24586],{"className":24587,"style":2693},[2246],[1865,24589,1955],{"className":24590},[2697],[1865,24592],{"className":24593,"style":2693},[2246],[1865,24595,24597,24600,24603],{"className":24596},[2071],[1865,24598],{"className":24599,"style":15003},[2075],[1865,24601,1935],{"className":24602},[2080],[1865,24604,23030],{"className":24605},[2080]," ✓",[1798,24608,24609,24612],{},[3048,24610,24611],{},"解释",": 价格上涨导致需求减少8.33单位，其中：",[1805,24614,24615,24618],{},[1808,24616,24617],{},"4.59单位是因为商品1相对变贵（替代效应）",[1808,24619,24620],{},"3.74单位是因为实际购买力下降（收入效应，正常品）",[3421,24622],{},[1794,24624,24626],{"id":24625},"_6-应用案例","6. 应用案例",[1854,24628,24630],{"id":24629},"_61-税收归宿分析","6.1 税收归宿分析",[1798,24632,24633,24635,24636,24665,24666,11716,24694,24760],{},[3048,24634,11096],{},": 政府对商品1征收从价税",[1865,24637,24639,24652],{"className":24638},[1872],[1865,24640,24642],{"className":24641},[1876],[1878,24643,24644],{"xmlns":1880},[1883,24645,24646,24650],{},[1903,24647,24648],{},[1911,24649,16824],{},[2060,24651,16824],{"encoding":2062},[1865,24653,24655],{"className":24654,"ariaHidden":1901},[2067],[1865,24656,24658,24662],{"className":24657},[2071],[1865,24659],{"className":24660,"style":24661},[2075],"height:0.6151em;",[1865,24663,16824],{"className":24664},[2080,2154],"（价格从",[1865,24667,24669,24682],{"className":24668},[1872],[1865,24670,24672],{"className":24671},[1876],[1878,24673,24674],{"xmlns":1880},[1883,24675,24676,24680],{},[1903,24677,24678],{},[1911,24679,1798],{},[2060,24681,1798],{"encoding":2062},[1865,24683,24685],{"className":24684,"ariaHidden":1901},[2067],[1865,24686,24688,24691],{"className":24687},[2071],[1865,24689],{"className":24690,"style":2948},[2075],[1865,24692,1798],{"className":24693},[2080,2154],[1865,24695,24697,24721],{"className":24696},[1872],[1865,24698,24700],{"className":24699},[1876],[1878,24701,24702],{"xmlns":1880},[1883,24703,24704,24718],{},[1903,24705,24706,24708,24710,24712,24714,24716],{},[1933,24707,4942],{"stretchy":3501},[1929,24709,1931],{},[1933,24711,2029],{},[1911,24713,16824],{},[1933,24715,4963],{"stretchy":3501},[1911,24717,1798],{},[2060,24719,24720],{"encoding":2062},"(1+t)p",[1865,24722,24724,24745],{"className":24723,"ariaHidden":1901},[2067],[1865,24725,24727,24730,24733,24736,24739,24742],{"className":24726},[2071],[1865,24728],{"className":24729,"style":5030},[2075],[1865,24731,4942],{"className":24732},[2119],[1865,24734,1931],{"className":24735},[2080],[1865,24737],{"className":24738,"style":2247},[2246],[1865,24740,2029],{"className":24741},[2251],[1865,24743],{"className":24744,"style":2247},[2246],[1865,24746,24748,24751,24754,24757],{"className":24747},[2071],[1865,24749],{"className":24750,"style":5030},[2075],[1865,24752,16824],{"className":24753},[2080,2154],[1865,24755,4963],{"className":24756},[2242],[1865,24758,1798],{"className":24759},[2080,2154],"），如何评估对消费者的福利损失？",[1805,24762,24763,24766,24932],{},[1808,24764,24765],{},"使用CV测度：消费者的真实福利损失",[1808,24767,24768,24769],{},"使用税收收入：",[1865,24770,24772,24814],{"className":24771},[1872],[1865,24773,24775],{"className":24774},[1876],[1878,24776,24777],{"xmlns":1880},[1883,24778,24779,24811],{},[1903,24780,24781,24783,24785,24787,24789,24795,24797,24799,24801,24803,24805,24807,24809],{},[1911,24782,16824],{},[1933,24784,5600],{},[1911,24786,1798],{},[1933,24788,5600],{},[1923,24790,24791,24793],{},[1911,24792,1927],{},[1929,24794,1931],{},[1933,24796,4942],{"stretchy":3501},[1911,24798,1798],{},[1933,24800,4942],{"stretchy":3501},[1929,24802,1931],{},[1933,24804,2029],{},[1911,24806,16824],{},[1933,24808,4963],{"stretchy":3501},[1933,24810,4963],{"stretchy":3501},[2060,24812,24813],{"encoding":2062},"t \\cdot p \\cdot x_1(p(1+t))",[1865,24815,24817,24835,24853,24920],{"className":24816,"ariaHidden":1901},[2067],[1865,24818,24820,24823,24826,24829,24832],{"className":24819},[2071],[1865,24821],{"className":24822,"style":24661},[2075],[1865,24824,16824],{"className":24825},[2080,2154],[1865,24827],{"className":24828,"style":2247},[2246],[1865,24830,5600],{"className":24831},[2251],[1865,24833],{"className":24834,"style":2247},[2246],[1865,24836,24838,24841,24844,24847,24850],{"className":24837},[2071],[1865,24839],{"className":24840,"style":15022},[2075],[1865,24842,1798],{"className":24843},[2080,2154],[1865,24845],{"className":24846,"style":2247},[2246],[1865,24848,5600],{"className":24849},[2251],[1865,24851],{"className":24852,"style":2247},[2246],[1865,24854,24856,24859,24899,24902,24905,24908,24911,24914,24917],{"className":24855},[2071],[1865,24857],{"className":24858,"style":5030},[2075],[1865,24860,24862,24865],{"className":24861},[2080],[1865,24863,1927],{"className":24864},[2080,2154],[1865,24866,24868],{"className":24867},[2158],[1865,24869,24871,24891],{"className":24870},[2091,2092],[1865,24872,24874,24888],{"className":24873},[2096],[1865,24875,24877],{"className":24876,"style":2168},[2100],[1865,24878,24879,24882],{"style":2171},[1865,24880],{"className":24881,"style":2175},[2108],[1865,24883,24885],{"className":24884},[2179,2180,2181,2182],[1865,24886,1931],{"className":24887},[2080,2182],[1865,24889,2190],{"className":24890},[2189],[1865,24892,24894],{"className":24893},[2096],[1865,24895,24897],{"className":24896,"style":2197},[2100],[1865,24898],{},[1865,24900,4942],{"className":24901},[2119],[1865,24903,1798],{"className":24904},[2080,2154],[1865,24906,4942],{"className":24907},[2119],[1865,24909,1931],{"className":24910},[2080],[1865,24912],{"className":24913,"style":2247},[2246],[1865,24915,2029],{"className":24916},[2251],[1865,24918],{"className":24919,"style":2247},[2246],[1865,24921,24923,24926,24929],{"className":24922},[2071],[1865,24924],{"className":24925,"style":5030},[2075],[1865,24927,16824],{"className":24928},[2080,2154],[1865,24930,5427],{"className":24931},[2242],[1808,24933,24934],{},"额外负担（Excess Burden）= CV - 税收收入",[1798,24936,24937,24940],{},[3048,24938,24939],{},"洞见",": 即使政府将税收全部返还给消费者，他们的福利仍然受损，因为税收扭曲了相对价格，导致资源配置低效。",[1854,24942,24944],{"id":24943},"_62-价格补贴的效率","6.2 价格补贴的效率",[1798,24946,24947,24949],{},[3048,24948,11096],{},": 两种福利政策：",[3406,24951,24952,24984],{},[1808,24953,24954,24955],{},"直接给消费者现金",[1865,24956,24958,24972],{"className":24957},[1872],[1865,24959,24961],{"className":24960},[1876],[1878,24962,24963],{"xmlns":1880},[1883,24964,24965,24970],{},[1903,24966,24967],{},[1911,24968,24969],{},"G",[2060,24971,24969],{"encoding":2062},[1865,24973,24975],{"className":24974,"ariaHidden":1901},[2067],[1865,24976,24978,24981],{"className":24977},[2071],[1865,24979],{"className":24980,"style":8815},[2075],[1865,24982,24969],{"className":24983},[2080,2154],[1808,24985,24986,24987],{},"对商品1进行价格补贴，使价格下降，花费同样金额",[1865,24988,24990,25003],{"className":24989},[1872],[1865,24991,24993],{"className":24992},[1876],[1878,24994,24995],{"xmlns":1880},[1883,24996,24997,25001],{},[1903,24998,24999],{},[1911,25000,24969],{},[2060,25002,24969],{"encoding":2062},[1865,25004,25006],{"className":25005,"ariaHidden":1901},[2067],[1865,25007,25009,25012],{"className":25008},[2071],[1865,25010],{"className":25011,"style":8815},[2075],[1865,25013,24969],{"className":25014},[2080,2154],[1798,25016,25017,25019],{},[3048,25018,21862],{},"（通过CV\u002FEV分析）: 现金转移总是优于等价值的价格补贴，因为：",[1805,25021,25022,25025],{},[1808,25023,25024],{},"现金给予消费者更大的选择自由",[1808,25026,25027],{},"价格补贴扭曲了相对价格",[1798,25029,25030],{},"这解释了经济学家通常偏好现金转移而非实物补贴。",[1854,25032,25034],{"id":25033},"_63-需求弹性与税收政策","6.3 需求弹性与税收政策",[1798,25036,25037],{},"价格弹性定义：",[1865,25039,25041],{"className":25040},[1868],[1865,25042,25044,25083],{"className":25043},[1872],[1865,25045,25047],{"className":25046},[1876],[1878,25048,25049],{"xmlns":1880,"display":1881},[1883,25050,25051,25080],{},[1903,25052,25053,25056,25058,25072,25074],{},[1911,25054,25055],{},"ϵ",[1933,25057,1955],{},[1906,25059,25060,25066],{},[1903,25061,25062,25064],{},[1911,25063,1914],{"mathvariant":1913},[1911,25065,1927],{},[1903,25067,25068,25070],{},[1911,25069,1914],{"mathvariant":1913},[1911,25071,1798],{},[1933,25073,5600],{},[1906,25075,25076,25078],{},[1911,25077,1798],{},[1911,25079,1927],{},[2060,25081,25082],{"encoding":2062},"\\epsilon = \\frac{\\partial x}{\\partial p} \\cdot \\frac{p}{x}",[1865,25084,25086,25104,25187],{"className":25085,"ariaHidden":1901},[2067],[1865,25087,25089,25092,25095,25098,25101],{"className":25088},[2071],[1865,25090],{"className":25091,"style":6852},[2075],[1865,25093,25055],{"className":25094},[2080,2154],[1865,25096],{"className":25097,"style":2693},[2246],[1865,25099,1955],{"className":25100},[2697],[1865,25102],{"className":25103,"style":2693},[2246],[1865,25105,25107,25110,25178,25181,25184],{"className":25106},[2071],[1865,25108],{"className":25109,"style":3257},[2075],[1865,25111,25113,25116,25175],{"className":25112},[2080],[1865,25114],{"className":25115},[2119,2120],[1865,25117,25119],{"className":25118},[1906],[1865,25120,25122,25167],{"className":25121},[2091,2092],[1865,25123,25125,25164],{"className":25124},[2096],[1865,25126,25128,25142,25150],{"className":25127,"style":2133},[2100],[1865,25129,25130,25133],{"style":2136},[1865,25131],{"className":25132,"style":2140},[2108],[1865,25134,25136,25139],{"className":25135},[2080],[1865,25137,1914],{"className":25138,"style":2147},[2080],[1865,25140,1798],{"className":25141},[2080,2154],[1865,25143,25144,25147],{"style":2202},[1865,25145],{"className":25146,"style":2140},[2108],[1865,25148],{"className":25149,"style":2210},[2209],[1865,25151,25152,25155],{"style":2213},[1865,25153],{"className":25154,"style":2140},[2108],[1865,25156,25158,25161],{"className":25157},[2080],[1865,25159,1914],{"className":25160,"style":2147},[2080],[1865,25162,1927],{"className":25163},[2080,2154],[1865,25165,2190],{"className":25166},[2189],[1865,25168,25170],{"className":25169},[2096],[1865,25171,25173],{"className":25172,"style":3396},[2100],[1865,25174],{},[1865,25176],{"className":25177},[2242,2120],[1865,25179],{"className":25180,"style":2247},[2246],[1865,25182,5600],{"className":25183},[2251],[1865,25185],{"className":25186,"style":2247},[2246],[1865,25188,25190,25194],{"className":25189},[2071],[1865,25191],{"className":25192,"style":25193},[2075],"height:1.7936em;vertical-align:-0.686em;",[1865,25195,25197,25200,25254],{"className":25196},[2080],[1865,25198],{"className":25199},[2119,2120],[1865,25201,25203],{"className":25202},[1906],[1865,25204,25206,25246],{"className":25205},[2091,2092],[1865,25207,25209,25243],{"className":25208},[2096],[1865,25210,25213,25224,25232],{"className":25211,"style":25212},[2100],"height:1.1076em;",[1865,25214,25215,25218],{"style":2136},[1865,25216],{"className":25217,"style":2140},[2108],[1865,25219,25221],{"className":25220},[2080],[1865,25222,1927],{"className":25223},[2080,2154],[1865,25225,25226,25229],{"style":2202},[1865,25227],{"className":25228,"style":2140},[2108],[1865,25230],{"className":25231,"style":2210},[2209],[1865,25233,25234,25237],{"style":2213},[1865,25235],{"className":25236,"style":2140},[2108],[1865,25238,25240],{"className":25239},[2080],[1865,25241,1798],{"className":25242},[2080,2154],[1865,25244,2190],{"className":25245},[2189],[1865,25247,25249],{"className":25248},[2096],[1865,25250,25252],{"className":25251,"style":4149},[2100],[1865,25253],{},[1865,25255],{"className":25256},[2242,2120],[1798,25258,25259],{},"斯勒茨基方程告诉我们：",[1865,25261,25263],{"className":25262},[1868],[1865,25264,25266,25300],{"className":25265},[1872],[1865,25267,25269],{"className":25268},[1876],[1878,25270,25271],{"xmlns":1880,"display":1881},[1883,25272,25273,25297],{},[1903,25274,25275,25277,25279,25285,25287,25293,25295],{},[1911,25276,25055],{},[1933,25278,1955],{},[1923,25280,25281,25283],{},[1911,25282,25055],{},[1911,25284,16818],{},[1933,25286,2029],{},[1923,25288,25289,25291],{},[1911,25290,25055],{},[1911,25292,2046],{},[1933,25294,5600],{},[1911,25296,16818],{},[2060,25298,25299],{"encoding":2062},"\\epsilon = \\epsilon_s + \\epsilon_m \\cdot s",[1865,25301,25303,25321,25377,25433],{"className":25302,"ariaHidden":1901},[2067],[1865,25304,25306,25309,25312,25315,25318],{"className":25305},[2071],[1865,25307],{"className":25308,"style":6852},[2075],[1865,25310,25055],{"className":25311},[2080,2154],[1865,25313],{"className":25314,"style":2693},[2246],[1865,25316,1955],{"className":25317},[2697],[1865,25319],{"className":25320,"style":2693},[2246],[1865,25322,25324,25327,25368,25371,25374],{"className":25323},[2071],[1865,25325],{"className":25326,"style":13699},[2075],[1865,25328,25330,25333],{"className":25329},[2080],[1865,25331,25055],{"className":25332},[2080,2154],[1865,25334,25336],{"className":25335},[2158],[1865,25337,25339,25360],{"className":25338},[2091,2092],[1865,25340,25342,25357],{"className":25341},[2096],[1865,25343,25346],{"className":25344,"style":25345},[2100],"height:0.1514em;",[1865,25347,25348,25351],{"style":2171},[1865,25349],{"className":25350,"style":2175},[2108],[1865,25352,25354],{"className":25353},[2179,2180,2181,2182],[1865,25355,16818],{"className":25356},[2080,2154,2182],[1865,25358,2190],{"className":25359},[2189],[1865,25361,25363],{"className":25362},[2096],[1865,25364,25366],{"className":25365,"style":2197},[2100],[1865,25367],{},[1865,25369],{"className":25370,"style":2247},[2246],[1865,25372,2029],{"className":25373},[2251],[1865,25375],{"className":25376,"style":2247},[2246],[1865,25378,25380,25384,25424,25427,25430],{"className":25379},[2071],[1865,25381],{"className":25382,"style":25383},[2075],"height:0.5945em;vertical-align:-0.15em;",[1865,25385,25387,25390],{"className":25386},[2080],[1865,25388,25055],{"className":25389},[2080,2154],[1865,25391,25393],{"className":25392},[2158],[1865,25394,25396,25416],{"className":25395},[2091,2092],[1865,25397,25399,25413],{"className":25398},[2096],[1865,25400,25402],{"className":25401,"style":25345},[2100],[1865,25403,25404,25407],{"style":2171},[1865,25405],{"className":25406,"style":2175},[2108],[1865,25408,25410],{"className":25409},[2179,2180,2181,2182],[1865,25411,2046],{"className":25412},[2080,2154,2182],[1865,25414,2190],{"className":25415},[2189],[1865,25417,25419],{"className":25418},[2096],[1865,25420,25422],{"className":25421,"style":2197},[2100],[1865,25423],{},[1865,25425],{"className":25426,"style":2247},[2246],[1865,25428,5600],{"className":25429},[2251],[1865,25431],{"className":25432,"style":2247},[2246],[1865,25434,25436,25439],{"className":25435},[2071],[1865,25437],{"className":25438,"style":6852},[2075],[1865,25440,16818],{"className":25441},[2080,2154],[1798,25443,4157],{},[1805,25445,25446,25519,25592],{},[1808,25447,25448,25518],{},[1865,25449,25451,25469],{"className":25450},[1872],[1865,25452,25454],{"className":25453},[1876],[1878,25455,25456],{"xmlns":1880},[1883,25457,25458,25466],{},[1903,25459,25460],{},[1923,25461,25462,25464],{},[1911,25463,25055],{},[1911,25465,16818],{},[2060,25467,25468],{"encoding":2062},"\\epsilon_s",[1865,25470,25472],{"className":25471,"ariaHidden":1901},[2067],[1865,25473,25475,25478],{"className":25474},[2071],[1865,25476],{"className":25477,"style":12589},[2075],[1865,25479,25481,25484],{"className":25480},[2080],[1865,25482,25055],{"className":25483},[2080,2154],[1865,25485,25487],{"className":25486},[2158],[1865,25488,25490,25510],{"className":25489},[2091,2092],[1865,25491,25493,25507],{"className":25492},[2096],[1865,25494,25496],{"className":25495,"style":25345},[2100],[1865,25497,25498,25501],{"style":2171},[1865,25499],{"className":25500,"style":2175},[2108],[1865,25502,25504],{"className":25503},[2179,2180,2181,2182],[1865,25505,16818],{"className":25506},[2080,2154,2182],[1865,25508,2190],{"className":25509},[2189],[1865,25511,25513],{"className":25512},[2096],[1865,25514,25516],{"className":25515,"style":2197},[2100],[1865,25517],{},": 替代弹性（希克斯）",[1808,25520,25521,25591],{},[1865,25522,25524,25542],{"className":25523},[1872],[1865,25525,25527],{"className":25526},[1876],[1878,25528,25529],{"xmlns":1880},[1883,25530,25531,25539],{},[1903,25532,25533],{},[1923,25534,25535,25537],{},[1911,25536,25055],{},[1911,25538,2046],{},[2060,25540,25541],{"encoding":2062},"\\epsilon_m",[1865,25543,25545],{"className":25544,"ariaHidden":1901},[2067],[1865,25546,25548,25551],{"className":25547},[2071],[1865,25549],{"className":25550,"style":12589},[2075],[1865,25552,25554,25557],{"className":25553},[2080],[1865,25555,25055],{"className":25556},[2080,2154],[1865,25558,25560],{"className":25559},[2158],[1865,25561,25563,25583],{"className":25562},[2091,2092],[1865,25564,25566,25580],{"className":25565},[2096],[1865,25567,25569],{"className":25568,"style":25345},[2100],[1865,25570,25571,25574],{"style":2171},[1865,25572],{"className":25573,"style":2175},[2108],[1865,25575,25577],{"className":25576},[2179,2180,2181,2182],[1865,25578,2046],{"className":25579},[2080,2154,2182],[1865,25581,2190],{"className":25582},[2189],[1865,25584,25586],{"className":25585},[2096],[1865,25587,25589],{"className":25588,"style":2197},[2100],[1865,25590],{},": 收入弹性",[1808,25593,25594,25677],{},[1865,25595,25597,25623],{"className":25596},[1872],[1865,25598,25600],{"className":25599},[1876],[1878,25601,25602],{"xmlns":1880},[1883,25603,25604,25620],{},[1903,25605,25606,25608,25610,25612,25614,25616,25618],{},[1911,25607,16818],{},[1933,25609,1955],{},[1911,25611,1798],{},[1933,25613,5600],{},[1911,25615,1927],{},[1911,25617,16443],{"mathvariant":1913},[1911,25619,2046],{},[2060,25621,25622],{"encoding":2062},"s = p \\cdot x \u002F m",[1865,25624,25626,25644,25662],{"className":25625,"ariaHidden":1901},[2067],[1865,25627,25629,25632,25635,25638,25641],{"className":25628},[2071],[1865,25630],{"className":25631,"style":6852},[2075],[1865,25633,16818],{"className":25634},[2080,2154],[1865,25636],{"className":25637,"style":2693},[2246],[1865,25639,1955],{"className":25640},[2697],[1865,25642],{"className":25643,"style":2693},[2246],[1865,25645,25647,25650,25653,25656,25659],{"className":25646},[2071],[1865,25648],{"className":25649,"style":15022},[2075],[1865,25651,1798],{"className":25652},[2080,2154],[1865,25654],{"className":25655,"style":2247},[2246],[1865,25657,5600],{"className":25658},[2251],[1865,25660],{"className":25661,"style":2247},[2246],[1865,25663,25665,25668,25671,25674],{"className":25664},[2071],[1865,25666],{"className":25667,"style":5030},[2075],[1865,25669,1927],{"className":25670},[2080,2154],[1865,25672,16443],{"className":25673},[2080],[1865,25675,2046],{"className":25676},[2080,2154],": 支出份额",[1798,25679,25680,25683],{},[3048,25681,25682],{},"政策含义",": 对需求缺乏弹性的商品（如烟草）征税，税收收入更稳定，但消费者福利损失也更大（因为难以替代）。",[3421,25685],{},[1794,25687,25689],{"id":25688},"_7-高级话题","7. 高级话题",[1854,25691,25693],{"id":25692},"_71-积分性条件","7.1 积分性条件",[1798,25695,25696],{},"不是所有的需求函数都能由效用最大化得出。一个函数要成为马歇尔需求，必须满足：",[3406,25698,25699,25819,25925,25958],{},[1808,25700,25701,7266,25704],{},[3048,25702,25703],{},"齐次性",[1865,25705,25707,25749],{"className":25706},[1872],[1865,25708,25710],{"className":25709},[1876],[1878,25711,25712],{"xmlns":1880},[1883,25713,25714,25746],{},[1903,25715,25716,25718,25720,25722,25724,25726,25728,25730,25732,25734,25736,25738,25740,25742,25744],{},[1911,25717,1927],{},[1933,25719,4942],{"stretchy":3501},[1911,25721,16824],{},[1911,25723,1798],{},[1933,25725,2784],{"separator":1901},[1911,25727,16824],{},[1911,25729,2046],{},[1933,25731,4963],{"stretchy":3501},[1933,25733,1955],{},[1911,25735,1927],{},[1933,25737,4942],{"stretchy":3501},[1911,25739,1798],{},[1933,25741,2784],{"separator":1901},[1911,25743,2046],{},[1933,25745,4963],{"stretchy":3501},[2060,25747,25748],{"encoding":2062},"x(tp, tm) = x(p, m)",[1865,25750,25752,25792],{"className":25751,"ariaHidden":1901},[2067],[1865,25753,25755,25758,25761,25764,25768,25771,25774,25777,25780,25783,25786,25789],{"className":25754},[2071],[1865,25756],{"className":25757,"style":5030},[2075],[1865,25759,1927],{"className":25760},[2080,2154],[1865,25762,4942],{"className":25763},[2119],[1865,25765,25767],{"className":25766},[2080,2154],"tp",[1865,25769,2784],{"className":25770},[2851],[1865,25772],{"className":25773,"style":2855},[2246],[1865,25775,16824],{"className":25776},[2080,2154],[1865,25778,2046],{"className":25779},[2080,2154],[1865,25781,4963],{"className":25782},[2242],[1865,25784],{"className":25785,"style":2693},[2246],[1865,25787,1955],{"className":25788},[2697],[1865,25790],{"className":25791,"style":2693},[2246],[1865,25793,25795,25798,25801,25804,25807,25810,25813,25816],{"className":25794},[2071],[1865,25796],{"className":25797,"style":5030},[2075],[1865,25799,1927],{"className":25800},[2080,2154],[1865,25802,4942],{"className":25803},[2119],[1865,25805,1798],{"className":25806},[2080,2154],[1865,25808,2784],{"className":25809},[2851],[1865,25811],{"className":25812,"style":2855},[2246],[1865,25814,2046],{"className":25815},[2080,2154],[1865,25817,4963],{"className":25818},[2242],[1808,25820,25821,7266,25824],{},[3048,25822,25823],{},"预算耗尽",[1865,25825,25827,25859],{"className":25826},[1872],[1865,25828,25830],{"className":25829},[1876],[1878,25831,25832],{"xmlns":1880},[1883,25833,25834,25856],{},[1903,25835,25836,25838,25840,25842,25844,25846,25848,25850,25852,25854],{},[1911,25837,1798],{},[1933,25839,5600],{},[1911,25841,1927],{},[1933,25843,4942],{"stretchy":3501},[1911,25845,1798],{},[1933,25847,2784],{"separator":1901},[1911,25849,2046],{},[1933,25851,4963],{"stretchy":3501},[1933,25853,1955],{},[1911,25855,2046],{},[2060,25857,25858],{"encoding":2062},"p \\cdot x(p, m) = m",[1865,25860,25862,25880,25916],{"className":25861,"ariaHidden":1901},[2067],[1865,25863,25865,25868,25871,25874,25877],{"className":25864},[2071],[1865,25866],{"className":25867,"style":15022},[2075],[1865,25869,1798],{"className":25870},[2080,2154],[1865,25872],{"className":25873,"style":2247},[2246],[1865,25875,5600],{"className":25876},[2251],[1865,25878],{"className":25879,"style":2247},[2246],[1865,25881,25883,25886,25889,25892,25895,25898,25901,25904,25907,25910,25913],{"className":25882},[2071],[1865,25884],{"className":25885,"style":5030},[2075],[1865,25887,1927],{"className":25888},[2080,2154],[1865,25890,4942],{"className":25891},[2119],[1865,25893,1798],{"className":25894},[2080,2154],[1865,25896,2784],{"className":25897},[2851],[1865,25899],{"className":25900,"style":2855},[2246],[1865,25902,2046],{"className":25903},[2080,2154],[1865,25905,4963],{"className":25906},[2242],[1865,25908],{"className":25909,"style":2693},[2246],[1865,25911,1955],{"className":25912},[2697],[1865,25914],{"className":25915,"style":2693},[2246],[1865,25917,25919,25922],{"className":25918},[2071],[1865,25920],{"className":25921,"style":6852},[2075],[1865,25923,2046],{"className":25924},[2080,2154],[1808,25926,25927,25929,25930,7425],{},[3048,25928,7425],{},": 斯勒茨基矩阵",[1865,25931,25933,25946],{"className":25932},[1872],[1865,25934,25936],{"className":25935},[1876],[1878,25937,25938],{"xmlns":1880},[1883,25939,25940,25944],{},[1903,25941,25942],{},[1911,25943,6896],{},[2060,25945,6896],{"encoding":2062},[1865,25947,25949],{"className":25948,"ariaHidden":1901},[2067],[1865,25950,25952,25955],{"className":25951},[2071],[1865,25953],{"className":25954,"style":8815},[2075],[1865,25956,6896],{"className":25957,"style":7058},[2080,2154],[1808,25959,25960,7266,25962,25990],{},[3048,25961,7265],{},[1865,25963,25965,25978],{"className":25964},[1872],[1865,25966,25968],{"className":25967},[1876],[1878,25969,25970],{"xmlns":1880},[1883,25971,25972,25976],{},[1903,25973,25974],{},[1911,25975,6896],{},[2060,25977,6896],{"encoding":2062},[1865,25979,25981],{"className":25980,"ariaHidden":1901},[2067],[1865,25982,25984,25987],{"className":25983},[2071],[1865,25985],{"className":25986,"style":8815},[2075],[1865,25988,6896],{"className":25989,"style":7058},[2080,2154],"对称",[1798,25992,25993,25994,13477],{},"这些条件统称为",[3048,25995,25996],{},"理性选择的可检验含义",[1854,25998,26000],{"id":25999},"_72-拟凹效用与凸偏好","7.2 拟凹效用与凸偏好",[1798,26002,26003,26006,26007,26035],{},[3048,26004,26005],{},"定理",": 如果效用函数",[1865,26008,26010,26023],{"className":26009},[1872],[1865,26011,26013],{"className":26012},[1876],[1878,26014,26015],{"xmlns":1880},[1883,26016,26017,26021],{},[1903,26018,26019],{},[1911,26020,1917],{},[2060,26022,1917],{"encoding":2062},[1865,26024,26026],{"className":26025,"ariaHidden":1901},[2067],[1865,26027,26029,26032],{"className":26028},[2071],[1865,26030],{"className":26031,"style":8815},[2075],[1865,26033,1917],{"className":26034,"style":2226},[2080,2154],"是拟凹的，则：",[3406,26037,26038,26041,26044],{},[1808,26039,26040],{},"最优解存在且唯一（在严格拟凹下）",[1808,26042,26043],{},"需求函数连续",[1808,26045,26046],{},"间接效用函数拟凸",[1798,26048,26049,26052],{},[3048,26050,26051],{},"证明要点",": 利用凸集的性质和Weierstrass定理。",[3421,26054],{},[1794,26056,26058],{"id":26057},"_8-文献与拓展阅读","8. 文献与拓展阅读",[1798,26060,26061,4915],{},[3048,26062,26063],{},"经典论文",[1805,26065,26066,26069,26076],{},[1808,26067,26068],{},"Slutsky, E. (1915). \"Sulla teoria del bilancio del consumatore\"",[1808,26070,26071,26072],{},"Hicks, J.R. (1939). ",[26073,26074,26075],"em",{},"Value and Capital",[1808,26077,26078,26079],{},"Samuelson, P.A. (1947). ",[26073,26080,26081],{},"Foundations of Economic Analysis",[1798,26083,26084,4915],{},[3048,26085,26086],{},"现代教材",[1805,26088,26089,26092,26095],{},[1808,26090,26091],{},"Mas-Colell et al. (1995), Chapter 2-3",[1808,26093,26094],{},"Varian (1992), Chapter 8-10",[1808,26096,26097],{},"Jehle & Reny (2011), Chapter 2",[3421,26099],{},[1794,26101,26103],{"id":26102},"_9-本章小结","9. 本章小结",[10806,26105,26106,26119],{},[10809,26107,26108],{},[10812,26109,26110,26113,26116],{},[10815,26111,26112],{},"核心概念",[10815,26114,26115],{},"关键公式",[10815,26117,26118],{},"经济学含义",[10824,26120,26121,26706,26856,27006],{},[10812,26122,26123,26128,26703],{},[10829,26124,26125],{},[3048,26126,26127],{},"斯勒茨基方程",[10829,26129,26130],{},[1865,26131,26133,26217],{"className":26132},[1872],[1865,26134,26136],{"className":26135},[1876],[1878,26137,26138],{"xmlns":1880},[1883,26139,26140,26214],{},[1903,26141,26142,26164,26166,26188,26190,26196],{},[1906,26143,26144,26154],{},[1903,26145,26146,26148],{},[1911,26147,1914],{"mathvariant":1913},[1923,26149,26150,26152],{},[1911,26151,1927],{},[1911,26153,3234],{},[1903,26155,26156,26158],{},[1911,26157,1914],{"mathvariant":1913},[1923,26159,26160,26162],{},[1911,26161,1798],{},[1911,26163,3471],{},[1933,26165,1955],{},[1906,26167,26168,26178],{},[1903,26169,26170,26172],{},[1911,26171,1914],{"mathvariant":1913},[1923,26173,26174,26176],{},[1911,26175,3484],{},[1911,26177,3234],{},[1903,26179,26180,26182],{},[1911,26181,1914],{"mathvariant":1913},[1923,26183,26184,26186],{},[1911,26185,1798],{},[1911,26187,3471],{},[1933,26189,1935],{},[1923,26191,26192,26194],{},[1911,26193,1927],{},[1911,26195,3471],{},[1906,26197,26198,26208],{},[1903,26199,26200,26202],{},[1911,26201,1914],{"mathvariant":1913},[1923,26203,26204,26206],{},[1911,26205,1927],{},[1911,26207,3234],{},[1903,26209,26210,26212],{},[1911,26211,1914],{"mathvariant":1913},[1911,26213,2046],{},[2060,26215,26216],{"encoding":2062},"\\frac{\\partial x_i}{\\partial p_j} = \\frac{\\partial h_i}{\\partial p_j} - x_j \\frac{\\partial x_i}{\\partial m}",[1865,26218,26220,26383,26546],{"className":26219,"ariaHidden":1901},[2067],[1865,26221,26223,26226,26374,26377,26380],{"className":26222},[2071],[1865,26224],{"className":26225,"style":4208},[2075],[1865,26227,26229,26232,26371],{"className":26228},[2080],[1865,26230],{"className":26231},[2119,2120],[1865,26233,26235],{"className":26234},[1906],[1865,26236,26238,26363],{"className":26237},[2091,2092],[1865,26239,26241,26360],{"className":26240},[2096],[1865,26242,26244,26298,26306],{"className":26243,"style":4227},[2100],[1865,26245,26246,26249],{"style":4230},[1865,26247],{"className":26248,"style":2140},[2108],[1865,26250,26252],{"className":26251},[2179,2180,2181,2182],[1865,26253,26255,26258],{"className":26254},[2080,2182],[1865,26256,1914],{"className":26257,"style":2147},[2080,2182],[1865,26259,26261,26264],{"className":26260},[2080,2182],[1865,26262,1798],{"className":26263},[2080,2154,2182],[1865,26265,26267],{"className":26266},[2158],[1865,26268,26270,26290],{"className":26269},[2091,2092],[1865,26271,26273,26287],{"className":26272},[2096],[1865,26274,26276],{"className":26275,"style":4261},[2100],[1865,26277,26278,26281],{"style":4264},[1865,26279],{"className":26280,"style":4268},[2108],[1865,26282,26284],{"className":26283},[2179,4272,4273,2182],[1865,26285,3471],{"className":26286,"style":3616},[2080,2154,2182],[1865,26288,2190],{"className":26289},[2189],[1865,26291,26293],{"className":26292},[2096],[1865,26294,26296],{"className":26295,"style":4286},[2100],[1865,26297],{},[1865,26299,26300,26303],{"style":2202},[1865,26301],{"className":26302,"style":2140},[2108],[1865,26304],{"className":26305,"style":2210},[2209],[1865,26307,26308,26311],{"style":4299},[1865,26309],{"className":26310,"style":2140},[2108],[1865,26312,26314],{"className":26313},[2179,2180,2181,2182],[1865,26315,26317,26320],{"className":26316},[2080,2182],[1865,26318,1914],{"className":26319,"style":2147},[2080,2182],[1865,26321,26323,26326],{"className":26322},[2080,2182],[1865,26324,1927],{"className":26325},[2080,2154,2182],[1865,26327,26329],{"className":26328},[2158],[1865,26330,26332,26352],{"className":26331},[2091,2092],[1865,26333,26335,26349],{"className":26334},[2096],[1865,26336,26338],{"className":26337,"style":4261},[2100],[1865,26339,26340,26343],{"style":4264},[1865,26341],{"className":26342,"style":4268},[2108],[1865,26344,26346],{"className":26345},[2179,4272,4273,2182],[1865,26347,3234],{"className":26348},[2080,2154,2182],[1865,26350,2190],{"className":26351},[2189],[1865,26353,26355],{"className":26354},[2096],[1865,26356,26358],{"className":26357,"style":4350},[2100],[1865,26359],{},[1865,26361,2190],{"className":26362},[2189],[1865,26364,26366],{"className":26365},[2096],[1865,26367,26369],{"className":26368,"style":4362},[2100],[1865,26370],{},[1865,26372],{"className":26373},[2242,2120],[1865,26375],{"className":26376,"style":2693},[2246],[1865,26378,1955],{"className":26379},[2697],[1865,26381],{"className":26382,"style":2693},[2246],[1865,26384,26386,26389,26537,26540,26543],{"className":26385},[2071],[1865,26387],{"className":26388,"style":4208},[2075],[1865,26390,26392,26395,26534],{"className":26391},[2080],[1865,26393],{"className":26394},[2119,2120],[1865,26396,26398],{"className":26397},[1906],[1865,26399,26401,26526],{"className":26400},[2091,2092],[1865,26402,26404,26523],{"className":26403},[2096],[1865,26405,26407,26461,26469],{"className":26406,"style":4227},[2100],[1865,26408,26409,26412],{"style":4230},[1865,26410],{"className":26411,"style":2140},[2108],[1865,26413,26415],{"className":26414},[2179,2180,2181,2182],[1865,26416,26418,26421],{"className":26417},[2080,2182],[1865,26419,1914],{"className":26420,"style":2147},[2080,2182],[1865,26422,26424,26427],{"className":26423},[2080,2182],[1865,26425,1798],{"className":26426},[2080,2154,2182],[1865,26428,26430],{"className":26429},[2158],[1865,26431,26433,26453],{"className":26432},[2091,2092],[1865,26434,26436,26450],{"className":26435},[2096],[1865,26437,26439],{"className":26438,"style":4261},[2100],[1865,26440,26441,26444],{"style":4264},[1865,26442],{"className":26443,"style":4268},[2108],[1865,26445,26447],{"className":26446},[2179,4272,4273,2182],[1865,26448,3471],{"className":26449,"style":3616},[2080,2154,2182],[1865,26451,2190],{"className":26452},[2189],[1865,26454,26456],{"className":26455},[2096],[1865,26457,26459],{"className":26458,"style":4286},[2100],[1865,26460],{},[1865,26462,26463,26466],{"style":2202},[1865,26464],{"className":26465,"style":2140},[2108],[1865,26467],{"className":26468,"style":2210},[2209],[1865,26470,26471,26474],{"style":4299},[1865,26472],{"className":26473,"style":2140},[2108],[1865,26475,26477],{"className":26476},[2179,2180,2181,2182],[1865,26478,26480,26483],{"className":26479},[2080,2182],[1865,26481,1914],{"className":26482,"style":2147},[2080,2182],[1865,26484,26486,26489],{"className":26485},[2080,2182],[1865,26487,3484],{"className":26488},[2080,2154,2182],[1865,26490,26492],{"className":26491},[2158],[1865,26493,26495,26515],{"className":26494},[2091,2092],[1865,26496,26498,26512],{"className":26497},[2096],[1865,26499,26501],{"className":26500,"style":4261},[2100],[1865,26502,26503,26506],{"style":4264},[1865,26504],{"className":26505,"style":4268},[2108],[1865,26507,26509],{"className":26508},[2179,4272,4273,2182],[1865,26510,3234],{"className":26511},[2080,2154,2182],[1865,26513,2190],{"className":26514},[2189],[1865,26516,26518],{"className":26517},[2096],[1865,26519,26521],{"className":26520,"style":4350},[2100],[1865,26522],{},[1865,26524,2190],{"className":26525},[2189],[1865,26527,26529],{"className":26528},[2096],[1865,26530,26532],{"className":26531,"style":4362},[2100],[1865,26533],{},[1865,26535],{"className":26536},[2242,2120],[1865,26538],{"className":26539,"style":2247},[2246],[1865,26541,1935],{"className":26542},[2251],[1865,26544],{"className":26545,"style":2247},[2246],[1865,26547,26549,26552,26592],{"className":26548},[2071],[1865,26550],{"className":26551,"style":4751},[2075],[1865,26553,26555,26558],{"className":26554},[2080],[1865,26556,1927],{"className":26557},[2080,2154],[1865,26559,26561],{"className":26560},[2158],[1865,26562,26564,26584],{"className":26563},[2091,2092],[1865,26565,26567,26581],{"className":26566},[2096],[1865,26568,26570],{"className":26569,"style":3364},[2100],[1865,26571,26572,26575],{"style":2171},[1865,26573],{"className":26574,"style":2175},[2108],[1865,26576,26578],{"className":26577},[2179,2180,2181,2182],[1865,26579,3471],{"className":26580,"style":3616},[2080,2154,2182],[1865,26582,2190],{"className":26583},[2189],[1865,26585,26587],{"className":26586},[2096],[1865,26588,26590],{"className":26589,"style":3626},[2100],[1865,26591],{},[1865,26593,26595,26598,26700],{"className":26594},[2080],[1865,26596],{"className":26597},[2119,2120],[1865,26599,26601],{"className":26600},[1906],[1865,26602,26604,26692],{"className":26603},[2091,2092],[1865,26605,26607,26689],{"className":26606},[2096],[1865,26608,26610,26627,26635],{"className":26609,"style":4227},[2100],[1865,26611,26612,26615],{"style":4230},[1865,26613],{"className":26614,"style":2140},[2108],[1865,26616,26618],{"className":26617},[2179,2180,2181,2182],[1865,26619,26621,26624],{"className":26620},[2080,2182],[1865,26622,1914],{"className":26623,"style":2147},[2080,2182],[1865,26625,2046],{"className":26626},[2080,2154,2182],[1865,26628,26629,26632],{"style":2202},[1865,26630],{"className":26631,"style":2140},[2108],[1865,26633],{"className":26634,"style":2210},[2209],[1865,26636,26637,26640],{"style":4299},[1865,26638],{"className":26639,"style":2140},[2108],[1865,26641,26643],{"className":26642},[2179,2180,2181,2182],[1865,26644,26646,26649],{"className":26645},[2080,2182],[1865,26647,1914],{"className":26648,"style":2147},[2080,2182],[1865,26650,26652,26655],{"className":26651},[2080,2182],[1865,26653,1927],{"className":26654},[2080,2154,2182],[1865,26656,26658],{"className":26657},[2158],[1865,26659,26661,26681],{"className":26660},[2091,2092],[1865,26662,26664,26678],{"className":26663},[2096],[1865,26665,26667],{"className":26666,"style":4261},[2100],[1865,26668,26669,26672],{"style":4264},[1865,26670],{"className":26671,"style":4268},[2108],[1865,26673,26675],{"className":26674},[2179,4272,4273,2182],[1865,26676,3234],{"className":26677},[2080,2154,2182],[1865,26679,2190],{"className":26680},[2189],[1865,26682,26684],{"className":26683},[2096],[1865,26685,26687],{"className":26686,"style":4350},[2100],[1865,26688],{},[1865,26690,2190],{"className":26691},[2189],[1865,26693,26695],{"className":26694},[2096],[1865,26696,26698],{"className":26697,"style":4901},[2100],[1865,26699],{},[1865,26701],{"className":26702},[2242,2120],[10829,26704,26705],{},"价格效应 = 替代 + 收入",[10812,26707,26708,26712,26853],{},[10829,26709,26710],{},[3048,26711,19411],{},[10829,26713,26714],{},[1865,26715,26717,26753],{"className":26716},[1872],[1865,26718,26720],{"className":26719},[1876],[1878,26721,26722],{"xmlns":1880},[1883,26723,26724,26750],{},[1903,26725,26726,26728,26730,26736,26738,26744,26746,26748],{},[1911,26727,8742],{},[1933,26729,4942],{"stretchy":3501},[6885,26731,26732,26734],{},[1911,26733,1798],{},[1929,26735,1931],{},[1933,26737,2784],{"separator":1901},[6885,26739,26740,26742],{},[1911,26741,3508],{},[1929,26743,1900],{},[1933,26745,4963],{"stretchy":3501},[1933,26747,1935],{},[1911,26749,2046],{},[2060,26751,26752],{"encoding":2062},"e(p^1, u^0) - m",[1865,26754,26756,26844],{"className":26755,"ariaHidden":1901},[2067],[1865,26757,26759,26762,26765,26768,26797,26800,26803,26832,26835,26838,26841],{"className":26758},[2071],[1865,26760],{"className":26761,"style":9243},[2075],[1865,26763,8742],{"className":26764},[2080,2154],[1865,26766,4942],{"className":26767},[2119],[1865,26769,26771,26774],{"className":26770},[2080],[1865,26772,1798],{"className":26773},[2080,2154],[1865,26775,26777],{"className":26776},[2158],[1865,26778,26780],{"className":26779},[2091],[1865,26781,26783],{"className":26782},[2096],[1865,26784,26786],{"className":26785,"style":8573},[2100],[1865,26787,26788,26791],{"style":7519},[1865,26789],{"className":26790,"style":2175},[2108],[1865,26792,26794],{"className":26793},[2179,2180,2181,2182],[1865,26795,1931],{"className":26796},[2080,2182],[1865,26798,2784],{"className":26799},[2851],[1865,26801],{"className":26802,"style":2855},[2246],[1865,26804,26806,26809],{"className":26805},[2080],[1865,26807,3508],{"className":26808},[2080,2154],[1865,26810,26812],{"className":26811},[2158],[1865,26813,26815],{"className":26814},[2091],[1865,26816,26818],{"className":26817},[2096],[1865,26819,26821],{"className":26820,"style":8573},[2100],[1865,26822,26823,26826],{"style":7519},[1865,26824],{"className":26825,"style":2175},[2108],[1865,26827,26829],{"className":26828},[2179,2180,2181,2182],[1865,26830,1900],{"className":26831},[2080,2182],[1865,26833,4963],{"className":26834},[2242],[1865,26836],{"className":26837,"style":2247},[2246],[1865,26839,1935],{"className":26840},[2251],[1865,26842],{"className":26843,"style":2247},[2246],[1865,26845,26847,26850],{"className":26846},[2071],[1865,26848],{"className":26849,"style":6852},[2075],[1865,26851,2046],{"className":26852},[2080,2154],[10829,26854,26855],{},"恢复原效用的补偿",[10812,26857,26858,26862,27003],{},[10829,26859,26860],{},[3048,26861,19535],{},[10829,26863,26864],{},[1865,26865,26867,26903],{"className":26866},[1872],[1865,26868,26870],{"className":26869},[1876],[1878,26871,26872],{"xmlns":1880},[1883,26873,26874,26900],{},[1903,26875,26876,26878,26880,26882,26884,26890,26892,26898],{},[1911,26877,2046],{},[1933,26879,1935],{},[1911,26881,8742],{},[1933,26883,4942],{"stretchy":3501},[6885,26885,26886,26888],{},[1911,26887,1798],{},[1929,26889,1900],{},[1933,26891,2784],{"separator":1901},[6885,26893,26894,26896],{},[1911,26895,3508],{},[1929,26897,1931],{},[1933,26899,4963],{"stretchy":3501},[2060,26901,26902],{"encoding":2062},"m - e(p^0, u^1)",[1865,26904,26906,26924],{"className":26905,"ariaHidden":1901},[2067],[1865,26907,26909,26912,26915,26918,26921],{"className":26908},[2071],[1865,26910],{"className":26911,"style":10638},[2075],[1865,26913,2046],{"className":26914},[2080,2154],[1865,26916],{"className":26917,"style":2247},[2246],[1865,26919,1935],{"className":26920},[2251],[1865,26922],{"className":26923,"style":2247},[2246],[1865,26925,26927,26930,26933,26936,26965,26968,26971,27000],{"className":26926},[2071],[1865,26928],{"className":26929,"style":9243},[2075],[1865,26931,8742],{"className":26932},[2080,2154],[1865,26934,4942],{"className":26935},[2119],[1865,26937,26939,26942],{"className":26938},[2080],[1865,26940,1798],{"className":26941},[2080,2154],[1865,26943,26945],{"className":26944},[2158],[1865,26946,26948],{"className":26947},[2091],[1865,26949,26951],{"className":26950},[2096],[1865,26952,26954],{"className":26953,"style":8573},[2100],[1865,26955,26956,26959],{"style":7519},[1865,26957],{"className":26958,"style":2175},[2108],[1865,26960,26962],{"className":26961},[2179,2180,2181,2182],[1865,26963,1900],{"className":26964},[2080,2182],[1865,26966,2784],{"className":26967},[2851],[1865,26969],{"className":26970,"style":2855},[2246],[1865,26972,26974,26977],{"className":26973},[2080],[1865,26975,3508],{"className":26976},[2080,2154],[1865,26978,26980],{"className":26979},[2158],[1865,26981,26983],{"className":26982},[2091],[1865,26984,26986],{"className":26985},[2096],[1865,26987,26989],{"className":26988,"style":8573},[2100],[1865,26990,26991,26994],{"style":7519},[1865,26992],{"className":26993,"style":2175},[2108],[1865,26995,26997],{"className":26996},[2179,2180,2181,2182],[1865,26998,1931],{"className":26999},[2080,2182],[1865,27001,4963],{"className":27002},[2242],[10829,27004,27005],{},"等价的收入变化",[10812,27007,27008,27013,27107],{},[10829,27009,27010],{},[3048,27011,27012],{},"消费者剩余",[10829,27014,27015],{},[1865,27016,27018,27050],{"className":27017},[1872],[1865,27019,27021],{"className":27020},[1876],[1878,27022,27023],{"xmlns":1880},[1883,27024,27025,27047],{},[1903,27026,27027,27029,27031,27033,27035,27037,27039,27041,27043,27045],{},[1933,27028,11392],{},[1911,27030,11316],{},[1933,27032,4942],{"stretchy":3501},[1911,27034,1927],{},[1933,27036,4963],{"stretchy":3501},[1911,27038,3144],{},[1911,27040,1927],{},[1933,27042,1935],{},[1911,27044,1798],{},[1911,27046,1927],{},[2060,27048,27049],{"encoding":2062},"\\int D(x)dx - px",[1865,27051,27053,27095],{"className":27052,"ariaHidden":1901},[2067],[1865,27054,27056,27060,27065,27068,27071,27074,27077,27080,27083,27086,27089,27092],{"className":27055},[2071],[1865,27057],{"className":27058,"style":27059},[2075],"height:1.1111em;vertical-align:-0.3061em;",[1865,27061,11392],{"className":27062,"style":27064},[11465,11469,27063],"small-op","margin-right:0.1945em;position:relative;top:-0.0006em;",[1865,27066],{"className":27067,"style":2855},[2246],[1865,27069,11316],{"className":27070,"style":11356},[2080,2154],[1865,27072,4942],{"className":27073},[2119],[1865,27075,1927],{"className":27076},[2080,2154],[1865,27078,4963],{"className":27079},[2242],[1865,27081,3144],{"className":27082},[2080,2154],[1865,27084,1927],{"className":27085},[2080,2154],[1865,27087],{"className":27088,"style":2247},[2246],[1865,27090,1935],{"className":27091},[2251],[1865,27093],{"className":27094,"style":2247},[2246],[1865,27096,27098,27101,27104],{"className":27097},[2071],[1865,27099],{"className":27100,"style":2948},[2075],[1865,27102,1798],{"className":27103},[2080,2154],[1865,27105,1927],{"className":27106},[2080,2154],[10829,27108,27109],{},"福利的近似测度",[1798,27111,27112,27115,27116,27119,27120,27122],{},[3048,27113,27114],{},"关键洞见",":\n✅ 需求变化可以分解为理性的替代和购买力的变化",[27117,27118],"br",{},"\n✅ 福利变化可以精确地用货币单位测量",[27117,27121],{},"\n✅ 政策评估需要考虑收入分配和效率的权衡",[1794,27124,27125],{"id":27125},"自学检查",[1798,27127,27128,27131],{},[3048,27129,27130],{},"核心直觉回看","：价格变化看起来只是需求曲线上的移动，但背后有两股力量：相对价格变化引起替代效应，实际购买力变化引起收入效应。福利测度则进一步追问：这些变化折算成钱，到底值多少？",[1798,27133,27134,27137],{},[3048,27135,27136],{},"关键模型提醒","：斯勒茨基方程",[1865,27139,27141],{"className":27140},[1868],[1865,27142,27144,27228],{"className":27143},[1872],[1865,27145,27147],{"className":27146},[1876],[1878,27148,27149],{"xmlns":1880,"display":1881},[1883,27150,27151,27225],{},[1903,27152,27153,27175,27177,27199,27201,27207],{},[1906,27154,27155,27165],{},[1903,27156,27157,27159],{},[1911,27158,1914],{"mathvariant":1913},[1923,27160,27161,27163],{},[1911,27162,1927],{},[1911,27164,3234],{},[1903,27166,27167,27169],{},[1911,27168,1914],{"mathvariant":1913},[1923,27170,27171,27173],{},[1911,27172,1798],{},[1911,27174,3471],{},[1933,27176,1955],{},[1906,27178,27179,27189],{},[1903,27180,27181,27183],{},[1911,27182,1914],{"mathvariant":1913},[1923,27184,27185,27187],{},[1911,27186,3484],{},[1911,27188,3234],{},[1903,27190,27191,27193],{},[1911,27192,1914],{"mathvariant":1913},[1923,27194,27195,27197],{},[1911,27196,1798],{},[1911,27198,3471],{},[1933,27200,1935],{},[1923,27202,27203,27205],{},[1911,27204,1927],{},[1911,27206,3471],{},[1906,27208,27209,27219],{},[1903,27210,27211,27213],{},[1911,27212,1914],{"mathvariant":1913},[1923,27214,27215,27217],{},[1911,27216,1927],{},[1911,27218,3234],{},[1903,27220,27221,27223],{},[1911,27222,1914],{"mathvariant":1913},[1911,27224,2046],{},[2060,27226,27227],{"encoding":2062},"\\frac{\\partial x_i}{\\partial p_j}\n=\n\\frac{\\partial h_i}{\\partial p_j}\n-x_j\\frac{\\partial x_i}{\\partial m}",[1865,27229,27231,27388,27545],{"className":27230,"ariaHidden":1901},[2067],[1865,27232,27234,27237,27379,27382,27385],{"className":27233},[2071],[1865,27235],{"className":27236,"style":3557},[2075],[1865,27238,27240,27243,27376],{"className":27239},[2080],[1865,27241],{"className":27242},[2119,2120],[1865,27244,27246],{"className":27245},[1906],[1865,27247,27249,27368],{"className":27248},[2091,2092],[1865,27250,27252,27365],{"className":27251},[2096],[1865,27253,27255,27306,27314],{"className":27254,"style":2133},[2100],[1865,27256,27257,27260],{"style":2136},[1865,27258],{"className":27259,"style":2140},[2108],[1865,27261,27263,27266],{"className":27262},[2080],[1865,27264,1914],{"className":27265,"style":2147},[2080],[1865,27267,27269,27272],{"className":27268},[2080],[1865,27270,1798],{"className":27271},[2080,2154],[1865,27273,27275],{"className":27274},[2158],[1865,27276,27278,27298],{"className":27277},[2091,2092],[1865,27279,27281,27295],{"className":27280},[2096],[1865,27282,27284],{"className":27283,"style":3364},[2100],[1865,27285,27286,27289],{"style":2171},[1865,27287],{"className":27288,"style":2175},[2108],[1865,27290,27292],{"className":27291},[2179,2180,2181,2182],[1865,27293,3471],{"className":27294,"style":3616},[2080,2154,2182],[1865,27296,2190],{"className":27297},[2189],[1865,27299,27301],{"className":27300},[2096],[1865,27302,27304],{"className":27303,"style":3626},[2100],[1865,27305],{},[1865,27307,27308,27311],{"style":2202},[1865,27309],{"className":27310,"style":2140},[2108],[1865,27312],{"className":27313,"style":2210},[2209],[1865,27315,27316,27319],{"style":2213},[1865,27317],{"className":27318,"style":2140},[2108],[1865,27320,27322,27325],{"className":27321},[2080],[1865,27323,1914],{"className":27324,"style":2147},[2080],[1865,27326,27328,27331],{"className":27327},[2080],[1865,27329,1927],{"className":27330},[2080,2154],[1865,27332,27334],{"className":27333},[2158],[1865,27335,27337,27357],{"className":27336},[2091,2092],[1865,27338,27340,27354],{"className":27339},[2096],[1865,27341,27343],{"className":27342,"style":3364},[2100],[1865,27344,27345,27348],{"style":2171},[1865,27346],{"className":27347,"style":2175},[2108],[1865,27349,27351],{"className":27350},[2179,2180,2181,2182],[1865,27352,3234],{"className":27353},[2080,2154,2182],[1865,27355,2190],{"className":27356},[2189],[1865,27358,27360],{"className":27359},[2096],[1865,27361,27363],{"className":27362,"style":2197},[2100],[1865,27364],{},[1865,27366,2190],{"className":27367},[2189],[1865,27369,27371],{"className":27370},[2096],[1865,27372,27374],{"className":27373,"style":3697},[2100],[1865,27375],{},[1865,27377],{"className":27378},[2242,2120],[1865,27380],{"className":27381,"style":2693},[2246],[1865,27383,1955],{"className":27384},[2697],[1865,27386],{"className":27387,"style":2693},[2246],[1865,27389,27391,27394,27536,27539,27542],{"className":27390},[2071],[1865,27392],{"className":27393,"style":3557},[2075],[1865,27395,27397,27400,27533],{"className":27396},[2080],[1865,27398],{"className":27399},[2119,2120],[1865,27401,27403],{"className":27402},[1906],[1865,27404,27406,27525],{"className":27405},[2091,2092],[1865,27407,27409,27522],{"className":27408},[2096],[1865,27410,27412,27463,27471],{"className":27411,"style":2133},[2100],[1865,27413,27414,27417],{"style":2136},[1865,27415],{"className":27416,"style":2140},[2108],[1865,27418,27420,27423],{"className":27419},[2080],[1865,27421,1914],{"className":27422,"style":2147},[2080],[1865,27424,27426,27429],{"className":27425},[2080],[1865,27427,1798],{"className":27428},[2080,2154],[1865,27430,27432],{"className":27431},[2158],[1865,27433,27435,27455],{"className":27434},[2091,2092],[1865,27436,27438,27452],{"className":27437},[2096],[1865,27439,27441],{"className":27440,"style":3364},[2100],[1865,27442,27443,27446],{"style":2171},[1865,27444],{"className":27445,"style":2175},[2108],[1865,27447,27449],{"className":27448},[2179,2180,2181,2182],[1865,27450,3471],{"className":27451,"style":3616},[2080,2154,2182],[1865,27453,2190],{"className":27454},[2189],[1865,27456,27458],{"className":27457},[2096],[1865,27459,27461],{"className":27460,"style":3626},[2100],[1865,27462],{},[1865,27464,27465,27468],{"style":2202},[1865,27466],{"className":27467,"style":2140},[2108],[1865,27469],{"className":27470,"style":2210},[2209],[1865,27472,27473,27476],{"style":2213},[1865,27474],{"className":27475,"style":2140},[2108],[1865,27477,27479,27482],{"className":27478},[2080],[1865,27480,1914],{"className":27481,"style":2147},[2080],[1865,27483,27485,27488],{"className":27484},[2080],[1865,27486,3484],{"className":27487},[2080,2154],[1865,27489,27491],{"className":27490},[2158],[1865,27492,27494,27514],{"className":27493},[2091,2092],[1865,27495,27497,27511],{"className":27496},[2096],[1865,27498,27500],{"className":27499,"style":3364},[2100],[1865,27501,27502,27505],{"style":2171},[1865,27503],{"className":27504,"style":2175},[2108],[1865,27506,27508],{"className":27507},[2179,2180,2181,2182],[1865,27509,3234],{"className":27510},[2080,2154,2182],[1865,27512,2190],{"className":27513},[2189],[1865,27515,27517],{"className":27516},[2096],[1865,27518,27520],{"className":27519,"style":2197},[2100],[1865,27521],{},[1865,27523,2190],{"className":27524},[2189],[1865,27526,27528],{"className":27527},[2096],[1865,27529,27531],{"className":27530,"style":3697},[2100],[1865,27532],{},[1865,27534],{"className":27535},[2242,2120],[1865,27537],{"className":27538,"style":2247},[2246],[1865,27540,1935],{"className":27541},[2251],[1865,27543],{"className":27544,"style":2247},[2246],[1865,27546,27548,27551,27591],{"className":27547},[2071],[1865,27549],{"className":27550,"style":4008},[2075],[1865,27552,27554,27557],{"className":27553},[2080],[1865,27555,1927],{"className":27556},[2080,2154],[1865,27558,27560],{"className":27559},[2158],[1865,27561,27563,27583],{"className":27562},[2091,2092],[1865,27564,27566,27580],{"className":27565},[2096],[1865,27567,27569],{"className":27568,"style":3364},[2100],[1865,27570,27571,27574],{"style":2171},[1865,27572],{"className":27573,"style":2175},[2108],[1865,27575,27577],{"className":27576},[2179,2180,2181,2182],[1865,27578,3471],{"className":27579,"style":3616},[2080,2154,2182],[1865,27581,2190],{"className":27582},[2189],[1865,27584,27586],{"className":27585},[2096],[1865,27587,27589],{"className":27588,"style":3626},[2100],[1865,27590],{},[1865,27592,27594,27597,27693],{"className":27593},[2080],[1865,27595],{"className":27596},[2119,2120],[1865,27598,27600],{"className":27599},[1906],[1865,27601,27603,27685],{"className":27602},[2091,2092],[1865,27604,27606,27682],{"className":27605},[2096],[1865,27607,27609,27623,27631],{"className":27608,"style":2133},[2100],[1865,27610,27611,27614],{"style":2136},[1865,27612],{"className":27613,"style":2140},[2108],[1865,27615,27617,27620],{"className":27616},[2080],[1865,27618,1914],{"className":27619,"style":2147},[2080],[1865,27621,2046],{"className":27622},[2080,2154],[1865,27624,27625,27628],{"style":2202},[1865,27626],{"className":27627,"style":2140},[2108],[1865,27629],{"className":27630,"style":2210},[2209],[1865,27632,27633,27636],{"style":2213},[1865,27634],{"className":27635,"style":2140},[2108],[1865,27637,27639,27642],{"className":27638},[2080],[1865,27640,1914],{"className":27641,"style":2147},[2080],[1865,27643,27645,27648],{"className":27644},[2080],[1865,27646,1927],{"className":27647},[2080,2154],[1865,27649,27651],{"className":27650},[2158],[1865,27652,27654,27674],{"className":27653},[2091,2092],[1865,27655,27657,27671],{"className":27656},[2096],[1865,27658,27660],{"className":27659,"style":3364},[2100],[1865,27661,27662,27665],{"style":2171},[1865,27663],{"className":27664,"style":2175},[2108],[1865,27666,27668],{"className":27667},[2179,2180,2181,2182],[1865,27669,3234],{"className":27670},[2080,2154,2182],[1865,27672,2190],{"className":27673},[2189],[1865,27675,27677],{"className":27676},[2096],[1865,27678,27680],{"className":27679,"style":2197},[2100],[1865,27681],{},[1865,27683,2190],{"className":27684},[2189],[1865,27686,27688],{"className":27687},[2096],[1865,27689,27691],{"className":27690,"style":4149},[2100],[1865,27692],{},[1865,27694],{"className":27695},[2242,2120],[1798,27697,27698,27699,27757,27758,27816],{},"是本章的主线。CV 使用原效用 ",[1865,27700,27702,27719],{"className":27701},[1872],[1865,27703,27705],{"className":27704},[1876],[1878,27706,27707],{"xmlns":1880},[1883,27708,27709,27717],{},[1903,27710,27711],{},[6885,27712,27713,27715],{},[1911,27714,3508],{},[1929,27716,1900],{},[2060,27718,10857],{"encoding":2062},[1865,27720,27722],{"className":27721,"ariaHidden":1901},[2067],[1865,27723,27725,27728],{"className":27724},[2071],[1865,27726],{"className":27727,"style":8573},[2075],[1865,27729,27731,27734],{"className":27730},[2080],[1865,27732,3508],{"className":27733},[2080,2154],[1865,27735,27737],{"className":27736},[2158],[1865,27738,27740],{"className":27739},[2091],[1865,27741,27743],{"className":27742},[2096],[1865,27744,27746],{"className":27745,"style":8573},[2100],[1865,27747,27748,27751],{"style":7519},[1865,27749],{"className":27750,"style":2175},[2108],[1865,27752,27754],{"className":27753},[2179,2180,2181,2182],[1865,27755,1900],{"className":27756},[2080,2182],"，EV 使用新效用 ",[1865,27759,27761,27778],{"className":27760},[1872],[1865,27762,27764],{"className":27763},[1876],[1878,27765,27766],{"xmlns":1880},[1883,27767,27768,27776],{},[1903,27769,27770],{},[6885,27771,27772,27774],{},[1911,27773,3508],{},[1929,27775,1931],{},[2060,27777,10919],{"encoding":2062},[1865,27779,27781],{"className":27780,"ariaHidden":1901},[2067],[1865,27782,27784,27787],{"className":27783},[2071],[1865,27785],{"className":27786,"style":8573},[2075],[1865,27788,27790,27793],{"className":27789},[2080],[1865,27791,3508],{"className":27792},[2080,2154],[1865,27794,27796],{"className":27795},[2158],[1865,27797,27799],{"className":27798},[2091],[1865,27800,27802],{"className":27801},[2096],[1865,27803,27805],{"className":27804,"style":8573},[2100],[1865,27806,27807,27810],{"style":7519},[1865,27808],{"className":27809,"style":2175},[2108],[1865,27811,27813],{"className":27812},[2179,2180,2181,2182],[1865,27814,1931],{"className":27815},[2080,2182],"；消费者剩余在拟线性或小变化时最可靠。",[1854,27818,27819],{"id":27819},"常见误区",[1805,27821,27822,27825,27828,27831],{},[1808,27823,27824],{},"把观察到的需求变化全部叫作替代效应，忘记马歇尔需求里还包含收入效应。",[1808,27826,27827],{},"混用 CV、EV 的符号约定，没有说明自己是在报告“有符号转移”还是“正的福利损失”。",[1808,27829,27830],{},"认为劣等品一定是吉芬品。吉芬品需要收入效应强到超过替代效应。",[1808,27832,27833],{},"用消费者剩余替代所有福利测度，却不检查收入效应是否显著。",[1854,27835,27836],{"id":27836},"自测题",[3406,27838,27839,27842,27845,27848,27851],{},[1808,27840,27841],{},"对正常品而言，价格上涨时替代效应和收入效应分别是什么方向？",[1808,27843,27844],{},"为什么希克斯需求的自身价格效应一定非正，而马歇尔需求可能为正？",[1808,27846,27847],{},"价格上涨时，CV 和 EV 分别以哪个效用水平为参照？",[1808,27849,27850],{},"拟线性效用为什么会让 CV、EV 和消费者剩余变化相等？",[1808,27852,27853],{},"比较等额现金补贴和价格补贴，为什么现金补贴通常弱优于价格补贴？",[1854,27855,27856],{"id":27856},"下一步学习提示",[1798,27858,27859],{},"复习时请画出一张标准的斯勒茨基分解图，再画一张劣等品的版本。下一章进入不确定性后，福利分析会从“价格变化”扩展到“随机结果带来的风险成本”。",[1798,27861,27862,27865,27866,27869],{},[3048,27863,27864],{},"下一章预告",": 在确定性环境下，我们假设消费者知道每个选择的确切结果。但现实中，许多决策面临",[3048,27867,27868],{},"不确定性"," —— 投资可能赚也可能亏，保险可能用上也可能用不上。下一章我们将学习期望效用理论，分析风险态度，并探讨保险和投资决策。",{"title":10,"searchDepth":27871,"depth":27871,"links":27872},2,[27873,27874,27875,27880,27886,27893,27898,27902,27907,27911,27912,27913],{"id":1796,"depth":27871,"text":1796},{"id":1844,"depth":27871,"text":1845},{"id":1851,"depth":27871,"text":1852,"children":27876},[27877,27879],{"id":1856,"depth":27878,"text":1857},3,{"id":3054,"depth":27878,"text":3055},{"id":3425,"depth":27871,"text":3426,"children":27881},[27882,27883,27884,27885],{"id":3429,"depth":27878,"text":3430},{"id":6821,"depth":27878,"text":6822},{"id":7622,"depth":27878,"text":7623},{"id":7672,"depth":27878,"text":7673},{"id":8512,"depth":27871,"text":8513,"children":27887},[27888,27889,27890,27891,27892],{"id":8516,"depth":27878,"text":8517},{"id":8702,"depth":27878,"text":8703},{"id":9900,"depth":27878,"text":9901},{"id":10803,"depth":27878,"text":10804},{"id":11267,"depth":27878,"text":11268},{"id":11286,"depth":27871,"text":11287,"children":27894},[27895,27896,27897],{"id":11290,"depth":27878,"text":11291},{"id":11653,"depth":27878,"text":11654},{"id":12638,"depth":27878,"text":12639},{"id":12680,"depth":27871,"text":12681,"children":27899},[27900,27901],{"id":12684,"depth":27878,"text":12685},{"id":21977,"depth":27878,"text":21978},{"id":24625,"depth":27871,"text":24626,"children":27903},[27904,27905,27906],{"id":24629,"depth":27878,"text":24630},{"id":24943,"depth":27878,"text":24944},{"id":25033,"depth":27878,"text":25034},{"id":25688,"depth":27871,"text":25689,"children":27908},[27909,27910],{"id":25692,"depth":27878,"text":25693},{"id":25999,"depth":27878,"text":26000},{"id":26057,"depth":27871,"text":26058},{"id":26102,"depth":27871,"text":26103},{"id":27125,"depth":27871,"text":27125,"children":27914},[27915,27916,27917],{"id":27819,"depth":27878,"text":27819},{"id":27836,"depth":27878,"text":27836},{"id":27856,"depth":27878,"text":27856},"斯勒茨基方程、替代效应与收入效应、福利变化的精确测量","md",null,{},true,{"title":1560,"description":27918},"xfQccoKw67Zs_7XoDqh0FRUzCdG6e3S7ahkVv7--RNM",[27926,27928],{"title":1554,"path":1555,"stem":1556,"description":27927,"children":-1},"偏好、效用最大化、支出最小化、对偶理论与需求函数",{"title":1566,"path":1567,"stem":1568,"description":27929,"children":-1},"期望效用理论、风险态度、保险需求与资产组合选择",1785754753014]