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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 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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. 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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":728},{"id":1784,"title":1554,"body":1785,"description":29157,"extension":29158,"features":29159,"hero":29159,"layout":29159,"locale":29159,"meta":29160,"navigation":29159,"path":1555,"published":29161,"seo":29162,"stem":1556,"__hash__":29163},"docs\u002Fzh\u002Fmicroeconomics\u002F01-fundations\u002Findex.md",{"type":1786,"value":1787,"toc":29107},"minimark",[1788,1793,1797,1801,1804,1820,1823,1832,1836,1839,1842,1846,1851,1859,1903,1906,1935,1939,1942,1964,1968,1972,1990,1995,2017,2048,2052,4539,4543,7145,7147,7151,7155,7169,7421,7427,7430,7434,7437,7984,7990,8581,8584,8588,8591,9137,9140,10325,10336,10611,10883,10890,11447,11449,11453,11457,11464,12004,12010,12283,12555,12558,12568,13214,13218,13221,13681,13694,13698,13701,14072,14075,14079,14082,14085,14087,14090,14133,14135,14139,14143,14675,14686,14691,14696,14699,15048,15051,16083,16086,16540,16543,16892,17169,17305,17308,17476,17679,17685,18140,18594,18999,19004,19456,19459,19979,19984,20039,20042,20543,20575,20578,20915,20919,21583,21587,21590,21731,21733,21896,22074,22175,22551,22874,22876,22880,22884,22891,23332,23341,23347,23659,23663,23666,24162,24165,24169,24172,24486,24492,24496,24908,24910,24914,24918,24944,24948,24954,24959,25193,25198,25428,25433,25977,25981,25987,25992,26154,26220,26225,26488,26490,26494,26498,26501,26985,26988,26992,27024,27523,27527,27530,27536,28238,28338,28340,28344,28347,28376,28381,28392,28394,28398,28401,28443,28446,28452,28574,28577,28775,28778,29092,29095,29098],[1789,1790,1792],"h1",{"id":1791},"第-1-讲消费者理论与分析基础","第 1 讲：消费者理论与分析基础",[1794,1795,1796],"h2",{"id":1796},"本章导学",[1798,1799,1800],"p",{},"这一章是整门课的工具箱。你需要在这里把“消费者会怎么选”这个直觉问题，翻译成偏好关系、效用函数、预算约束和最优化问题。后面无论是福利分析、风险选择、一般均衡，还是机制设计，本质上都在反复使用这一章建立的语言。",[1798,1802,1803],{},"学完本章后，你应当能够：",[1805,1806,1807,1811,1814,1817],"ul",{},[1808,1809,1810],"li",{},"用偏好公理判断一个效用函数是否能代表某类选择行为。",[1808,1812,1813],{},"写出并求解效用最大化问题（UMP）和支出最小化问题（EMP）。",[1808,1815,1816],{},"区分马歇尔需求、希克斯需求、间接效用函数和支出函数。",[1808,1818,1819],{},"解释罗伊恒等式、谢泼德引理和包络定理为什么有经济含义，而不只是公式。",[1798,1821,1822],{},"常见作业和考试会要求你从一个具体效用函数出发，推导需求函数、支出函数或间接效用函数，并解释收入、价格和偏好参数变化带来的影响。做题时不要跳过模型设定：先写预算约束和拉格朗日函数，再讨论内部解、角点解和经济直觉。",[1798,1824,1825,1826,1831],{},"承接关系上，本章为",[1827,1828,1830],"a",{"href":1829},"..\u002F02-comparative-statics\u002F","第 2 章","的斯勒茨基分解和福利测度打基础；如果这一章的对偶关系没有掌握，后面的 CV、EV 和一般均衡会变得很吃力。",[1794,1833,1835],{"id":1834},"经济动机-economic-motivation","经济动机 (Economic Motivation)",[1798,1837,1838],{},"理解消费者如何在预算约束下做出最优选择，是分析所有经济行为的基础。这是微观经济学的核心问题，旨在解释个人和家庭如何在有限的资源下实现最大的满足感（效用）。",[1840,1841],"hr",{},[1794,1843,1845],{"id":1844},"_1-消费者偏好与效用函数","1. 消费者偏好与效用函数",[1847,1848,1850],"h3",{"id":1849},"_11-偏好公理-axioms-of-preferences","1.1 偏好公理 (Axioms of Preferences)",[1798,1852,1853,1854,1858],{},"为了建立一个理性的消费者模型，我们假设消费者的偏好 ",[1855,1856,1857],"code",{},"≽"," (读作“至少一样偏好”) 满足三个基本公理：",[1860,1861,1862,1879,1888],"ol",{},[1808,1863,1864,1868,1869,1871,1872,1874,1875,1878],{},[1865,1866,1867],"strong",{},"完备性 (Completeness)",": 对于任意两个消费束 (consumption bundle) A 和 B，消费者总能做出明确的判断：A ",[1855,1870,1857],{}," B，或 B ",[1855,1873,1857],{}," A，或两者都成立 (A ",[1855,1876,1877],{},"~"," B，表示无差异)。这意味着消费者不会感到困惑。",[1808,1880,1881,1884,1885,1887],{},[1865,1882,1883],{},"反身性 (Reflexivity)",": 任何消费束 A 至少和其本身一样好，即 A ",[1855,1886,1857],{}," A。这是一个平凡的公理。",[1808,1889,1890,1893,1894,1896,1897,1899,1900,1902],{},[1865,1891,1892],{},"传递性 (Transitivity)",": 如果 A ",[1855,1895,1857],{}," B 且 B ",[1855,1898,1857],{}," C，那么必然有 A ",[1855,1901,1857],{}," C。这保证了消费者选择的一致性，避免了循环选择。",[1798,1904,1905],{},"另外两个常用的假设是：",[1860,1907,1909,1919],{"start":1908},4,[1808,1910,1911,1914,1915,1918],{},[1865,1912,1913],{},"单调性 (Monotonicity)",": “越多越好”。如果消费束 A 中每种商品的数量都不少于 B，且至少有一种商品严格更多，则 A ",[1855,1916,1917],{},"≻"," B (严格偏好)。",[1808,1920,1921,1924,1925,1927,1928,1931,1932,1934],{},[1865,1922,1923],{},"凸性 (Convexity)",": “多样化优于极端化”。如果消费者对 A 和 B 无差异 (A ",[1855,1926,1877],{}," B)，那么对于任意 ",[1855,1929,1930],{},"0 \u003C t \u003C 1","，由 A 和 B 混合而成的消费束 C = tA + (1-t)B，都有 C ",[1855,1933,1857],{}," A。",[1847,1936,1938],{"id":1937},"_12-无差异曲线-indifference-curves","1.2 无差异曲线 (Indifference Curves)",[1798,1940,1941],{},"无差异曲线是所有能给消费者带来相同满足程度的消费束的集合。",[1805,1943,1944],{},[1808,1945,1946,1949,1950],{},[1865,1947,1948],{},"性质",":\n",[1860,1951,1952,1955,1958,1961],{},[1808,1953,1954],{},"无差异曲线密集分布在坐标平面上。",[1808,1956,1957],{},"任意两条无差异曲线永不相交（由传递性和单调性保证）。",[1808,1959,1960],{},"在单调性假设下，无差异曲线斜率为负。",[1808,1962,1963],{},"在凸性假设下，无差异曲线凸向原点。",[1965,1966],"mermaid-diagram",{"code64":1967,"locale":7},"eHljaGFydC1iZXRhCiAgdGl0bGUgIuaXoOW3ruW8guabsue6v+WbviAoSW5kaWZmZXJlbmNlIE1hcCkiCiAgeC1heGlzICLllYblk4EgWOKCgSIgWzEsIDIsIDQsIDgsIDEwXQogIHktYXhpcyAi5ZWG5ZOBIFjigoIiIDAgLS0+IDE0CiAgbGluZSBbMTAsIDUsIDIuNSwgMS4yNSwgMV0KICBsaW5lIFsxNCwgMTAsIDUsIDIuNSwgMl0=",[1847,1969,1971],{"id":1970},"_13-效用函数-utility-function","1.3 效用函数 (Utility Function)",[1798,1973,1974,1975,1978,1979,1982,1983,1985,1986,1989],{},"效用函数 ",[1855,1976,1977],{},"U(x₁, x₂)"," 是一个为每个消费束 ",[1855,1980,1981],{},"(x₁, x₂)"," 分配一个数值的方式，使得如果 A ",[1855,1984,1857],{}," B，则 ",[1855,1987,1988],{},"U(A) ≥ U(B)","。",[1991,1992,1994],"h4",{"id":1993},"_131-序数效用与基数效用","1.3.1 序数效用与基数效用",[1805,1996,1997,2011],{},[1808,1998,1999,2002,2003,2006,2007,2010],{},[1865,2000,2001],{},"序数效用 (Ordinal Utility)",": 效用数值的大小只表示偏好顺序，不表示满足程度的差异。例如 ",[1855,2004,2005],{},"U"," 和 ",[1855,2008,2009],{},"2U+1"," 代表完全相同的偏好。",[1808,2012,2013,2016],{},[1865,2014,2015],{},"基数效用 (Cardinal Utility)",": 历史上，经济学家曾试图测量\"满足程度\"的绝对大小，但现代微观经济学普遍采用序数效用观点。",[1798,2018,2019,2022,2023,2026,2027,2030,2031,2034,2035,2038,2039,2006,2042,2044,2045,1989],{},[1865,2020,2021],{},"重要性质",": 如果 ",[1855,2024,2025],{},"V(x)"," 是 ",[1855,2028,2029],{},"U(x)"," 的严格递增变换，即 ",[1855,2032,2033],{},"V(x) = f(U(x))","，其中 ",[1855,2036,2037],{},"f'(·) > 0","，那么 ",[1855,2040,2041],{},"V",[1855,2043,2005],{}," 代表相同的偏好关系。这被称为",[1865,2046,2047],{},"单调变换不变性",[1991,2049,2051],{"id":2050},"_132-边际效用与边际替代率","1.3.2 边际效用与边际替代率",[1805,2053,2054,2696],{},[1808,2055,2056,2059,2060,2460,2463,2466,2467],{},[1865,2057,2058],{},"边际效用 (Marginal Utility, MU)",": 消费一单位额外商品带来的效用增量。",[2061,2062,2065],"span",{"className":2063},[2064],"katex-display",[2061,2066,2069,2153],{"className":2067},[2068],"katex",[2061,2070,2073],{"className":2071},[2072],"katex-mathml",[2074,2075,2078],"math",{"xmlns":2076,"display":2077},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML","block",[2079,2080,2081,2148],"semantics",{},[2082,2083,2084,2088,2096,2100],"mrow",{},[2085,2086,2087],"mi",{},"M",[2089,2090,2091,2093],"msub",{},[2085,2092,2005],{},[2085,2094,2095],{},"i",[2097,2098,2099],"mo",{},"=",[2101,2102,2103,2138],"mfrac",{},[2082,2104,2105,2109,2111,2115,2124,2128,2135],{},[2085,2106,2108],{"mathvariant":2107},"normal","∂",[2085,2110,2005],{},[2097,2112,2114],{"stretchy":2113},"false","(",[2089,2116,2117,2120],{},[2085,2118,2119],{},"x",[2121,2122,2123],"mn",{},"1",[2097,2125,2127],{"separator":2126},"true",",",[2089,2129,2130,2132],{},[2085,2131,2119],{},[2121,2133,2134],{},"2",[2097,2136,2137],{"stretchy":2113},")",[2082,2139,2140,2142],{},[2085,2141,2108],{"mathvariant":2107},[2089,2143,2144,2146],{},[2085,2145,2119],{},[2085,2147,2095],{},[2149,2150,2152],"annotation",{"encoding":2151},"application\u002Fx-tex","MU_i = \\frac{\\partial U(x_1, x_2)}{\\partial x_i}",[2061,2154,2157,2240],{"className":2155,"ariaHidden":2126},[2156],"katex-html",[2061,2158,2161,2166,2172,2228,2233,2237],{"className":2159},[2160],"base",[2061,2162],{"className":2163,"style":2165},[2164],"strut","height:0.8333em;vertical-align:-0.15em;",[2061,2167,2087],{"className":2168,"style":2171},[2169,2170],"mord","mathnormal","margin-right:0.109em;",[2061,2173,2175,2178],{"className":2174},[2169],[2061,2176,2005],{"className":2177,"style":2171},[2169,2170],[2061,2179,2182],{"className":2180},[2181],"msupsub",[2061,2183,2187,2219],{"className":2184},[2185,2186],"vlist-t","vlist-t2",[2061,2188,2191,2214],{"className":2189},[2190],"vlist-r",[2061,2192,2196],{"className":2193,"style":2195},[2194],"vlist","height:0.3117em;",[2061,2197,2199,2204],{"style":2198},"top:-2.55em;margin-left:-0.109em;margin-right:0.05em;",[2061,2200],{"className":2201,"style":2203},[2202],"pstrut","height:2.7em;",[2061,2205,2211],{"className":2206},[2207,2208,2209,2210],"sizing","reset-size6","size3","mtight",[2061,2212,2095],{"className":2213},[2169,2170,2210],[2061,2215,2218],{"className":2216},[2217],"vlist-s","​",[2061,2220,2222],{"className":2221},[2190],[2061,2223,2226],{"className":2224,"style":2225},[2194],"height:0.15em;",[2061,2227],{},[2061,2229],{"className":2230,"style":2232},[2231],"mspace","margin-right:0.2778em;",[2061,2234,2099],{"className":2235},[2236],"mrel",[2061,2238],{"className":2239,"style":2232},[2231],[2061,2241,2243,2247],{"className":2242},[2160],[2061,2244],{"className":2245,"style":2246},[2164],"height:2.263em;vertical-align:-0.836em;",[2061,2248,2250,2255,2457],{"className":2249},[2169],[2061,2251],{"className":2252},[2253,2254],"mopen","nulldelimiter",[2061,2256,2258],{"className":2257},[2101],[2061,2259,2261,2448],{"className":2260},[2185,2186],[2061,2262,2264,2445],{"className":2263},[2190],[2061,2265,2268,2323,2334],{"className":2266,"style":2267},[2194],"height:1.427em;",[2061,2269,2271,2275],{"style":2270},"top:-2.314em;",[2061,2272],{"className":2273,"style":2274},[2202],"height:3em;",[2061,2276,2278,2282],{"className":2277},[2169],[2061,2279,2108],{"className":2280,"style":2281},[2169],"margin-right:0.0556em;",[2061,2283,2285,2288],{"className":2284},[2169],[2061,2286,2119],{"className":2287},[2169,2170],[2061,2289,2291],{"className":2290},[2181],[2061,2292,2294,2315],{"className":2293},[2185,2186],[2061,2295,2297,2312],{"className":2296},[2190],[2061,2298,2300],{"className":2299,"style":2195},[2194],[2061,2301,2303,2306],{"style":2302},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[2061,2304],{"className":2305,"style":2203},[2202],[2061,2307,2309],{"className":2308},[2207,2208,2209,2210],[2061,2310,2095],{"className":2311},[2169,2170,2210],[2061,2313,2218],{"className":2314},[2217],[2061,2316,2318],{"className":2317},[2190],[2061,2319,2321],{"className":2320,"style":2225},[2194],[2061,2322],{},[2061,2324,2326,2329],{"style":2325},"top:-3.23em;",[2061,2327],{"className":2328,"style":2274},[2202],[2061,2330],{"className":2331,"style":2333},[2332],"frac-line","border-bottom-width:0.04em;",[2061,2335,2337,2340],{"style":2336},"top:-3.677em;",[2061,2338],{"className":2339,"style":2274},[2202],[2061,2341,2343,2346,2349,2352,2393,2397,2401,2441],{"className":2342},[2169],[2061,2344,2108],{"className":2345,"style":2281},[2169],[2061,2347,2005],{"className":2348,"style":2171},[2169,2170],[2061,2350,2114],{"className":2351},[2253],[2061,2353,2355,2358],{"className":2354},[2169],[2061,2356,2119],{"className":2357},[2169,2170],[2061,2359,2361],{"className":2360},[2181],[2061,2362,2364,2385],{"className":2363},[2185,2186],[2061,2365,2367,2382],{"className":2366},[2190],[2061,2368,2371],{"className":2369,"style":2370},[2194],"height:0.3011em;",[2061,2372,2373,2376],{"style":2302},[2061,2374],{"className":2375,"style":2203},[2202],[2061,2377,2379],{"className":2378},[2207,2208,2209,2210],[2061,2380,2123],{"className":2381},[2169,2210],[2061,2383,2218],{"className":2384},[2217],[2061,2386,2388],{"className":2387},[2190],[2061,2389,2391],{"className":2390,"style":2225},[2194],[2061,2392],{},[2061,2394,2127],{"className":2395},[2396],"mpunct",[2061,2398],{"className":2399,"style":2400},[2231],"margin-right:0.1667em;",[2061,2402,2404,2407],{"className":2403},[2169],[2061,2405,2119],{"className":2406},[2169,2170],[2061,2408,2410],{"className":2409},[2181],[2061,2411,2413,2433],{"className":2412},[2185,2186],[2061,2414,2416,2430],{"className":2415},[2190],[2061,2417,2419],{"className":2418,"style":2370},[2194],[2061,2420,2421,2424],{"style":2302},[2061,2422],{"className":2423,"style":2203},[2202],[2061,2425,2427],{"className":2426},[2207,2208,2209,2210],[2061,2428,2134],{"className":2429},[2169,2210],[2061,2431,2218],{"className":2432},[2217],[2061,2434,2436],{"className":2435},[2190],[2061,2437,2439],{"className":2438,"style":2225},[2194],[2061,2440],{},[2061,2442,2137],{"className":2443},[2444],"mclose",[2061,2446,2218],{"className":2447},[2217],[2061,2449,2451],{"className":2450},[2190],[2061,2452,2455],{"className":2453,"style":2454},[2194],"height:0.836em;",[2061,2456],{},[2061,2458],{"className":2459},[2444,2254],[2461,2462],"br",{},[1865,2464,2465],{},"边际效用递减规律",": 在其他商品消费量不变的情况下，随着某种商品消费量的增加，其边际效用通常递减。数学上表示为：",[2061,2468,2470],{"className":2469},[2064],[2061,2471,2473,2517],{"className":2472},[2068],[2061,2474,2476],{"className":2475},[2072],[2074,2477,2478],{"xmlns":2076,"display":2077},[2079,2479,2480,2514],{},[2082,2481,2482,2508,2511],{},[2101,2483,2484,2495],{},[2082,2485,2486,2493],{},[2487,2488,2489,2491],"msup",{},[2085,2490,2108],{"mathvariant":2107},[2121,2492,2134],{},[2085,2494,2005],{},[2082,2496,2497,2499],{},[2085,2498,2108],{"mathvariant":2107},[2500,2501,2502,2504,2506],"msubsup",{},[2085,2503,2119],{},[2085,2505,2095],{},[2121,2507,2134],{},[2097,2509,2510],{},"\u003C",[2121,2512,2513],{},"0",[2149,2515,2516],{"encoding":2151},"\\frac{\\partial^2 U}{\\partial x_i^2} \u003C 0",[2061,2518,2520,2686],{"className":2519,"ariaHidden":2126},[2156],[2061,2521,2523,2527,2677,2680,2683],{"className":2522},[2160],[2061,2524],{"className":2525,"style":2526},[2164],"height:2.454em;vertical-align:-0.9629em;",[2061,2528,2530,2533,2674],{"className":2529},[2169],[2061,2531],{"className":2532},[2253,2254],[2061,2534,2536],{"className":2535},[2101],[2061,2537,2539,2665],{"className":2538},[2185,2186],[2061,2540,2542,2662],{"className":2541},[2190],[2061,2543,2546,2612,2620],{"className":2544,"style":2545},[2194],"height:1.4911em;",[2061,2547,2548,2551],{"style":2270},[2061,2549],{"className":2550,"style":2274},[2202],[2061,2552,2554,2557],{"className":2553},[2169],[2061,2555,2108],{"className":2556,"style":2281},[2169],[2061,2558,2560,2563],{"className":2559},[2169],[2061,2561,2119],{"className":2562},[2169,2170],[2061,2564,2566],{"className":2565},[2181],[2061,2567,2569,2603],{"className":2568},[2185,2186],[2061,2570,2572,2600],{"className":2571},[2190],[2061,2573,2576,2588],{"className":2574,"style":2575},[2194],"height:0.7959em;",[2061,2577,2579,2582],{"style":2578},"top:-2.4231em;margin-left:0em;margin-right:0.05em;",[2061,2580],{"className":2581,"style":2203},[2202],[2061,2583,2585],{"className":2584},[2207,2208,2209,2210],[2061,2586,2095],{"className":2587},[2169,2170,2210],[2061,2589,2591,2594],{"style":2590},"top:-3.0448em;margin-right:0.05em;",[2061,2592],{"className":2593,"style":2203},[2202],[2061,2595,2597],{"className":2596},[2207,2208,2209,2210],[2061,2598,2134],{"className":2599},[2169,2210],[2061,2601,2218],{"className":2602},[2217],[2061,2604,2606],{"className":2605},[2190],[2061,2607,2610],{"className":2608,"style":2609},[2194],"height:0.2769em;",[2061,2611],{},[2061,2613,2614,2617],{"style":2325},[2061,2615],{"className":2616,"style":2274},[2202],[2061,2618],{"className":2619,"style":2333},[2332],[2061,2621,2622,2625],{"style":2336},[2061,2623],{"className":2624,"style":2274},[2202],[2061,2626,2628,2659],{"className":2627},[2169],[2061,2629,2631,2634],{"className":2630},[2169],[2061,2632,2108],{"className":2633,"style":2281},[2169],[2061,2635,2637],{"className":2636},[2181],[2061,2638,2640],{"className":2639},[2185],[2061,2641,2643],{"className":2642},[2190],[2061,2644,2647],{"className":2645,"style":2646},[2194],"height:0.8141em;",[2061,2648,2650,2653],{"style":2649},"top:-3.063em;margin-right:0.05em;",[2061,2651],{"className":2652,"style":2203},[2202],[2061,2654,2656],{"className":2655},[2207,2208,2209,2210],[2061,2657,2134],{"className":2658},[2169,2210],[2061,2660,2005],{"className":2661,"style":2171},[2169,2170],[2061,2663,2218],{"className":2664},[2217],[2061,2666,2668],{"className":2667},[2190],[2061,2669,2672],{"className":2670,"style":2671},[2194],"height:0.9629em;",[2061,2673],{},[2061,2675],{"className":2676},[2444,2254],[2061,2678],{"className":2679,"style":2232},[2231],[2061,2681,2510],{"className":2682},[2236],[2061,2684],{"className":2685,"style":2232},[2231],[2061,2687,2689,2693],{"className":2688},[2160],[2061,2690],{"className":2691,"style":2692},[2164],"height:0.6444em;",[2061,2694,2513],{"className":2695},[2169],[1808,2697,2698,2701,2702,2704,2707,2708,2711,2712,3160,3162,3163,3762,3764,3765,4530,4532,4535,4536,1989],{},[1865,2699,2700],{},"边际替代率 (Marginal Rate of Substitution, MRS)",": 在保持效用不变的情况下，消费者愿意用多少单位的商品2来交换一单位的商品1。它是无差异曲线斜率的绝对值。",[2461,2703],{},[1865,2705,2706],{},"推导",": 沿着无差异曲线，效用保持不变，即 ",[1855,2709,2710],{},"dU = 0","。利用全微分：",[2061,2713,2715],{"className":2714},[2064],[2061,2716,2718,2796],{"className":2717},[2068],[2061,2719,2721],{"className":2720},[2072],[2074,2722,2723],{"xmlns":2076,"display":2077},[2079,2724,2725,2793],{},[2082,2726,2727,2730,2732,2734,2752,2754,2760,2763,2781,2783,2789,2791],{},[2085,2728,2729],{},"d",[2085,2731,2005],{},[2097,2733,2099],{},[2101,2735,2736,2742],{},[2082,2737,2738,2740],{},[2085,2739,2108],{"mathvariant":2107},[2085,2741,2005],{},[2082,2743,2744,2746],{},[2085,2745,2108],{"mathvariant":2107},[2089,2747,2748,2750],{},[2085,2749,2119],{},[2121,2751,2123],{},[2085,2753,2729],{},[2089,2755,2756,2758],{},[2085,2757,2119],{},[2121,2759,2123],{},[2097,2761,2762],{},"+",[2101,2764,2765,2771],{},[2082,2766,2767,2769],{},[2085,2768,2108],{"mathvariant":2107},[2085,2770,2005],{},[2082,2772,2773,2775],{},[2085,2774,2108],{"mathvariant":2107},[2089,2776,2777,2779],{},[2085,2778,2119],{},[2121,2780,2134],{},[2085,2782,2729],{},[2089,2784,2785,2787],{},[2085,2786,2119],{},[2121,2788,2134],{},[2097,2790,2099],{},[2121,2792,2513],{},[2149,2794,2795],{"encoding":2151},"dU = \\frac{\\partial U}{\\partial x_1}dx_1 + \\frac{\\partial U}{\\partial x_2}dx_2 = 0",[2061,2797,2799,2821,2988,3151],{"className":2798,"ariaHidden":2126},[2156],[2061,2800,2802,2806,2809,2812,2815,2818],{"className":2801},[2160],[2061,2803],{"className":2804,"style":2805},[2164],"height:0.6944em;",[2061,2807,2729],{"className":2808},[2169,2170],[2061,2810,2005],{"className":2811,"style":2171},[2169,2170],[2061,2813],{"className":2814,"style":2232},[2231],[2061,2816,2099],{"className":2817},[2236],[2061,2819],{"className":2820,"style":2232},[2231],[2061,2822,2824,2828,2934,2937,2977,2981,2985],{"className":2823},[2160],[2061,2825],{"className":2826,"style":2827},[2164],"height:2.2074em;vertical-align:-0.836em;",[2061,2829,2831,2834,2931],{"className":2830},[2169],[2061,2832],{"className":2833},[2253,2254],[2061,2835,2837],{"className":2836},[2101],[2061,2838,2840,2923],{"className":2839},[2185,2186],[2061,2841,2843,2920],{"className":2842},[2190],[2061,2844,2847,2898,2906],{"className":2845,"style":2846},[2194],"height:1.3714em;",[2061,2848,2849,2852],{"style":2270},[2061,2850],{"className":2851,"style":2274},[2202],[2061,2853,2855,2858],{"className":2854},[2169],[2061,2856,2108],{"className":2857,"style":2281},[2169],[2061,2859,2861,2864],{"className":2860},[2169],[2061,2862,2119],{"className":2863},[2169,2170],[2061,2865,2867],{"className":2866},[2181],[2061,2868,2870,2890],{"className":2869},[2185,2186],[2061,2871,2873,2887],{"className":2872},[2190],[2061,2874,2876],{"className":2875,"style":2370},[2194],[2061,2877,2878,2881],{"style":2302},[2061,2879],{"className":2880,"style":2203},[2202],[2061,2882,2884],{"className":2883},[2207,2208,2209,2210],[2061,2885,2123],{"className":2886},[2169,2210],[2061,2888,2218],{"className":2889},[2217],[2061,2891,2893],{"className":2892},[2190],[2061,2894,2896],{"className":2895,"style":2225},[2194],[2061,2897],{},[2061,2899,2900,2903],{"style":2325},[2061,2901],{"className":2902,"style":2274},[2202],[2061,2904],{"className":2905,"style":2333},[2332],[2061,2907,2908,2911],{"style":2336},[2061,2909],{"className":2910,"style":2274},[2202],[2061,2912,2914,2917],{"className":2913},[2169],[2061,2915,2108],{"className":2916,"style":2281},[2169],[2061,2918,2005],{"className":2919,"style":2171},[2169,2170],[2061,2921,2218],{"className":2922},[2217],[2061,2924,2926],{"className":2925},[2190],[2061,2927,2929],{"className":2928,"style":2454},[2194],[2061,2930],{},[2061,2932],{"className":2933},[2444,2254],[2061,2935,2729],{"className":2936},[2169,2170],[2061,2938,2940,2943],{"className":2939},[2169],[2061,2941,2119],{"className":2942},[2169,2170],[2061,2944,2946],{"className":2945},[2181],[2061,2947,2949,2969],{"className":2948},[2185,2186],[2061,2950,2952,2966],{"className":2951},[2190],[2061,2953,2955],{"className":2954,"style":2370},[2194],[2061,2956,2957,2960],{"style":2302},[2061,2958],{"className":2959,"style":2203},[2202],[2061,2961,2963],{"className":2962},[2207,2208,2209,2210],[2061,2964,2123],{"className":2965},[2169,2210],[2061,2967,2218],{"className":2968},[2217],[2061,2970,2972],{"className":2971},[2190],[2061,2973,2975],{"className":2974,"style":2225},[2194],[2061,2976],{},[2061,2978],{"className":2979,"style":2980},[2231],"margin-right:0.2222em;",[2061,2982,2762],{"className":2983},[2984],"mbin",[2061,2986],{"className":2987,"style":2980},[2231],[2061,2989,2991,2994,3099,3102,3142,3145,3148],{"className":2990},[2160],[2061,2992],{"className":2993,"style":2827},[2164],[2061,2995,2997,3000,3096],{"className":2996},[2169],[2061,2998],{"className":2999},[2253,2254],[2061,3001,3003],{"className":3002},[2101],[2061,3004,3006,3088],{"className":3005},[2185,2186],[2061,3007,3009,3085],{"className":3008},[2190],[2061,3010,3012,3063,3071],{"className":3011,"style":2846},[2194],[2061,3013,3014,3017],{"style":2270},[2061,3015],{"className":3016,"style":2274},[2202],[2061,3018,3020,3023],{"className":3019},[2169],[2061,3021,2108],{"className":3022,"style":2281},[2169],[2061,3024,3026,3029],{"className":3025},[2169],[2061,3027,2119],{"className":3028},[2169,2170],[2061,3030,3032],{"className":3031},[2181],[2061,3033,3035,3055],{"className":3034},[2185,2186],[2061,3036,3038,3052],{"className":3037},[2190],[2061,3039,3041],{"className":3040,"style":2370},[2194],[2061,3042,3043,3046],{"style":2302},[2061,3044],{"className":3045,"style":2203},[2202],[2061,3047,3049],{"className":3048},[2207,2208,2209,2210],[2061,3050,2134],{"className":3051},[2169,2210],[2061,3053,2218],{"className":3054},[2217],[2061,3056,3058],{"className":3057},[2190],[2061,3059,3061],{"className":3060,"style":2225},[2194],[2061,3062],{},[2061,3064,3065,3068],{"style":2325},[2061,3066],{"className":3067,"style":2274},[2202],[2061,3069],{"className":3070,"style":2333},[2332],[2061,3072,3073,3076],{"style":2336},[2061,3074],{"className":3075,"style":2274},[2202],[2061,3077,3079,3082],{"className":3078},[2169],[2061,3080,2108],{"className":3081,"style":2281},[2169],[2061,3083,2005],{"className":3084,"style":2171},[2169,2170],[2061,3086,2218],{"className":3087},[2217],[2061,3089,3091],{"className":3090},[2190],[2061,3092,3094],{"className":3093,"style":2454},[2194],[2061,3095],{},[2061,3097],{"className":3098},[2444,2254],[2061,3100,2729],{"className":3101},[2169,2170],[2061,3103,3105,3108],{"className":3104},[2169],[2061,3106,2119],{"className":3107},[2169,2170],[2061,3109,3111],{"className":3110},[2181],[2061,3112,3114,3134],{"className":3113},[2185,2186],[2061,3115,3117,3131],{"className":3116},[2190],[2061,3118,3120],{"className":3119,"style":2370},[2194],[2061,3121,3122,3125],{"style":2302},[2061,3123],{"className":3124,"style":2203},[2202],[2061,3126,3128],{"className":3127},[2207,2208,2209,2210],[2061,3129,2134],{"className":3130},[2169,2210],[2061,3132,2218],{"className":3133},[2217],[2061,3135,3137],{"className":3136},[2190],[2061,3138,3140],{"className":3139,"style":2225},[2194],[2061,3141],{},[2061,3143],{"className":3144,"style":2232},[2231],[2061,3146,2099],{"className":3147},[2236],[2061,3149],{"className":3150,"style":2232},[2231],[2061,3152,3154,3157],{"className":3153},[2160],[2061,3155],{"className":3156,"style":2692},[2164],[2061,3158,2513],{"className":3159},[2169],[2461,3161],{},"整理得：",[2061,3164,3166],{"className":3165},[2064],[2061,3167,3169,3269],{"className":3168},[2068],[2061,3170,3172],{"className":3171},[2072],[2074,3173,3174],{"xmlns":2076,"display":2077},[2079,3175,3176,3266],{},[2082,3177,3178,3200,3202,3205,3240,3242,3244],{},[2101,3179,3180,3190],{},[2082,3181,3182,3184],{},[2085,3183,2729],{},[2089,3185,3186,3188],{},[2085,3187,2119],{},[2121,3189,2134],{},[2082,3191,3192,3194],{},[2085,3193,2729],{},[2089,3195,3196,3198],{},[2085,3197,2119],{},[2121,3199,2123],{},[2097,3201,2099],{},[2097,3203,3204],{},"−",[2101,3206,3207,3224],{},[2082,3208,3209,3211,3213,3216,3218],{},[2085,3210,2108],{"mathvariant":2107},[2085,3212,2005],{},[2085,3214,3215],{"mathvariant":2107},"\u002F",[2085,3217,2108],{"mathvariant":2107},[2089,3219,3220,3222],{},[2085,3221,2119],{},[2121,3223,2123],{},[2082,3225,3226,3228,3230,3232,3234],{},[2085,3227,2108],{"mathvariant":2107},[2085,3229,2005],{},[2085,3231,3215],{"mathvariant":2107},[2085,3233,2108],{"mathvariant":2107},[2089,3235,3236,3238],{},[2085,3237,2119],{},[2121,3239,2134],{},[2097,3241,2099],{},[2097,3243,3204],{},[2101,3245,3246,3256],{},[2082,3247,3248,3250],{},[2085,3249,2087],{},[2089,3251,3252,3254],{},[2085,3253,2005],{},[2121,3255,2123],{},[2082,3257,3258,3260],{},[2085,3259,2087],{},[2089,3261,3262,3264],{},[2085,3263,2005],{},[2121,3265,2134],{},[2149,3267,3268],{"encoding":2151},"\\frac{dx_2}{dx_1} = -\\frac{\\partial U \u002F \\partial x_1}{\\partial U \u002F \\partial x_2} = -\\frac{MU_1}{MU_2}",[2061,3270,3272,3429,3609],{"className":3271,"ariaHidden":2126},[2156],[2061,3273,3275,3278,3420,3423,3426],{"className":3274},[2160],[2061,3276],{"className":3277,"style":2827},[2164],[2061,3279,3281,3284,3417],{"className":3280},[2169],[2061,3282],{"className":3283},[2253,2254],[2061,3285,3287],{"className":3286},[2101],[2061,3288,3290,3409],{"className":3289},[2185,2186],[2061,3291,3293,3406],{"className":3292},[2190],[2061,3294,3296,3347,3355],{"className":3295,"style":2846},[2194],[2061,3297,3298,3301],{"style":2270},[2061,3299],{"className":3300,"style":2274},[2202],[2061,3302,3304,3307],{"className":3303},[2169],[2061,3305,2729],{"className":3306},[2169,2170],[2061,3308,3310,3313],{"className":3309},[2169],[2061,3311,2119],{"className":3312},[2169,2170],[2061,3314,3316],{"className":3315},[2181],[2061,3317,3319,3339],{"className":3318},[2185,2186],[2061,3320,3322,3336],{"className":3321},[2190],[2061,3323,3325],{"className":3324,"style":2370},[2194],[2061,3326,3327,3330],{"style":2302},[2061,3328],{"className":3329,"style":2203},[2202],[2061,3331,3333],{"className":3332},[2207,2208,2209,2210],[2061,3334,2123],{"className":3335},[2169,2210],[2061,3337,2218],{"className":3338},[2217],[2061,3340,3342],{"className":3341},[2190],[2061,3343,3345],{"className":3344,"style":2225},[2194],[2061,3346],{},[2061,3348,3349,3352],{"style":2325},[2061,3350],{"className":3351,"style":2274},[2202],[2061,3353],{"className":3354,"style":2333},[2332],[2061,3356,3357,3360],{"style":2336},[2061,3358],{"className":3359,"style":2274},[2202],[2061,3361,3363,3366],{"className":3362},[2169],[2061,3364,2729],{"className":3365},[2169,2170],[2061,3367,3369,3372],{"className":3368},[2169],[2061,3370,2119],{"className":3371},[2169,2170],[2061,3373,3375],{"className":3374},[2181],[2061,3376,3378,3398],{"className":3377},[2185,2186],[2061,3379,3381,3395],{"className":3380},[2190],[2061,3382,3384],{"className":3383,"style":2370},[2194],[2061,3385,3386,3389],{"style":2302},[2061,3387],{"className":3388,"style":2203},[2202],[2061,3390,3392],{"className":3391},[2207,2208,2209,2210],[2061,3393,2134],{"className":3394},[2169,2210],[2061,3396,2218],{"className":3397},[2217],[2061,3399,3401],{"className":3400},[2190],[2061,3402,3404],{"className":3403,"style":2225},[2194],[2061,3405],{},[2061,3407,2218],{"className":3408},[2217],[2061,3410,3412],{"className":3411},[2190],[2061,3413,3415],{"className":3414,"style":2454},[2194],[2061,3416],{},[2061,3418],{"className":3419},[2444,2254],[2061,3421],{"className":3422,"style":2232},[2231],[2061,3424,2099],{"className":3425},[2236],[2061,3427],{"className":3428,"style":2232},[2231],[2061,3430,3432,3436,3439,3600,3603,3606],{"className":3431},[2160],[2061,3433],{"className":3434,"style":3435},[2164],"height:2.363em;vertical-align:-0.936em;",[2061,3437,3204],{"className":3438},[2169],[2061,3440,3442,3445,3597],{"className":3441},[2169],[2061,3443],{"className":3444},[2253,2254],[2061,3446,3448],{"className":3447},[2101],[2061,3449,3451,3588],{"className":3450},[2185,2186],[2061,3452,3454,3585],{"className":3453},[2190],[2061,3455,3457,3517,3525],{"className":3456,"style":2267},[2194],[2061,3458,3459,3462],{"style":2270},[2061,3460],{"className":3461,"style":2274},[2202],[2061,3463,3465,3468,3471,3474,3477],{"className":3464},[2169],[2061,3466,2108],{"className":3467,"style":2281},[2169],[2061,3469,2005],{"className":3470,"style":2171},[2169,2170],[2061,3472,3215],{"className":3473},[2169],[2061,3475,2108],{"className":3476,"style":2281},[2169],[2061,3478,3480,3483],{"className":3479},[2169],[2061,3481,2119],{"className":3482},[2169,2170],[2061,3484,3486],{"className":3485},[2181],[2061,3487,3489,3509],{"className":3488},[2185,2186],[2061,3490,3492,3506],{"className":3491},[2190],[2061,3493,3495],{"className":3494,"style":2370},[2194],[2061,3496,3497,3500],{"style":2302},[2061,3498],{"className":3499,"style":2203},[2202],[2061,3501,3503],{"className":3502},[2207,2208,2209,2210],[2061,3504,2134],{"className":3505},[2169,2210],[2061,3507,2218],{"className":3508},[2217],[2061,3510,3512],{"className":3511},[2190],[2061,3513,3515],{"className":3514,"style":2225},[2194],[2061,3516],{},[2061,3518,3519,3522],{"style":2325},[2061,3520],{"className":3521,"style":2274},[2202],[2061,3523],{"className":3524,"style":2333},[2332],[2061,3526,3527,3530],{"style":2336},[2061,3528],{"className":3529,"style":2274},[2202],[2061,3531,3533,3536,3539,3542,3545],{"className":3532},[2169],[2061,3534,2108],{"className":3535,"style":2281},[2169],[2061,3537,2005],{"className":3538,"style":2171},[2169,2170],[2061,3540,3215],{"className":3541},[2169],[2061,3543,2108],{"className":3544,"style":2281},[2169],[2061,3546,3548,3551],{"className":3547},[2169],[2061,3549,2119],{"className":3550},[2169,2170],[2061,3552,3554],{"className":3553},[2181],[2061,3555,3557,3577],{"className":3556},[2185,2186],[2061,3558,3560,3574],{"className":3559},[2190],[2061,3561,3563],{"className":3562,"style":2370},[2194],[2061,3564,3565,3568],{"style":2302},[2061,3566],{"className":3567,"style":2203},[2202],[2061,3569,3571],{"className":3570},[2207,2208,2209,2210],[2061,3572,2123],{"className":3573},[2169,2210],[2061,3575,2218],{"className":3576},[2217],[2061,3578,3580],{"className":3579},[2190],[2061,3581,3583],{"className":3582,"style":2225},[2194],[2061,3584],{},[2061,3586,2218],{"className":3587},[2217],[2061,3589,3591],{"className":3590},[2190],[2061,3592,3595],{"className":3593,"style":3594},[2194],"height:0.936em;",[2061,3596],{},[2061,3598],{"className":3599},[2444,2254],[2061,3601],{"className":3602,"style":2232},[2231],[2061,3604,2099],{"className":3605},[2236],[2061,3607],{"className":3608,"style":2232},[2231],[2061,3610,3612,3616,3619],{"className":3611},[2160],[2061,3613],{"className":3614,"style":3615},[2164],"height:2.1963em;vertical-align:-0.836em;",[2061,3617,3204],{"className":3618},[2169],[2061,3620,3622,3625,3759],{"className":3621},[2169],[2061,3623],{"className":3624},[2253,2254],[2061,3626,3628],{"className":3627},[2101],[2061,3629,3631,3751],{"className":3630},[2185,2186],[2061,3632,3634,3748],{"className":3633},[2190],[2061,3635,3638,3689,3697],{"className":3636,"style":3637},[2194],"height:1.3603em;",[2061,3639,3640,3643],{"style":2270},[2061,3641],{"className":3642,"style":2274},[2202],[2061,3644,3646,3649],{"className":3645},[2169],[2061,3647,2087],{"className":3648,"style":2171},[2169,2170],[2061,3650,3652,3655],{"className":3651},[2169],[2061,3653,2005],{"className":3654,"style":2171},[2169,2170],[2061,3656,3658],{"className":3657},[2181],[2061,3659,3661,3681],{"className":3660},[2185,2186],[2061,3662,3664,3678],{"className":3663},[2190],[2061,3665,3667],{"className":3666,"style":2370},[2194],[2061,3668,3669,3672],{"style":2198},[2061,3670],{"className":3671,"style":2203},[2202],[2061,3673,3675],{"className":3674},[2207,2208,2209,2210],[2061,3676,2134],{"className":3677},[2169,2210],[2061,3679,2218],{"className":3680},[2217],[2061,3682,3684],{"className":3683},[2190],[2061,3685,3687],{"className":3686,"style":2225},[2194],[2061,3688],{},[2061,3690,3691,3694],{"style":2325},[2061,3692],{"className":3693,"style":2274},[2202],[2061,3695],{"className":3696,"style":2333},[2332],[2061,3698,3699,3702],{"style":2336},[2061,3700],{"className":3701,"style":2274},[2202],[2061,3703,3705,3708],{"className":3704},[2169],[2061,3706,2087],{"className":3707,"style":2171},[2169,2170],[2061,3709,3711,3714],{"className":3710},[2169],[2061,3712,2005],{"className":3713,"style":2171},[2169,2170],[2061,3715,3717],{"className":3716},[2181],[2061,3718,3720,3740],{"className":3719},[2185,2186],[2061,3721,3723,3737],{"className":3722},[2190],[2061,3724,3726],{"className":3725,"style":2370},[2194],[2061,3727,3728,3731],{"style":2198},[2061,3729],{"className":3730,"style":2203},[2202],[2061,3732,3734],{"className":3733},[2207,2208,2209,2210],[2061,3735,2123],{"className":3736},[2169,2210],[2061,3738,2218],{"className":3739},[2217],[2061,3741,3743],{"className":3742},[2190],[2061,3744,3746],{"className":3745,"style":2225},[2194],[2061,3747],{},[2061,3749,2218],{"className":3750},[2217],[2061,3752,3754],{"className":3753},[2190],[2061,3755,3757],{"className":3756,"style":2454},[2194],[2061,3758],{},[2061,3760],{"className":3761},[2444,2254],[2461,3763],{},"因此：",[2061,3766,3768],{"className":3767},[2064],[2061,3769,3771,3887],{"className":3770},[2068],[2061,3772,3774],{"className":3773},[2072],[2074,3775,3776],{"xmlns":2076,"display":2077},[2079,3777,3778,3884],{},[2082,3779,3780,3782,3785,3793,3795,3824,3826,3848,3850],{},[2085,3781,2087],{},[2085,3783,3784],{},"R",[2089,3786,3787,3790],{},[2085,3788,3789],{},"S",[2121,3791,3792],{},"12",[2097,3794,2099],{},[2082,3796,3797,3800,3822],{},[2097,3798,3799],{"fence":2126},"∣",[2101,3801,3802,3812],{},[2082,3803,3804,3806],{},[2085,3805,2729],{},[2089,3807,3808,3810],{},[2085,3809,2119],{},[2121,3811,2134],{},[2082,3813,3814,3816],{},[2085,3815,2729],{},[2089,3817,3818,3820],{},[2085,3819,2119],{},[2121,3821,2123],{},[2097,3823,3799],{"fence":2126},[2097,3825,2099],{},[2101,3827,3828,3838],{},[2082,3829,3830,3832],{},[2085,3831,2087],{},[2089,3833,3834,3836],{},[2085,3835,2005],{},[2121,3837,2123],{},[2082,3839,3840,3842],{},[2085,3841,2087],{},[2089,3843,3844,3846],{},[2085,3845,2005],{},[2121,3847,2134],{},[2097,3849,2099],{},[2101,3851,3852,3868],{},[2082,3853,3854,3856,3858,3860,3862],{},[2085,3855,2108],{"mathvariant":2107},[2085,3857,2005],{},[2085,3859,3215],{"mathvariant":2107},[2085,3861,2108],{"mathvariant":2107},[2089,3863,3864,3866],{},[2085,3865,2119],{},[2121,3867,2123],{},[2082,3869,3870,3872,3874,3876,3878],{},[2085,3871,2108],{"mathvariant":2107},[2085,3873,2005],{},[2085,3875,3215],{"mathvariant":2107},[2085,3877,2108],{"mathvariant":2107},[2089,3879,3880,3882],{},[2085,3881,2119],{},[2121,3883,2134],{},[2149,3885,3886],{"encoding":2151},"MRS_{12} = \\left| \\frac{dx_2}{dx_1} \\right| = \\frac{MU_1}{MU_2} = \\frac{\\partial U \u002F \\partial x_1}{\\partial U \u002F \\partial 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x_2) = x_1^{\\alpha} x_2^{\\beta}, \\quad \\alpha, \\beta > 0",[2061,4626,4628,4739,4895],{"className":4627,"ariaHidden":2126},[2156],[2061,4629,4631,4635,4638,4641,4681,4684,4687,4727,4730,4733,4736],{"className":4630},[2160],[2061,4632],{"className":4633,"style":4634},[2164],"height:1em;vertical-align:-0.25em;",[2061,4636,2005],{"className":4637,"style":2171},[2169,2170],[2061,4639,2114],{"className":4640},[2253],[2061,4642,4644,4647],{"className":4643},[2169],[2061,4645,2119],{"className":4646},[2169,2170],[2061,4648,4650],{"className":4649},[2181],[2061,4651,4653,4673],{"className":4652},[2185,2186],[2061,4654,4656,4670],{"className":4655},[2190],[2061,4657,4659],{"className":4658,"style":2370},[2194],[2061,4660,4661,4664],{"style":2302},[2061,4662],{"className":4663,"style":2203},[2202],[2061,4665,4667],{"className":4666},[2207,2208,2209,2210],[2061,4668,2123],{"className":4669},[2169,2210],[2061,4671,2218],{"className":4672},[2217],[2061,4674,4676],{"className":4675},[2190],[2061,4677,4679],{"className":4678,"style":2225},[2194],[2061,4680],{},[2061,4682,2127],{"className":4683},[2396],[2061,4685],{"className":4686,"style":2400},[2231],[2061,4688,4690,4693],{"className":4689},[2169],[2061,4691,2119],{"className":4692},[2169,2170],[2061,4694,4696],{"className":4695},[2181],[2061,4697,4699,4719],{"className":4698},[2185,2186],[2061,4700,4702,4716],{"className":4701},[2190],[2061,4703,4705],{"className":4704,"style":2370},[2194],[2061,4706,4707,4710],{"style":2302},[2061,4708],{"className":4709,"style":2203},[2202],[2061,4711,4713],{"className":4712},[2207,2208,2209,2210],[2061,4714,2134],{"className":4715},[2169,2210],[2061,4717,2218],{"className":4718},[2217],[2061,4720,4722],{"className":4721},[2190],[2061,4723,4725],{"className":4724,"style":2225},[2194],[2061,4726],{},[2061,4728,2137],{"className":4729},[2444],[2061,4731],{"className":4732,"style":2232},[2231],[2061,4734,2099],{"className":4735},[2236],[2061,4737],{"className":4738,"style":2232},[2231],[2061,4740,4742,4746,4805,4864,4867,4871,4874,4877,4880,4883,4886,4889,4892],{"className":4741},[2160],[2061,4743],{"className":4744,"style":4745},[2164],"height:1.2333em;vertical-align:-0.2663em;",[2061,4747,4749,4752],{"className":4748},[2169],[2061,4750,2119],{"className":4751},[2169,2170],[2061,4753,4755],{"className":4754},[2181],[2061,4756,4758,4796],{"className":4757},[2185,2186],[2061,4759,4761,4793],{"className":4760},[2190],[2061,4762,4765,4777],{"className":4763,"style":4764},[2194],"height:0.7144em;",[2061,4766,4768,4771],{"style":4767},"top:-2.453em;margin-left:0em;margin-right:0.05em;",[2061,4769],{"className":4770,"style":2203},[2202],[2061,4772,4774],{"className":4773},[2207,2208,2209,2210],[2061,4775,2123],{"className":4776},[2169,2210],[2061,4778,4780,4783],{"style":4779},"top:-3.113em;margin-right:0.05em;",[2061,4781],{"className":4782,"style":2203},[2202],[2061,4784,4786],{"className":4785},[2207,2208,2209,2210],[2061,4787,4789],{"className":4788},[2169,2210],[2061,4790,4596],{"className":4791,"style":4792},[2169,2170,2210],"margin-right:0.0037em;",[2061,4794,2218],{"className":4795},[2217],[2061,4797,4799],{"className":4798},[2190],[2061,4800,4803],{"className":4801,"style":4802},[2194],"height:0.247em;",[2061,4804],{},[2061,4806,4808,4811],{"className":4807},[2169],[2061,4809,2119],{"className":4810},[2169,2170],[2061,4812,4814],{"className":4813},[2181],[2061,4815,4817,4855],{"className":4816},[2185,2186],[2061,4818,4820,4852],{"className":4819},[2190],[2061,4821,4824,4836],{"className":4822,"style":4823},[2194],"height:0.967em;",[2061,4825,4827,4830],{"style":4826},"top:-2.4337em;margin-left:0em;margin-right:0.05em;",[2061,4828],{"className":4829,"style":2203},[2202],[2061,4831,4833],{"className":4832},[2207,2208,2209,2210],[2061,4834,2134],{"className":4835},[2169,2210],[2061,4837,4839,4842],{"style":4838},"top:-3.1809em;margin-right:0.05em;",[2061,4840],{"className":4841,"style":2203},[2202],[2061,4843,4845],{"className":4844},[2207,2208,2209,2210],[2061,4846,4848],{"className":4847},[2169,2210],[2061,4849,4605],{"className":4850,"style":4851},[2169,2170,2210],"margin-right:0.0528em;",[2061,4853,2218],{"className":4854},[2217],[2061,4856,4858],{"className":4857},[2190],[2061,4859,4862],{"className":4860,"style":4861},[2194],"height:0.2663em;",[2061,4863],{},[2061,4865,2127],{"className":4866},[2396],[2061,4868],{"className":4869,"style":4870},[2231],"margin-right:1em;",[2061,4872],{"className":4873,"style":2400},[2231],[2061,4875,4596],{"className":4876,"style":4792},[2169,2170],[2061,4878,2127],{"className":4879},[2396],[2061,4881],{"className":4882,"style":2400},[2231],[2061,4884,4605],{"className":4885,"style":4851},[2169,2170],[2061,4887],{"className":4888,"style":2232},[2231],[2061,4890,4619],{"className":4891},[2236],[2061,4893],{"className":4894,"style":2232},[2231],[2061,4896,4898,4901],{"className":4897},[2160],[2061,4899],{"className":4900,"style":2692},[2164],[2061,4902,2513],{"className":4903},[2169],[2461,4905],{},"或取对数形式：",[2061,4908,4910],{"className":4909},[2064],[2061,4911,4913,4975],{"className":4912},[2068],[2061,4914,4916],{"className":4915},[2072],[2074,4917,4918],{"xmlns":2076,"display":2077},[2079,4919,4920,4972],{},[2082,4921,4922,4924,4926,4932,4934,4940,4942,4944,4946,4949,4952,4958,4960,4962,4964,4966],{},[2085,4923,2005],{},[2097,4925,2114],{"stretchy":2113},[2089,4927,4928,4930],{},[2085,4929,2119],{},[2121,4931,2123],{},[2097,4933,2127],{"separator":2126},[2089,4935,4936,4938],{},[2085,4937,2119],{},[2121,4939,2134],{},[2097,4941,2137],{"stretchy":2113},[2097,4943,2099],{},[2085,4945,4596],{},[2085,4947,4948],{},"ln",[2097,4950,4951],{},"⁡",[2089,4953,4954,4956],{},[2085,4955,2119],{},[2121,4957,2123],{},[2097,4959,2762],{},[2085,4961,4605],{},[2085,4963,4948],{},[2097,4965,4951],{},[2089,4967,4968,4970],{},[2085,4969,2119],{},[2121,4971,2134],{},[2149,4973,4974],{"encoding":2151},"U(x_1, x_2) = \\alpha \\ln x_1 + \\beta \\ln x_2",[2061,4976,4978,5088,5157],{"className":4977,"ariaHidden":2126},[2156],[2061,4979,4981,4984,4987,4990,5030,5033,5036,5076,5079,5082,5085],{"className":4980},[2160],[2061,4982],{"className":4983,"style":4634},[2164],[2061,4985,2005],{"className":4986,"style":2171},[2169,2170],[2061,4988,2114],{"className":4989},[2253],[2061,4991,4993,4996],{"className":4992},[2169],[2061,4994,2119],{"className":4995},[2169,2170],[2061,4997,4999],{"className":4998},[2181],[2061,5000,5002,5022],{"className":5001},[2185,2186],[2061,5003,5005,5019],{"className":5004},[2190],[2061,5006,5008],{"className":5007,"style":2370},[2194],[2061,5009,5010,5013],{"style":2302},[2061,5011],{"className":5012,"style":2203},[2202],[2061,5014,5016],{"className":5015},[2207,2208,2209,2210],[2061,5017,2123],{"className":5018},[2169,2210],[2061,5020,2218],{"className":5021},[2217],[2061,5023,5025],{"className":5024},[2190],[2061,5026,5028],{"className":5027,"style":2225},[2194],[2061,5029],{},[2061,5031,2127],{"className":5032},[2396],[2061,5034],{"className":5035,"style":2400},[2231],[2061,5037,5039,5042],{"className":5038},[2169],[2061,5040,2119],{"className":5041},[2169,2170],[2061,5043,5045],{"className":5044},[2181],[2061,5046,5048,5068],{"className":5047},[2185,2186],[2061,5049,5051,5065],{"className":5050},[2190],[2061,5052,5054],{"className":5053,"style":2370},[2194],[2061,5055,5056,5059],{"style":2302},[2061,5057],{"className":5058,"style":2203},[2202],[2061,5060,5062],{"className":5061},[2207,2208,2209,2210],[2061,5063,2134],{"className":5064},[2169,2210],[2061,5066,2218],{"className":5067},[2217],[2061,5069,5071],{"className":5070},[2190],[2061,5072,5074],{"className":5073,"style":2225},[2194],[2061,5075],{},[2061,5077,2137],{"className":5078},[2444],[2061,5080],{"className":5081,"style":2232},[2231],[2061,5083,2099],{"className":5084},[2236],[2061,5086],{"className":5087,"style":2232},[2231],[2061,5089,5091,5095,5098,5101,5105,5108,5148,5151,5154],{"className":5090},[2160],[2061,5092],{"className":5093,"style":5094},[2164],"height:0.8444em;vertical-align:-0.15em;",[2061,5096,4596],{"className":5097,"style":4792},[2169,2170],[2061,5099],{"className":5100,"style":2400},[2231],[2061,5102,4948],{"className":5103},[5104],"mop",[2061,5106],{"className":5107,"style":2400},[2231],[2061,5109,5111,5114],{"className":5110},[2169],[2061,5112,2119],{"className":5113},[2169,2170],[2061,5115,5117],{"className":5116},[2181],[2061,5118,5120,5140],{"className":5119},[2185,2186],[2061,5121,5123,5137],{"className":5122},[2190],[2061,5124,5126],{"className":5125,"style":2370},[2194],[2061,5127,5128,5131],{"style":2302},[2061,5129],{"className":5130,"style":2203},[2202],[2061,5132,5134],{"className":5133},[2207,2208,2209,2210],[2061,5135,2123],{"className":5136},[2169,2210],[2061,5138,2218],{"className":5139},[2217],[2061,5141,5143],{"className":5142},[2190],[2061,5144,5146],{"className":5145,"style":2225},[2194],[2061,5147],{},[2061,5149],{"className":5150,"style":2980},[2231],[2061,5152,2762],{"className":5153},[2984],[2061,5155],{"className":5156,"style":2980},[2231],[2061,5158,5160,5164,5167,5170,5173,5176],{"className":5159},[2160],[2061,5161],{"className":5162,"style":5163},[2164],"height:0.8889em;vertical-align:-0.1944em;",[2061,5165,4605],{"className":5166,"style":4851},[2169,2170],[2061,5168],{"className":5169,"style":2400},[2231],[2061,5171,4948],{"className":5172},[5104],[2061,5174],{"className":5175,"style":2400},[2231],[2061,5177,5179,5182],{"className":5178},[2169],[2061,5180,2119],{"className":5181},[2169,2170],[2061,5183,5185],{"className":5184},[2181],[2061,5186,5188,5208],{"className":5187},[2185,2186],[2061,5189,5191,5205],{"className":5190},[2190],[2061,5192,5194],{"className":5193,"style":2370},[2194],[2061,5195,5196,5199],{"style":2302},[2061,5197],{"className":5198,"style":2203},[2202],[2061,5200,5202],{"className":5201},[2207,2208,2209,2210],[2061,5203,2134],{"className":5204},[2169,2210],[2061,5206,2218],{"className":5207},[2217],[2061,5209,5211],{"className":5210},[2190],[2061,5212,5214],{"className":5213,"style":2225},[2194],[2061,5215],{},[1805,5217,5218,5428],{},[1808,5219,5220,5222,5223],{},[1865,5221,1948],{},": MRS 为 ",[2061,5224,5226,5260],{"className":5225},[2068],[2061,5227,5229],{"className":5228},[2072],[2074,5230,5231],{"xmlns":2076},[2079,5232,5233,5257],{},[2082,5234,5235],{},[2101,5236,5237,5247],{},[2082,5238,5239,5241],{},[2085,5240,4596],{},[2089,5242,5243,5245],{},[2085,5244,2119],{},[2121,5246,2134],{},[2082,5248,5249,5251],{},[2085,5250,4605],{},[2089,5252,5253,5255],{},[2085,5254,2119],{},[2121,5256,2123],{},[2149,5258,5259],{"encoding":2151},"\\frac{\\alpha x_2}{\\beta x_1}",[2061,5261,5263],{"className":5262,"ariaHidden":2126},[2156],[2061,5264,5266,5270],{"className":5265},[2160],[2061,5267],{"className":5268,"style":5269},[2164],"height:1.1926em;vertical-align:-0.4811em;",[2061,5271,5273,5276,5425],{"className":5272},[2169],[2061,5274],{"className":5275},[2253,2254],[2061,5277,5279],{"className":5278},[2101],[2061,5280,5282,5416],{"className":5281},[2185,2186],[2061,5283,5285,5413],{"className":5284},[2190],[2061,5286,5289,5350,5358],{"className":5287,"style":5288},[2194],"height:0.7115em;",[2061,5290,5292,5295],{"style":5291},"top:-2.655em;",[2061,5293],{"className":5294,"style":2274},[2202],[2061,5296,5298],{"className":5297},[2207,2208,2209,2210],[2061,5299,5301,5304],{"className":5300},[2169,2210],[2061,5302,4605],{"className":5303,"style":4851},[2169,2170,2210],[2061,5305,5307,5310],{"className":5306},[2169,2210],[2061,5308,2119],{"className":5309},[2169,2170,2210],[2061,5311,5313],{"className":5312},[2181],[2061,5314,5316,5341],{"className":5315},[2185,2186],[2061,5317,5319,5338],{"className":5318},[2190],[2061,5320,5323],{"className":5321,"style":5322},[2194],"height:0.3173em;",[2061,5324,5326,5330],{"style":5325},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[2061,5327],{"className":5328,"style":5329},[2202],"height:2.5em;",[2061,5331,5335],{"className":5332},[2207,5333,5334,2210],"reset-size3","size1",[2061,5336,2123],{"className":5337},[2169,2210],[2061,5339,2218],{"className":5340},[2217],[2061,5342,5344],{"className":5343},[2190],[2061,5345,5348],{"className":5346,"style":5347},[2194],"height:0.143em;",[2061,5349],{},[2061,5351,5352,5355],{"style":2325},[2061,5353],{"className":5354,"style":2274},[2202],[2061,5356],{"className":5357,"style":2333},[2332],[2061,5359,5361,5364],{"style":5360},"top:-3.4101em;",[2061,5362],{"className":5363,"style":2274},[2202],[2061,5365,5367],{"className":5366},[2207,2208,2209,2210],[2061,5368,5370,5373],{"className":5369},[2169,2210],[2061,5371,4596],{"className":5372,"style":4792},[2169,2170,2210],[2061,5374,5376,5379],{"className":5375},[2169,2210],[2061,5377,2119],{"className":5378},[2169,2170,2210],[2061,5380,5382],{"className":5381},[2181],[2061,5383,5385,5405],{"className":5384},[2185,2186],[2061,5386,5388,5402],{"className":5387},[2190],[2061,5389,5391],{"className":5390,"style":5322},[2194],[2061,5392,5393,5396],{"style":5325},[2061,5394],{"className":5395,"style":5329},[2202],[2061,5397,5399],{"className":5398},[2207,5333,5334,2210],[2061,5400,2134],{"className":5401},[2169,2210],[2061,5403,2218],{"className":5404},[2217],[2061,5406,5408],{"className":5407},[2190],[2061,5409,5411],{"className":5410,"style":5347},[2194],[2061,5412],{},[2061,5414,2218],{"className":5415},[2217],[2061,5417,5419],{"className":5418},[2190],[2061,5420,5423],{"className":5421,"style":5422},[2194],"height:0.4811em;",[2061,5424],{},[2061,5426],{"className":5427},[2444,2254],[1808,5429,5430,5433],{},[1865,5431,5432],{},"应用",": 常用于实证研究，收入弹性为1（同比例扩张消费）",[1808,5435,5436,4550,5439,5719],{},[1865,5437,5438],{},"完全替代品 (Perfect Substitutes)",[2061,5440,5442],{"className":5441},[2064],[2061,5443,5445,5498],{"className":5444},[2068],[2061,5446,5448],{"className":5447},[2072],[2074,5449,5450],{"xmlns":2076,"display":2077},[2079,5451,5452,5495],{},[2082,5453,5454,5456,5458,5464,5466,5472,5474,5476,5478,5484,5486,5489],{},[2085,5455,2005],{},[2097,5457,2114],{"stretchy":2113},[2089,5459,5460,5462],{},[2085,5461,2119],{},[2121,5463,2123],{},[2097,5465,2127],{"separator":2126},[2089,5467,5468,5470],{},[2085,5469,2119],{},[2121,5471,2134],{},[2097,5473,2137],{"stretchy":2113},[2097,5475,2099],{},[2085,5477,1827],{},[2089,5479,5480,5482],{},[2085,5481,2119],{},[2121,5483,2123],{},[2097,5485,2762],{},[2085,5487,5488],{},"b",[2089,5490,5491,5493],{},[2085,5492,2119],{},[2121,5494,2134],{},[2149,5496,5497],{"encoding":2151},"U(x_1, x_2) = ax_1 + 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Substitution)",[2061,6045,6047],{"className":6046},[2064],[2061,6048,6050,6137],{"className":6049},[2068],[2061,6051,6053],{"className":6052},[2072],[2074,6054,6055],{"xmlns":2076,"display":2077},[2079,6056,6057,6134],{},[2082,6058,6059,6061,6063,6069,6071,6077,6079,6081,6083,6092,6094,6102,6114,6116,6118,6120,6123,6125,6127,6129,6132],{},[2085,6060,2005],{},[2097,6062,2114],{"stretchy":2113},[2089,6064,6065,6067],{},[2085,6066,2119],{},[2121,6068,2123],{},[2097,6070,2127],{"separator":2126},[2089,6072,6073,6075],{},[2085,6074,2119],{},[2121,6076,2134],{},[2097,6078,2137],{"stretchy":2113},[2097,6080,2099],{},[2097,6082,2114],{"stretchy":2113},[2500,6084,6085,6087,6089],{},[2085,6086,2119],{},[2121,6088,2123],{},[2085,6090,6091],{},"ρ",[2097,6093,2762],{},[2500,6095,6096,6098,6100],{},[2085,6097,2119],{},[2121,6099,2134],{},[2085,6101,6091],{},[2487,6103,6104,6106],{},[2097,6105,2137],{"stretchy":2113},[2082,6107,6108,6110,6112],{},[2121,6109,2123],{},[2085,6111,3215],{"mathvariant":2107},[2085,6113,6091],{},[2097,6115,2127],{"separator":2126},[2231,6117],{"width":4610},[2085,6119,6091],{},[2097,6121,6122],{},"≤",[2121,6124,2123],{},[2097,6126,2127],{"separator":2126},[2085,6128,6091],{},[2097,6130,6131],{"mathvariant":2107},"≠",[2121,6133,2513],{},[2149,6135,6136],{"encoding":2151},"U(x_1, x_2) = (x_1^{\\rho} + x_2^{\\rho})^{1\u002F\\rho}, \\quad \\rho \\le 1, \\rho \\neq 0",[2061,6138,6140,6250,6324,6443,6510],{"className":6139,"ariaHidden":2126},[2156],[2061,6141,6143,6146,6149,6152,6192,6195,6198,6238,6241,6244,6247],{"className":6142},[2160],[2061,6144],{"className":6145,"style":4634},[2164],[2061,6147,2005],{"className":6148,"style":2171},[2169,2170],[2061,6150,2114],{"className":6151},[2253],[2061,6153,6155,6158],{"className":6154},[2169],[2061,6156,2119],{"className":6157},[2169,2170],[2061,6159,6161],{"className":6160},[2181],[2061,6162,6164,6184],{"className":6163},[2185,2186],[2061,6165,6167,6181],{"className":6166},[2190],[2061,6168,6170],{"className":6169,"style":2370},[2194],[2061,6171,6172,6175],{"style":2302},[2061,6173],{"className":6174,"style":2203},[2202],[2061,6176,6178],{"className":6177},[2207,2208,2209,2210],[2061,6179,2123],{"className":6180},[2169,2210],[2061,6182,2218],{"className":6183},[2217],[2061,6185,6187],{"className":6186},[2190],[2061,6188,6190],{"className":6189,"style":2225},[2194],[2061,6191],{},[2061,6193,2127],{"className":6194},[2396],[2061,6196],{"className":6197,"style":2400},[2231],[2061,6199,6201,6204],{"className":6200},[2169],[2061,6202,2119],{"className":6203},[2169,2170],[2061,6205,6207],{"className":6206},[2181],[2061,6208,6210,6230],{"className":6209},[2185,2186],[2061,6211,6213,6227],{"className":6212},[2190],[2061,6214,6216],{"className":6215,"style":2370},[2194],[2061,6217,6218,6221],{"style":2302},[2061,6219],{"className":6220,"style":2203},[2202],[2061,6222,6224],{"className":6223},[2207,2208,2209,2210],[2061,6225,2134],{"className":6226},[2169,2210],[2061,6228,2218],{"className":6229},[2217],[2061,6231,6233],{"className":6232},[2190],[2061,6234,6236],{"className":6235,"style":2225},[2194],[2061,6237],{},[2061,6239,2137],{"className":6240},[2444],[2061,6242],{"className":6243,"style":2232},[2231],[2061,6245,2099],{"className":6246},[2236],[2061,6248],{"className":6249,"style":2232},[2231],[2061,6251,6253,6257,6260,6315,6318,6321],{"className":6252},[2160],[2061,6254],{"className":6255,"style":6256},[2164],"height:1.0486em;vertical-align:-0.2663em;",[2061,6258,2114],{"className":6259},[2253],[2061,6261,6263,6266],{"className":6262},[2169],[2061,6264,2119],{"className":6265},[2169,2170],[2061,6267,6269],{"className":6268},[2181],[2061,6270,6272,6307],{"className":6271},[2185,2186],[2061,6273,6275,6304],{"className":6274},[2190],[2061,6276,6279,6290],{"className":6277,"style":6278},[2194],"height:0.7823em;",[2061,6280,6281,6284],{"style":4826},[2061,6282],{"className":6283,"style":2203},[2202],[2061,6285,6287],{"className":6286},[2207,2208,2209,2210],[2061,6288,2123],{"className":6289},[2169,2210],[2061,6291,6292,6295],{"style":4838},[2061,6293],{"className":6294,"style":2203},[2202],[2061,6296,6298],{"className":6297},[2207,2208,2209,2210],[2061,6299,6301],{"className":6300},[2169,2210],[2061,6302,6091],{"className":6303},[2169,2170,2210],[2061,6305,2218],{"className":6306},[2217],[2061,6308,6310],{"className":6309},[2190],[2061,6311,6313],{"className":6312,"style":4861},[2194],[2061,6314],{},[2061,6316],{"className":6317,"style":2980},[2231],[2061,6319,2762],{"className":6320},[2984],[2061,6322],{"className":6323,"style":2980},[2231],[2061,6325,6327,6331,6385,6422,6425,6428,6431,6434,6437,6440],{"className":6326},[2160],[2061,6328],{"className":6329,"style":6330},[2164],"height:1.2043em;vertical-align:-0.2663em;",[2061,6332,6334,6337],{"className":6333},[2169],[2061,6335,2119],{"className":6336},[2169,2170],[2061,6338,6340],{"className":6339},[2181],[2061,6341,6343,6377],{"className":6342},[2185,2186],[2061,6344,6346,6374],{"className":6345},[2190],[2061,6347,6349,6360],{"className":6348,"style":6278},[2194],[2061,6350,6351,6354],{"style":4826},[2061,6352],{"className":6353,"style":2203},[2202],[2061,6355,6357],{"className":6356},[2207,2208,2209,2210],[2061,6358,2134],{"className":6359},[2169,2210],[2061,6361,6362,6365],{"style":4838},[2061,6363],{"className":6364,"style":2203},[2202],[2061,6366,6368],{"className":6367},[2207,2208,2209,2210],[2061,6369,6371],{"className":6370},[2169,2210],[2061,6372,6091],{"className":6373},[2169,2170,2210],[2061,6375,2218],{"className":6376},[2217],[2061,6378,6380],{"className":6379},[2190],[2061,6381,6383],{"className":6382,"style":4861},[2194],[2061,6384],{},[2061,6386,6388,6391],{"className":6387},[2444],[2061,6389,2137],{"className":6390},[2444],[2061,6392,6394],{"className":6393},[2181],[2061,6395,6397],{"className":6396},[2185],[2061,6398,6400],{"className":6399},[2190],[2061,6401,6404],{"className":6402,"style":6403},[2194],"height:0.938em;",[2061,6405,6406,6409],{"style":4779},[2061,6407],{"className":6408,"style":2203},[2202],[2061,6410,6412],{"className":6411},[2207,2208,2209,2210],[2061,6413,6415,6419],{"className":6414},[2169,2210],[2061,6416,6418],{"className":6417},[2169,2210],"1\u002F",[2061,6420,6091],{"className":6421},[2169,2170,2210],[2061,6423,2127],{"className":6424},[2396],[2061,6426],{"className":6427,"style":4870},[2231],[2061,6429],{"className":6430,"style":2400},[2231],[2061,6432,6091],{"className":6433},[2169,2170],[2061,6435],{"className":6436,"style":2232},[2231],[2061,6438,6122],{"className":6439},[2236],[2061,6441],{"className":6442,"style":2232},[2231],[2061,6444,6446,6449,6452,6455,6458,6461,6464,6507],{"className":6445},[2160],[2061,6447],{"className":6448,"style":5163},[2164],[2061,6450,2123],{"className":6451},[2169],[2061,6453,2127],{"className":6454},[2396],[2061,6456],{"className":6457,"style":2400},[2231],[2061,6459,6091],{"className":6460},[2169,2170],[2061,6462],{"className":6463,"style":2232},[2231],[2061,6465,6467,6500,6504],{"className":6466},[2236],[2061,6468,6470],{"className":6469},[2236],[2061,6471,6474],{"className":6472},[2169,6473],"vbox",[2061,6475,6478],{"className":6476},[6477],"thinbox",[2061,6479,6482,6485,6496],{"className":6480},[6481],"rlap",[2061,6483],{"className":6484,"style":5163},[2164],[2061,6486,6489],{"className":6487},[6488],"inner",[2061,6490,6492],{"className":6491},[2169],[2061,6493,6495],{"className":6494},[2236],"",[2061,6497],{"className":6498},[6499],"fix",[2061,6501],{"className":6502},[2231,6503],"nobreak",[2061,6505,2099],{"className":6506},[2236],[2061,6508],{"className":6509,"style":2232},[2231],[2061,6511,6513,6516],{"className":6512},[2160],[2061,6514],{"className":6515,"style":2692},[2164],[2061,6517,2513],{"className":6518},[2169],[1805,6520,6521,6665],{},[1808,6522,6523,6526,6527],{},[1865,6524,6525],{},"特点",": 替代弹性为常数 ",[2061,6528,6530,6559],{"className":6529},[2068],[2061,6531,6533],{"className":6532},[2072],[2074,6534,6535],{"xmlns":2076},[2079,6536,6537,6556],{},[2082,6538,6539,6542,6544],{},[2085,6540,6541],{},"σ",[2097,6543,2099],{},[2101,6545,6546,6548],{},[2121,6547,2123],{},[2082,6549,6550,6552,6554],{},[2121,6551,2123],{},[2097,6553,3204],{},[2085,6555,6091],{},[2149,6557,6558],{"encoding":2151},"\\sigma = \\frac{1}{1-\\rho}",[2061,6560,6562,6582],{"className":6561,"ariaHidden":2126},[2156],[2061,6563,6565,6569,6573,6576,6579],{"className":6564},[2160],[2061,6566],{"className":6567,"style":6568},[2164],"height:0.4306em;",[2061,6570,6541],{"className":6571,"style":6572},[2169,2170],"margin-right:0.0359em;",[2061,6574],{"className":6575,"style":2232},[2231],[2061,6577,2099],{"className":6578},[2236],[2061,6580],{"className":6581,"style":2232},[2231],[2061,6583,6585,6589],{"className":6584},[2160],[2061,6586],{"className":6587,"style":6588},[2164],"height:1.3262em;vertical-align:-0.4811em;",[2061,6590,6592,6595,6662],{"className":6591},[2169],[2061,6593],{"className":6594},[2253,2254],[2061,6596,6598],{"className":6597},[2101],[2061,6599,6601,6654],{"className":6600},[2185,2186],[2061,6602,6604,6651],{"className":6603},[2190],[2061,6605,6608,6628,6636],{"className":6606,"style":6607},[2194],"height:0.8451em;",[2061,6609,6610,6613],{"style":5291},[2061,6611],{"className":6612,"style":2274},[2202],[2061,6614,6616],{"className":6615},[2207,2208,2209,2210],[2061,6617,6619,6622,6625],{"className":6618},[2169,2210],[2061,6620,2123],{"className":6621},[2169,2210],[2061,6623,3204],{"className":6624},[2984,2210],[2061,6626,6091],{"className":6627},[2169,2170,2210],[2061,6629,6630,6633],{"style":2325},[2061,6631],{"className":6632,"style":2274},[2202],[2061,6634],{"className":6635,"style":2333},[2332],[2061,6637,6639,6642],{"style":6638},"top:-3.394em;",[2061,6640],{"className":6641,"style":2274},[2202],[2061,6643,6645],{"className":6644},[2207,2208,2209,2210],[2061,6646,6648],{"className":6647},[2169,2210],[2061,6649,2123],{"className":6650},[2169,2210],[2061,6652,2218],{"className":6653},[2217],[2061,6655,6657],{"className":6656},[2190],[2061,6658,6660],{"className":6659,"style":5422},[2194],[2061,6661],{},[2061,6663],{"className":6664},[2444,2254],[1808,6666,6667,1949,6670],{},[1865,6668,6669],{},"极限情况",[1805,6671,6672,6728,6782],{},[1808,6673,6674,6727],{},[2061,6675,6677,6696],{"className":6676},[2068],[2061,6678,6680],{"className":6679},[2072],[2074,6681,6682],{"xmlns":2076},[2079,6683,6684,6693],{},[2082,6685,6686,6688,6691],{},[2085,6687,6091],{},[2097,6689,6690],{},"→",[2121,6692,2513],{},[2149,6694,6695],{"encoding":2151},"\\rho \\to 0",[2061,6697,6699,6718],{"className":6698,"ariaHidden":2126},[2156],[2061,6700,6702,6706,6709,6712,6715],{"className":6701},[2160],[2061,6703],{"className":6704,"style":6705},[2164],"height:0.625em;vertical-align:-0.1944em;",[2061,6707,6091],{"className":6708},[2169,2170],[2061,6710],{"className":6711,"style":2232},[2231],[2061,6713,6690],{"className":6714},[2236],[2061,6716],{"className":6717,"style":2232},[2231],[2061,6719,6721,6724],{"className":6720},[2160],[2061,6722],{"className":6723,"style":2692},[2164],[2061,6725,2513],{"className":6726},[2169],": 柯布-道格拉斯",[1808,6729,6730,6781],{},[2061,6731,6733,6751],{"className":6732},[2068],[2061,6734,6736],{"className":6735},[2072],[2074,6737,6738],{"xmlns":2076},[2079,6739,6740,6748],{},[2082,6741,6742,6744,6746],{},[2085,6743,6091],{},[2097,6745,2099],{},[2121,6747,2123],{},[2149,6749,6750],{"encoding":2151},"\\rho = 1",[2061,6752,6754,6772],{"className":6753,"ariaHidden":2126},[2156],[2061,6755,6757,6760,6763,6766,6769],{"className":6756},[2160],[2061,6758],{"className":6759,"style":6705},[2164],[2061,6761,6091],{"className":6762},[2169,2170],[2061,6764],{"className":6765,"style":2232},[2231],[2061,6767,2099],{"className":6768},[2236],[2061,6770],{"className":6771,"style":2232},[2231],[2061,6773,6775,6778],{"className":6774},[2160],[2061,6776],{"className":6777,"style":2692},[2164],[2061,6779,2123],{"className":6780},[2169],": 完全替代",[1808,6783,6784,6842],{},[2061,6785,6787,6808],{"className":6786},[2068],[2061,6788,6790],{"className":6789},[2072],[2074,6791,6792],{"xmlns":2076},[2079,6793,6794,6805],{},[2082,6795,6796,6798,6800,6802],{},[2085,6797,6091],{},[2097,6799,6690],{},[2097,6801,3204],{},[2085,6803,6804],{"mathvariant":2107},"∞",[2149,6806,6807],{"encoding":2151},"\\rho \\to -\\infty",[2061,6809,6811,6829],{"className":6810,"ariaHidden":2126},[2156],[2061,6812,6814,6817,6820,6823,6826],{"className":6813},[2160],[2061,6815],{"className":6816,"style":6705},[2164],[2061,6818,6091],{"className":6819},[2169,2170],[2061,6821],{"className":6822,"style":2232},[2231],[2061,6824,6690],{"className":6825},[2236],[2061,6827],{"className":6828,"style":2232},[2231],[2061,6830,6832,6836,6839],{"className":6831},[2160],[2061,6833],{"className":6834,"style":6835},[2164],"height:0.6667em;vertical-align:-0.0833em;",[2061,6837,3204],{"className":6838},[2169],[2061,6840,6804],{"className":6841},[2169],": 完全互补",[1808,6844,6845,4550,6848,7133],{},[1865,6846,6847],{},"拟线性效用函数 (Quasi-linear)",[2061,6849,6851],{"className":6850},[2064],[2061,6852,6854,6909],{"className":6853},[2068],[2061,6855,6857],{"className":6856},[2072],[2074,6858,6859],{"xmlns":2076,"display":2077},[2079,6860,6861,6906],{},[2082,6862,6863,6865,6867,6873,6875,6881,6883,6885,6888,6890,6896,6898,6900],{},[2085,6864,2005],{},[2097,6866,2114],{"stretchy":2113},[2089,6868,6869,6871],{},[2085,6870,2119],{},[2121,6872,2123],{},[2097,6874,2127],{"separator":2126},[2089,6876,6877,6879],{},[2085,6878,2119],{},[2121,6880,2134],{},[2097,6882,2137],{"stretchy":2113},[2097,6884,2099],{},[2085,6886,6887],{},"v",[2097,6889,2114],{"stretchy":2113},[2089,6891,6892,6894],{},[2085,6893,2119],{},[2121,6895,2123],{},[2097,6897,2137],{"stretchy":2113},[2097,6899,2762],{},[2089,6901,6902,6904],{},[2085,6903,2119],{},[2121,6905,2134],{},[2149,6907,6908],{"encoding":2151},"U(x_1, x_2) = v(x_1) + x_2",[2061,6910,6912,7022,7086],{"className":6911,"ariaHidden":2126},[2156],[2061,6913,6915,6918,6921,6924,6964,6967,6970,7010,7013,7016,7019],{"className":6914},[2160],[2061,6916],{"className":6917,"style":4634},[2164],[2061,6919,2005],{"className":6920,"style":2171},[2169,2170],[2061,6922,2114],{"className":6923},[2253],[2061,6925,6927,6930],{"className":6926},[2169],[2061,6928,2119],{"className":6929},[2169,2170],[2061,6931,6933],{"className":6932},[2181],[2061,6934,6936,6956],{"className":6935},[2185,2186],[2061,6937,6939,6953],{"className":6938},[2190],[2061,6940,6942],{"className":6941,"style":2370},[2194],[2061,6943,6944,6947],{"style":2302},[2061,6945],{"className":6946,"style":2203},[2202],[2061,6948,6950],{"className":6949},[2207,2208,2209,2210],[2061,6951,2123],{"className":6952},[2169,2210],[2061,6954,2218],{"className":6955},[2217],[2061,6957,6959],{"className":6958},[2190],[2061,6960,6962],{"className":6961,"style":2225},[2194],[2061,6963],{},[2061,6965,2127],{"className":6966},[2396],[2061,6968],{"className":6969,"style":2400},[2231],[2061,6971,6973,6976],{"className":6972},[2169],[2061,6974,2119],{"className":6975},[2169,2170],[2061,6977,6979],{"className":6978},[2181],[2061,6980,6982,7002],{"className":6981},[2185,2186],[2061,6983,6985,6999],{"className":6984},[2190],[2061,6986,6988],{"className":6987,"style":2370},[2194],[2061,6989,6990,6993],{"style":2302},[2061,6991],{"className":6992,"style":2203},[2202],[2061,6994,6996],{"className":6995},[2207,2208,2209,2210],[2061,6997,2134],{"className":6998},[2169,2210],[2061,7000,2218],{"className":7001},[2217],[2061,7003,7005],{"className":7004},[2190],[2061,7006,7008],{"className":7007,"style":2225},[2194],[2061,7009],{},[2061,7011,2137],{"className":7012},[2444],[2061,7014],{"className":7015,"style":2232},[2231],[2061,7017,2099],{"className":7018},[2236],[2061,7020],{"className":7021,"style":2232},[2231],[2061,7023,7025,7028,7031,7034,7074,7077,7080,7083],{"className":7024},[2160],[2061,7026],{"className":7027,"style":4634},[2164],[2061,7029,6887],{"className":7030,"style":6572},[2169,2170],[2061,7032,2114],{"className":7033},[2253],[2061,7035,7037,7040],{"className":7036},[2169],[2061,7038,2119],{"className":7039},[2169,2170],[2061,7041,7043],{"className":7042},[2181],[2061,7044,7046,7066],{"className":7045},[2185,2186],[2061,7047,7049,7063],{"className":7048},[2190],[2061,7050,7052],{"className":7051,"style":2370},[2194],[2061,7053,7054,7057],{"style":2302},[2061,7055],{"className":7056,"style":2203},[2202],[2061,7058,7060],{"className":7059},[2207,2208,2209,2210],[2061,7061,2123],{"className":7062},[2169,2210],[2061,7064,2218],{"className":7065},[2217],[2061,7067,7069],{"className":7068},[2190],[2061,7070,7072],{"className":7071,"style":2225},[2194],[2061,7073],{},[2061,7075,2137],{"className":7076},[2444],[2061,7078],{"className":7079,"style":2980},[2231],[2061,7081,2762],{"className":7082},[2984],[2061,7084],{"className":7085,"style":2980},[2231],[2061,7087,7089,7093],{"className":7088},[2160],[2061,7090],{"className":7091,"style":7092},[2164],"height:0.5806em;vertical-align:-0.15em;",[2061,7094,7096,7099],{"className":7095},[2169],[2061,7097,2119],{"className":7098},[2169,2170],[2061,7100,7102],{"className":7101},[2181],[2061,7103,7105,7125],{"className":7104},[2185,2186],[2061,7106,7108,7122],{"className":7107},[2190],[2061,7109,7111],{"className":7110,"style":2370},[2194],[2061,7112,7113,7116],{"style":2302},[2061,7114],{"className":7115,"style":2203},[2202],[2061,7117,7119],{"className":7118},[2207,2208,2209,2210],[2061,7120,2134],{"className":7121},[2169,2210],[2061,7123,2218],{"className":7124},[2217],[2061,7126,7128],{"className":7127},[2190],[2061,7129,7131],{"className":7130,"style":2225},[2194],[2061,7132],{},[1805,7134,7135,7140],{},[1808,7136,7137,7139],{},[1865,7138,6525],{},": 对商品2无收入效应",[1808,7141,7142,7144],{},[1865,7143,5432],{},": 当商品2代表\"其他所有商品\"时简化分析",[1840,7146],{},[1794,7148,7150],{"id":7149},"_2-效用最大化问题-utility-maximization-problem-ump","2. 效用最大化问题 (Utility Maximization Problem, UMP)",[1847,7152,7154],{"id":7153},"_21-预算约束-budget-constraint","2.1 预算约束 (Budget Constraint)",[1798,7156,7157,7158,7161,7162,2006,7165,7168],{},"假设消费者有收入 ",[1855,7159,7160],{},"m","，商品1和2的价格分别为 ",[1855,7163,7164],{},"p₁",[1855,7166,7167],{},"p₂","。预算约束为：",[2061,7170,7172],{"className":7171},[2064],[2061,7173,7175,7217],{"className":7174},[2068],[2061,7176,7178],{"className":7177},[2072],[2074,7179,7180],{"xmlns":2076,"display":2077},[2079,7181,7182,7214],{},[2082,7183,7184,7190,7196,7198,7204,7210,7212],{},[2089,7185,7186,7188],{},[2085,7187,1798],{},[2121,7189,2123],{},[2089,7191,7192,7194],{},[2085,7193,2119],{},[2121,7195,2123],{},[2097,7197,2762],{},[2089,7199,7200,7202],{},[2085,7201,1798],{},[2121,7203,2134],{},[2089,7205,7206,7208],{},[2085,7207,2119],{},[2121,7209,2134],{},[2097,7211,6122],{},[2085,7213,7160],{},[2149,7215,7216],{"encoding":2151},"p_1 x_1 + p_2 x_2 \\le m",[2061,7218,7220,7316,7412],{"className":7219,"ariaHidden":2126},[2156],[2061,7221,7223,7227,7267,7307,7310,7313],{"className":7222},[2160],[2061,7224],{"className":7225,"style":7226},[2164],"height:0.7778em;vertical-align:-0.1944em;",[2061,7228,7230,7233],{"className":7229},[2169],[2061,7231,1798],{"className":7232},[2169,2170],[2061,7234,7236],{"className":7235},[2181],[2061,7237,7239,7259],{"className":7238},[2185,2186],[2061,7240,7242,7256],{"className":7241},[2190],[2061,7243,7245],{"className":7244,"style":2370},[2194],[2061,7246,7247,7250],{"style":2302},[2061,7248],{"className":7249,"style":2203},[2202],[2061,7251,7253],{"className":7252},[2207,2208,2209,2210],[2061,7254,2123],{"className":7255},[2169,2210],[2061,7257,2218],{"className":7258},[2217],[2061,7260,7262],{"className":7261},[2190],[2061,7263,7265],{"className":7264,"style":2225},[2194],[2061,7266],{},[2061,7268,7270,7273],{"className":7269},[2169],[2061,7271,2119],{"className":7272},[2169,2170],[2061,7274,7276],{"className":7275},[2181],[2061,7277,7279,7299],{"className":7278},[2185,2186],[2061,7280,7282,7296],{"className":7281},[2190],[2061,7283,7285],{"className":7284,"style":2370},[2194],[2061,7286,7287,7290],{"style":2302},[2061,7288],{"className":7289,"style":2203},[2202],[2061,7291,7293],{"className":7292},[2207,2208,2209,2210],[2061,7294,2123],{"className":7295},[2169,2210],[2061,7297,2218],{"className":7298},[2217],[2061,7300,7302],{"className":7301},[2190],[2061,7303,7305],{"className":7304,"style":2225},[2194],[2061,7306],{},[2061,7308],{"className":7309,"style":2980},[2231],[2061,7311,2762],{"className":7312},[2984],[2061,7314],{"className":7315,"style":2980},[2231],[2061,7317,7319,7323,7363,7403,7406,7409],{"className":7318},[2160],[2061,7320],{"className":7321,"style":7322},[2164],"height:0.8304em;vertical-align:-0.1944em;",[2061,7324,7326,7329],{"className":7325},[2169],[2061,7327,1798],{"className":7328},[2169,2170],[2061,7330,7332],{"className":7331},[2181],[2061,7333,7335,7355],{"className":7334},[2185,2186],[2061,7336,7338,7352],{"className":7337},[2190],[2061,7339,7341],{"className":7340,"style":2370},[2194],[2061,7342,7343,7346],{"style":2302},[2061,7344],{"className":7345,"style":2203},[2202],[2061,7347,7349],{"className":7348},[2207,2208,2209,2210],[2061,7350,2134],{"className":7351},[2169,2210],[2061,7353,2218],{"className":7354},[2217],[2061,7356,7358],{"className":7357},[2190],[2061,7359,7361],{"className":7360,"style":2225},[2194],[2061,7362],{},[2061,7364,7366,7369],{"className":7365},[2169],[2061,7367,2119],{"className":7368},[2169,2170],[2061,7370,7372],{"className":7371},[2181],[2061,7373,7375,7395],{"className":7374},[2185,2186],[2061,7376,7378,7392],{"className":7377},[2190],[2061,7379,7381],{"className":7380,"style":2370},[2194],[2061,7382,7383,7386],{"style":2302},[2061,7384],{"className":7385,"style":2203},[2202],[2061,7387,7389],{"className":7388},[2207,2208,2209,2210],[2061,7390,2134],{"className":7391},[2169,2210],[2061,7393,2218],{"className":7394},[2217],[2061,7396,7398],{"className":7397},[2190],[2061,7399,7401],{"className":7400,"style":2225},[2194],[2061,7402],{},[2061,7404],{"className":7405,"style":2232},[2231],[2061,7407,6122],{"className":7408},[2236],[2061,7410],{"className":7411,"style":2232},[2231],[2061,7413,7415,7418],{"className":7414},[2160],[2061,7416],{"className":7417,"style":6568},[2164],[2061,7419,7160],{"className":7420},[2169,2170],[1798,7422,7423,7424,1989],{},"预算线是所有刚好花光所有收入的消费束的集合，其斜率为 ",[1855,7425,7426],{},"-p₁\u002Fp₂",[1965,7428],{"code64":7429,"locale":7},"eHljaGFydC1iZXRhCiAgdGl0bGUgIumihOeul+e6vyAoQnVkZ2V0IExpbmUpIgogIHgtYXhpcyAi5ZWG5ZOBIFjigoEiIFswLCAyLCA0LCA2LCA4LCAxMF0KICB5LWF4aXMgIuWVhuWTgSBY4oKCIiAwIC0tPiA3CiAgbGluZSBbNSwgNCwgMywgMiwgMSwgMF0=",[1847,7431,7433],{"id":7432},"_22-最优选择-optimal-choice","2.2 最优选择 (Optimal Choice)",[1798,7435,7436],{},"消费者的目标是在预算约束下，选择一个消费束使其效用最大化。",[2061,7438,7440],{"className":7439},[2064],[2061,7441,7443,7539],{"className":7442},[2068],[2061,7444,7446],{"className":7445},[2072],[2074,7447,7448],{"xmlns":2076,"display":2077},[2079,7449,7450,7536],{},[2082,7451,7452,7478,7480,7482,7488,7490,7496,7498,7500,7504,7506,7512,7518,7520,7526,7532,7534],{},[7453,7454,7455,7462],"munder",{},[2082,7456,7457,7460],{},[2085,7458,7459],{},"max",[2097,7461,4951],{},[2082,7463,7464,7470,7472],{},[2089,7465,7466,7468],{},[2085,7467,2119],{},[2121,7469,2123],{},[2097,7471,2127],{"separator":2126},[2089,7473,7474,7476],{},[2085,7475,2119],{},[2121,7477,2134],{},[2085,7479,2005],{},[2097,7481,2114],{"stretchy":2113},[2089,7483,7484,7486],{},[2085,7485,2119],{},[2121,7487,2123],{},[2097,7489,2127],{"separator":2126},[2089,7491,7492,7494],{},[2085,7493,2119],{},[2121,7495,2134],{},[2097,7497,2137],{"stretchy":2113},[2231,7499],{"width":4610},[7501,7502,7503],"mtext",{},"s.t.",[2231,7505],{"width":4610},[2089,7507,7508,7510],{},[2085,7509,1798],{},[2121,7511,2123],{},[2089,7513,7514,7516],{},[2085,7515,2119],{},[2121,7517,2123],{},[2097,7519,2762],{},[2089,7521,7522,7524],{},[2085,7523,1798],{},[2121,7525,2134],{},[2089,7527,7528,7530],{},[2085,7529,2119],{},[2121,7531,2134],{},[2097,7533,6122],{},[2085,7535,7160],{},[2149,7537,7538],{"encoding":2151},"\\max_{x_1, x_2} U(x_1, x_2) \\quad \\text{s.t.} \\quad p_1 x_1 + p_2 x_2 \\le m",[2061,7540,7542,7880,7975],{"className":7541,"ariaHidden":2126},[2156],[2061,7543,7545,7549,7680,7683,7686,7689,7729,7732,7735,7775,7778,7781,7788,7791,7831,7871,7874,7877],{"className":7544},[2160],[2061,7546],{"className":7547,"style":7548},[2164],"height:1.5861em;vertical-align:-0.8361em;",[2061,7550,7553],{"className":7551},[5104,7552],"op-limits",[2061,7554,7556,7671],{"className":7555},[2185,2186],[2061,7557,7559,7668],{"className":7558},[2190],[2061,7560,7562,7657],{"className":7561,"style":6568},[2194],[2061,7563,7565,7568],{"style":7564},"top:-2.4em;margin-left:0em;",[2061,7566],{"className":7567,"style":2274},[2202],[2061,7569,7571],{"className":7570},[2207,2208,2209,2210],[2061,7572,7574,7614,7617],{"className":7573},[2169,2210],[2061,7575,7577,7580],{"className":7576},[2169,2210],[2061,7578,2119],{"className":7579},[2169,2170,2210],[2061,7581,7583],{"className":7582},[2181],[2061,7584,7586,7606],{"className":7585},[2185,2186],[2061,7587,7589,7603],{"className":7588},[2190],[2061,7590,7592],{"className":7591,"style":5322},[2194],[2061,7593,7594,7597],{"style":5325},[2061,7595],{"className":7596,"style":5329},[2202],[2061,7598,7600],{"className":7599},[2207,5333,5334,2210],[2061,7601,2123],{"className":7602},[2169,2210],[2061,7604,2218],{"className":7605},[2217],[2061,7607,7609],{"className":7608},[2190],[2061,7610,7612],{"className":7611,"style":5347},[2194],[2061,7613],{},[2061,7615,2127],{"className":7616},[2396,2210],[2061,7618,7620,7623],{"className":7619},[2169,2210],[2061,7621,2119],{"className":7622},[2169,2170,2210],[2061,7624,7626],{"className":7625},[2181],[2061,7627,7629,7649],{"className":7628},[2185,2186],[2061,7630,7632,7646],{"className":7631},[2190],[2061,7633,7635],{"className":7634,"style":5322},[2194],[2061,7636,7637,7640],{"style":5325},[2061,7638],{"className":7639,"style":5329},[2202],[2061,7641,7643],{"className":7642},[2207,5333,5334,2210],[2061,7644,2134],{"className":7645},[2169,2210],[2061,7647,2218],{"className":7648},[2217],[2061,7650,7652],{"className":7651},[2190],[2061,7653,7655],{"className":7654,"style":5347},[2194],[2061,7656],{},[2061,7658,7660,7663],{"style":7659},"top:-3em;",[2061,7661],{"className":7662,"style":2274},[2202],[2061,7664,7665],{},[2061,7666,7459],{"className":7667},[5104],[2061,7669,2218],{"className":7670},[2217],[2061,7672,7674],{"className":7673},[2190],[2061,7675,7678],{"className":7676,"style":7677},[2194],"height:0.8361em;",[2061,7679],{},[2061,7681],{"className":7682,"style":2400},[2231],[2061,7684,2005],{"className":7685,"style":2171},[2169,2170],[2061,7687,2114],{"className":7688},[2253],[2061,7690,7692,7695],{"className":7691},[2169],[2061,7693,2119],{"className":7694},[2169,2170],[2061,7696,7698],{"className":7697},[2181],[2061,7699,7701,7721],{"className":7700},[2185,2186],[2061,7702,7704,7718],{"className":7703},[2190],[2061,7705,7707],{"className":7706,"style":2370},[2194],[2061,7708,7709,7712],{"style":2302},[2061,7710],{"className":7711,"style":2203},[2202],[2061,7713,7715],{"className":7714},[2207,2208,2209,2210],[2061,7716,2123],{"className":7717},[2169,2210],[2061,7719,2218],{"className":7720},[2217],[2061,7722,7724],{"className":7723},[2190],[2061,7725,7727],{"className":7726,"style":2225},[2194],[2061,7728],{},[2061,7730,2127],{"className":7731},[2396],[2061,7733],{"className":7734,"style":2400},[2231],[2061,7736,7738,7741],{"className":7737},[2169],[2061,7739,2119],{"className":7740},[2169,2170],[2061,7742,7744],{"className":7743},[2181],[2061,7745,7747,7767],{"className":7746},[2185,2186],[2061,7748,7750,7764],{"className":7749},[2190],[2061,7751,7753],{"className":7752,"style":2370},[2194],[2061,7754,7755,7758],{"style":2302},[2061,7756],{"className":7757,"style":2203},[2202],[2061,7759,7761],{"className":7760},[2207,2208,2209,2210],[2061,7762,2134],{"className":7763},[2169,2210],[2061,7765,2218],{"className":7766},[2217],[2061,7768,7770],{"className":7769},[2190],[2061,7771,7773],{"className":7772,"style":2225},[2194],[2061,7774],{},[2061,7776,2137],{"className":7777},[2444],[2061,7779],{"className":7780,"style":4870},[2231],[2061,7782,7785],{"className":7783},[2169,7784],"text",[2061,7786,7503],{"className":7787},[2169],[2061,7789],{"className":7790,"style":4870},[2231],[2061,7792,7794,7797],{"className":7793},[2169],[2061,7795,1798],{"className":7796},[2169,2170],[2061,7798,7800],{"className":7799},[2181],[2061,7801,7803,7823],{"className":7802},[2185,2186],[2061,7804,7806,7820],{"className":7805},[2190],[2061,7807,7809],{"className":7808,"style":2370},[2194],[2061,7810,7811,7814],{"style":2302},[2061,7812],{"className":7813,"style":2203},[2202],[2061,7815,7817],{"className":7816},[2207,2208,2209,2210],[2061,7818,2123],{"className":7819},[2169,2210],[2061,7821,2218],{"className":7822},[2217],[2061,7824,7826],{"className":7825},[2190],[2061,7827,7829],{"className":7828,"style":2225},[2194],[2061,7830],{},[2061,7832,7834,7837],{"className":7833},[2169],[2061,7835,2119],{"className":7836},[2169,2170],[2061,7838,7840],{"className":7839},[2181],[2061,7841,7843,7863],{"className":7842},[2185,2186],[2061,7844,7846,7860],{"className":7845},[2190],[2061,7847,7849],{"className":7848,"style":2370},[2194],[2061,7850,7851,7854],{"style":2302},[2061,7852],{"className":7853,"style":2203},[2202],[2061,7855,7857],{"className":7856},[2207,2208,2209,2210],[2061,7858,2123],{"className":7859},[2169,2210],[2061,7861,2218],{"className":7862},[2217],[2061,7864,7866],{"className":7865},[2190],[2061,7867,7869],{"className":7868,"style":2225},[2194],[2061,7870],{},[2061,7872],{"className":7873,"style":2980},[2231],[2061,7875,2762],{"className":7876},[2984],[2061,7878],{"className":7879,"style":2980},[2231],[2061,7881,7883,7886,7926,7966,7969,7972],{"className":7882},[2160],[2061,7884],{"className":7885,"style":7322},[2164],[2061,7887,7889,7892],{"className":7888},[2169],[2061,7890,1798],{"className":7891},[2169,2170],[2061,7893,7895],{"className":7894},[2181],[2061,7896,7898,7918],{"className":7897},[2185,2186],[2061,7899,7901,7915],{"className":7900},[2190],[2061,7902,7904],{"className":7903,"style":2370},[2194],[2061,7905,7906,7909],{"style":2302},[2061,7907],{"className":7908,"style":2203},[2202],[2061,7910,7912],{"className":7911},[2207,2208,2209,2210],[2061,7913,2134],{"className":7914},[2169,2210],[2061,7916,2218],{"className":7917},[2217],[2061,7919,7921],{"className":7920},[2190],[2061,7922,7924],{"className":7923,"style":2225},[2194],[2061,7925],{},[2061,7927,7929,7932],{"className":7928},[2169],[2061,7930,2119],{"className":7931},[2169,2170],[2061,7933,7935],{"className":7934},[2181],[2061,7936,7938,7958],{"className":7937},[2185,2186],[2061,7939,7941,7955],{"className":7940},[2190],[2061,7942,7944],{"className":7943,"style":2370},[2194],[2061,7945,7946,7949],{"style":2302},[2061,7947],{"className":7948,"style":2203},[2202],[2061,7950,7952],{"className":7951},[2207,2208,2209,2210],[2061,7953,2134],{"className":7954},[2169,2210],[2061,7956,2218],{"className":7957},[2217],[2061,7959,7961],{"className":7960},[2190],[2061,7962,7964],{"className":7963,"style":2225},[2194],[2061,7965],{},[2061,7967],{"className":7968,"style":2232},[2231],[2061,7970,6122],{"className":7971},[2236],[2061,7973],{"className":7974,"style":2232},[2231],[2061,7976,7978,7981],{"className":7977},[2160],[2061,7979],{"className":7980,"style":6568},[2164],[2061,7982,7160],{"className":7983},[2169,2170],[1798,7985,7986,7987,1989],{},"在内部解（两种商品都消费）的情况下，最优解的特征是",[1865,7988,7989],{},"无差异曲线与预算线相切",[1805,7991,7992],{},[1808,7993,7994,1949,7997,8580],{},[1865,7995,7996],{},"相切条件",[2061,7998,8000],{"className":7999},[2064],[2061,8001,8003,8087],{"className":8002},[2068],[2061,8004,8006],{"className":8005},[2072],[2074,8007,8008],{"xmlns":2076,"display":2077},[2079,8009,8010,8084],{},[2082,8011,8012,8014,8016,8018,8020,8034,8036,8039,8042,8044,8046,8068,8070],{},[2085,8013,2087],{},[2085,8015,3784],{},[2085,8017,3789],{},[2097,8019,2099],{},[2101,8021,8022,8028],{},[2089,8023,8024,8026],{},[2085,8025,1798],{},[2121,8027,2123],{},[2089,8029,8030,8032],{},[2085,8031,1798],{},[2121,8033,2134],{},[2231,8035],{"width":4610},[7501,8037,8038],{},"  ",[2097,8040,8041],{},"⟹",[7501,8043,8038],{},[2231,8045],{"width":4610},[2101,8047,8048,8058],{},[2082,8049,8050,8052],{},[2085,8051,2087],{},[2089,8053,8054,8056],{},[2085,8055,2005],{},[2121,8057,2123],{},[2082,8059,8060,8062],{},[2085,8061,2087],{},[2089,8063,8064,8066],{},[2085,8065,2005],{},[2121,8067,2134],{},[2097,8069,2099],{},[2101,8071,8072,8078],{},[2089,8073,8074,8076],{},[2085,8075,1798],{},[2121,8077,2123],{},[2089,8079,8080,8082],{},[2085,8081,1798],{},[2121,8083,2134],{},[2149,8085,8086],{"encoding":2151},"MRS = \\frac{p_1}{p_2} \\quad \\implies \\quad \\frac{MU_1}{MU_2} = 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求解方法：拉格朗日法",[1798,8589,8590],{},"我们可以建立拉格朗日函数来求解约束最优化问题：",[2061,8592,8594],{"className":8593},[2064],[2061,8595,8597,8696],{"className":8596},[2068],[2061,8598,8600],{"className":8599},[2072],[2074,8601,8602],{"xmlns":2076,"display":2077},[2079,8603,8604,8693],{},[2082,8605,8606,8610,8612,8618,8620,8626,8628,8631,8633,8635,8637,8639,8645,8647,8653,8655,8657,8659,8661,8663,8665,8671,8677,8679,8685,8691],{},[2085,8607,8609],{"mathvariant":8608},"script","L",[2097,8611,2114],{"stretchy":2113},[2089,8613,8614,8616],{},[2085,8615,2119],{},[2121,8617,2123],{},[2097,8619,2127],{"separator":2126},[2089,8621,8622,8624],{},[2085,8623,2119],{},[2121,8625,2134],{},[2097,8627,2127],{"separator":2126},[2085,8629,8630],{},"λ",[2097,8632,2137],{"stretchy":2113},[2097,8634,2099],{},[2085,8636,2005],{},[2097,8638,2114],{"stretchy":2113},[2089,8640,8641,8643],{},[2085,8642,2119],{},[2121,8644,2123],{},[2097,8646,2127],{"separator":2126},[2089,8648,8649,8651],{},[2085,8650,2119],{},[2121,8652,2134],{},[2097,8654,2137],{"stretchy":2113},[2097,8656,2762],{},[2085,8658,8630],{},[2097,8660,2114],{"stretchy":2113},[2085,8662,7160],{},[2097,8664,3204],{},[2089,8666,8667,8669],{},[2085,8668,1798],{},[2121,8670,2123],{},[2089,8672,8673,8675],{},[2085,8674,2119],{},[2121,8676,2123],{},[2097,8678,3204],{},[2089,8680,8681,8683],{},[2085,8682,1798],{},[2121,8684,2134],{},[2089,8686,8687,8689],{},[2085,8688,2119],{},[2121,8690,2134],{},[2097,8692,2137],{"stretchy":2113},[2149,8694,8695],{"encoding":2151},"\\mathcal{L}(x_1, x_2, \\lambda) = U(x_1, x_2) + \\lambda(m - p_1 x_1 - p_2 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\\mathcal{L}}{\\partial x_1} &= \\frac{\\partial U}{\\partial x_1} - \\lambda p_1 = 0 \\\\\n\\frac{\\partial \\mathcal{L}}{\\partial x_2} &= \\frac{\\partial U}{\\partial x_2} - \\lambda p_2 = 0 \\\\\n\\frac{\\partial \\mathcal{L}}{\\partial \\lambda} &= m - p_1 x_1 - p_2 x_2 = 0\n\\end{align*}",[2061,9362,9364],{"className":9363,"ariaHidden":2126},[2156],[2061,9365,9367,9371],{"className":9366},[2160],[2061,9368],{"className":9369,"style":9370},[2164],"height:7.0723em;vertical-align:-3.2862em;",[2061,9372,9374],{"className":9373},[2169],[2061,9375,9377,9710],{"className":9376},[9154],[2061,9378,9381],{"className":9379},[9380],"col-align-r",[2061,9382,9384,9701],{"className":9383},[2185,2186],[2061,9385,9387,9698],{"className":9386},[2190],[2061,9388,9391,9506,9620],{"className":9389,"style":9390},[2194],"height:3.7862em;",[2061,9392,9394,9398],{"style":9393},"top:-5.7862em;",[2061,9395],{"className":9396,"style":9397},[2202],"height:3.3714em;",[2061,9399,9401],{"className":9400},[2169],[2061,9402,9404,9407,9503],{"className":9403},[2169],[2061,9405],{"className":9406},[2253,2254],[2061,9408,9410],{"className":9409},[2101],[2061,9411,9413,9495],{"className":9412},[2185,2186],[2061,9414,9416,9492],{"className":9415},[2190],[2061,9417,9419,9470,9478],{"className":9418,"style":2846},[2194],[2061,9420,9421,9424],{"style":2270},[2061,9422],{"className":9423,"style":2274},[2202],[2061,9425,9427,9430],{"className":9426},[2169],[2061,9428,2108],{"className":9429,"style":2281},[2169],[2061,9431,9433,9436],{"className":9432},[2169],[2061,9434,2119],{"className":9435},[2169,2170],[2061,9437,9439],{"className":9438},[2181],[2061,9440,9442,9462],{"className":9441},[2185,2186],[2061,9443,9445,9459],{"className":9444},[2190],[2061,9446,9448],{"className":9447,"style":2370},[2194],[2061,9449,9450,9453],{"style":2302},[2061,9451],{"className":9452,"style":2203},[2202],[2061,9454,9456],{"className":9455},[2207,2208,2209,2210],[2061,9457,2123],{"className":9458},[2169,2210],[2061,9460,2218],{"className":9461},[2217],[2061,9463,9465],{"className":9464},[2190],[2061,9466,9468],{"className":9467,"style":2225},[2194],[2061,9469],{},[2061,9471,9472,9475],{"style":2325},[2061,9473],{"className":9474,"style":2274},[2202],[2061,9476],{"className":9477,"style":2333},[2332],[2061,9479,9480,9483],{"style":2336},[2061,9481],{"className":9482,"style":2274},[2202],[2061,9484,9486,9489],{"className":9485},[2169],[2061,9487,2108],{"className":9488,"style":2281},[2169],[2061,9490,8609],{"className":9491},[2169,8708],[2061,9493,2218],{"className":9494},[2217],[2061,9496,9498],{"className":9497},[2190],[2061,9499,9501],{"className":9500,"style":2454},[2194],[2061,9502],{},[2061,9504],{"className":9505},[2444,2254],[2061,9507,9509,9512],{"style":9508},"top:-3.2787em;",[2061,9510],{"className":9511,"style":9397},[2202],[2061,9513,9515],{"className":9514},[2169],[2061,9516,9518,9521,9617],{"className":9517},[2169],[2061,9519],{"className":9520},[2253,2254],[2061,9522,9524],{"className":9523},[2101],[2061,9525,9527,9609],{"className":9526},[2185,2186],[2061,9528,9530,9606],{"className":9529},[2190],[2061,9531,9533,9584,9592],{"className":9532,"style":2846},[2194],[2061,9534,9535,9538],{"style":2270},[2061,9536],{"className":9537,"style":2274},[2202],[2061,9539,9541,9544],{"className":9540},[2169],[2061,9542,2108],{"className":9543,"style":2281},[2169],[2061,9545,9547,9550],{"className":9546},[2169],[2061,9548,2119],{"className":9549},[2169,2170],[2061,9551,9553],{"className":9552},[2181],[2061,9554,9556,9576],{"className":9555},[2185,2186],[2061,9557,9559,9573],{"className":9558},[2190],[2061,9560,9562],{"className":9561,"style":2370},[2194],[2061,9563,9564,9567],{"style":2302},[2061,9565],{"className":9566,"style":2203},[2202],[2061,9568,9570],{"className":9569},[2207,2208,2209,2210],[2061,9571,2134],{"className":9572},[2169,2210],[2061,9574,2218],{"className":9575},[2217],[2061,9577,9579],{"className":9578},[2190],[2061,9580,9582],{"className":9581,"style":2225},[2194],[2061,9583],{},[2061,9585,9586,9589],{"style":2325},[2061,9587],{"className":9588,"style":2274},[2202],[2061,9590],{"className":9591,"style":2333},[2332],[2061,9593,9594,9597],{"style":2336},[2061,9595],{"className":9596,"style":2274},[2202],[2061,9598,9600,9603],{"className":9599},[2169],[2061,9601,2108],{"className":9602,"style":2281},[2169],[2061,9604,8609],{"className":9605},[2169,8708],[2061,9607,2218],{"className":9608},[2217],[2061,9610,9612],{"className":9611},[2190],[2061,9613,9615],{"className":9614,"style":2454},[2194],[2061,9616],{},[2061,9618],{"className":9619},[2444,2254],[2061,9621,9623,9626],{"style":9622},"top:-0.7713em;",[2061,9624],{"className":9625,"style":9397},[2202],[2061,9627,9629],{"className":9628},[2169],[2061,9630,9632,9635,9695],{"className":9631},[2169],[2061,9633],{"className":9634},[2253,2254],[2061,9636,9638],{"className":9637},[2101],[2061,9639,9641,9686],{"className":9640},[2185,2186],[2061,9642,9644,9683],{"className":9643},[2190],[2061,9645,9647,9661,9669],{"className":9646,"style":2846},[2194],[2061,9648,9649,9652],{"style":2270},[2061,9650],{"className":9651,"style":2274},[2202],[2061,9653,9655,9658],{"className":9654},[2169],[2061,9656,2108],{"className":9657,"style":2281},[2169],[2061,9659,8630],{"className":9660}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ame":10247},[2207,2208,2209,2210],[2061,10249,2134],{"className":10250},[2169,2210],[2061,10252,2218],{"className":10253},[2217],[2061,10255,10257],{"className":10256},[2190],[2061,10258,10260],{"className":10259,"style":2225},[2194],[2061,10261],{},[2061,10263,10265,10268],{"className":10264},[2169],[2061,10266,2119],{"className":10267},[2169,2170],[2061,10269,10271],{"className":10270},[2181],[2061,10272,10274,10294],{"className":10273},[2185,2186],[2061,10275,10277,10291],{"className":10276},[2190],[2061,10278,10280],{"className":10279,"style":2370},[2194],[2061,10281,10282,10285],{"style":2302},[2061,10283],{"className":10284,"style":2203},[2202],[2061,10286,10288],{"className":10287},[2207,2208,2209,2210],[2061,10289,2134],{"className":10290},[2169,2210],[2061,10292,2218],{"className":10293},[2217],[2061,10295,10297],{"className":10296},[2190],[2061,10298,10300],{"className":10299,"style":2225},[2194],[2061,10301],{},[2061,10303],{"className":10304,"style":2232},[2231],[2061,10306,2099],{"className":10307},[2236],[2061,10309],{"className":10310,"style":2232},[2231],[2061,10312,2513],{"className":10313},[2169],[2061,10315,2218],{"className":10316},[2217],[2061,10318,10320],{"className":10319},[2190],[2061,10321,10323],{"className":10322,"style":9707},[2194],[2061,10324],{},[1798,10326,10327,10328,10331,10332,10335],{},"从前两个式子可以得到 ",[1855,10329,10330],{},"MU₁\u002FMU₂ = p₁\u002Fp₂","，即相切条件。联立求解这三个方程，可以得到",[1865,10333,10334],{},"马歇尔需求函数 (Marshallian Demand Functions)","：",[2061,10337,10339],{"className":10338},[2064],[2061,10340,10342,10393],{"className":10341},[2068],[2061,10343,10345],{"className":10344},[2072],[2074,10346,10347],{"xmlns":2076,"display":2077},[2079,10348,10349,10390],{},[2082,10350,10351,10360,10362,10368,10370,10376,10378,10384,10386,10388],{},[2500,10352,10353,10355,10357],{},[2085,10354,2119],{},[2121,10356,2123],{},[2097,10358,10359],{},"∗",[2097,10361,2099],{},[2089,10363,10364,10366],{},[2085,10365,2119],{},[2121,10367,2123],{},[2097,10369,2114],{"stretchy":2113},[2089,10371,10372,10374],{},[2085,10373,1798],{},[2121,10375,2123],{},[2097,10377,2127],{"separator":2126},[2089,10379,10380,10382],{},[2085,10381,1798],{},[2121,10383,2134],{},[2097,10385,2127],{"separator":2126},[2085,10387,7160],{},[2097,10389,2137],{"stretchy":2113},[2149,10391,10392],{"encoding":2151},"x_1^* = x_1(p_1, p_2, m)",[2061,10394,10396,10464],{"className":10395,"ariaHidden":2126},[2156],[2061,10397,10399,10403,10455,10458,10461],{"className":10398},[2160],[2061,10400],{"className":10401,"style":10402},[2164],"height:0.9857em;vertical-align:-0.247em;",[2061,10404,10406,10409],{"className":10405},[2169],[2061,10407,2119],{"className":10408},[2169,2170],[2061,10410,10412],{"className":10411},[2181],[2061,10413,10415,10447],{"className":10414},[2185,2186],[2061,10416,10418,10444],{"className":10417},[2190],[2061,10419,10422,10433],{"className":10420,"style":10421},[2194],"height:0.7387em;",[2061,10423,10424,10427],{"style":4767},[2061,10425],{"className":10426,"style":2203},[2202],[2061,10428,10430],{"className":10429},[2207,2208,2209,2210],[2061,10431,2123],{"className":10432},[2169,2210],[2061,10434,10435,10438],{"style":4779},[2061,10436],{"className":10437,"style":2203},[2202],[2061,10439,10441],{"className":10440},[2207,2208,2209,2210],[2061,10442,10359],{"className":10443},[2984,2210],[2061,10445,2218],{"className":10446},[2217],[2061,10448,10450],{"className":10449},[2190],[2061,10451,10453],{"className":10452,"style":4802},[2194],[2061,10454],{},[2061,10456],{"className":10457,"style":2232},[2231],[2061,10459,2099],{"className":10460},[2236],[2061,10462],{"className":10463,"style":2232},[2231],[2061,10465,10467,10470,10510,10513,10553,10556,10559,10599,10602,10605,10608],{"className":10466},[2160],[2061,10468],{"className":10469,"style":4634},[2164],[2061,10471,10473,10476],{"className":10472},[2169],[2061,10474,2119],{"className":10475},[2169,2170],[2061,10477,10479],{"className":10478},[2181],[2061,10480,10482,10502],{"className":10481},[2185,2186],[2061,10483,10485,10499],{"className":10484},[2190],[2061,10486,10488],{"className":10487,"style":2370},[2194],[2061,10489,10490,10493],{"style":2302},[2061,10491],{"className":10492,"style":2203},[2202],[2061,10494,10496],{"className":10495},[2207,2208,2209,2210],[2061,10497,2123],{"className":10498},[2169,2210],[2061,10500,2218],{"className":10501},[2217],[2061,10503,10505],{"className":10504},[2190],[2061,10506,10508],{"className":10507,"style":2225},[2194],[2061,10509],{},[2061,10511,2114],{"className":10512},[2253],[2061,10514,10516,10519],{"className":10515},[2169],[2061,10517,1798],{"className":10518},[2169,2170],[2061,10520,10522],{"className":10521},[2181],[2061,10523,10525,10545],{"className":10524},[2185,2186],[2061,10526,10528,10542],{"className":10527},[2190],[2061,10529,10531],{"className":10530,"style":2370},[2194],[2061,10532,10533,10536],{"style":2302},[2061,10534],{"className":10535,"style":2203},[2202],[2061,10537,10539],{"className":10538},[2207,2208,2209,2210],[2061,10540,2123],{"className":10541},[2169,2210],[2061,10543,2218],{"className":10544},[2217],[2061,10546,10548],{"className":10547},[2190],[2061,10549,10551],{"className":10550,"style":2225},[2194],[2061,10552],{},[2061,10554,2127],{"className":10555},[2396],[2061,10557],{"className":10558,"style":2400},[2231],[2061,10560,10562,10565],{"className":10561},[2169],[2061,10563,1798],{"className":10564},[2169,2170],[2061,10566,10568],{"className":10567},[2181],[2061,10569,10571,10591],{"className":10570},[2185,2186],[2061,10572,10574,10588],{"className":10573},[2190],[2061,10575,10577],{"className":10576,"style":2370},[2194],[2061,10578,10579,10582],{"style":2302},[2061,10580],{"className":10581,"style":2203},[2202],[2061,10583,10585],{"className":10584},[2207,2208,2209,2210],[2061,10586,2134],{"className":10587},[2169,2210],[2061,10589,2218],{"className":10590},[2217],[2061,10592,10594],{"className":10593},[2190],[2061,10595,10597],{"className":10596,"style":2225},[2194],[2061,10598],{},[2061,10600,2127],{"className":10601},[2396],[2061,10603],{"className":10604,"style":2400},[2231],[2061,10606,7160],{"className":10607},[2169,2170],[2061,10609,2137],{"className":10610},[2444],[2061,10612,10614],{"className":10613},[2064],[2061,10615,10617,10667],{"className":10616},[2068],[2061,10618,10620],{"className":10619},[2072],[2074,10621,10622],{"xmlns":2076,"display":2077},[2079,10623,10624,10664],{},[2082,10625,10626,10634,10636,10642,10644,10650,10652,10658,10660,10662],{},[2500,10627,10628,10630,10632],{},[2085,10629,2119],{},[2121,10631,2134],{},[2097,10633,10359],{},[2097,10635,2099],{},[2089,10637,10638,10640],{},[2085,10639,2119],{},[2121,10641,2134],{},[2097,10643,2114],{"stretchy":2113},[2089,10645,10646,10648],{},[2085,10647,1798],{},[2121,10649,2123],{},[2097,10651,2127],{"separator":2126},[2089,10653,10654,10656],{},[2085,10655,1798],{},[2121,10657,2134],{},[2097,10659,2127],{"separator":2126},[2085,10661,7160],{},[2097,10663,2137],{"stretchy":2113},[2149,10665,10666],{"encoding":2151},"x_2^* = x_2(p_1, p_2, m)",[2061,10668,10670,10736],{"className":10669,"ariaHidden":2126},[2156],[2061,10671,10673,10676,10727,10730,10733],{"className":10672},[2160],[2061,10674],{"className":10675,"style":10402},[2164],[2061,10677,10679,10682],{"className":10678},[2169],[2061,10680,2119],{"className":10681},[2169,2170],[2061,10683,10685],{"className":10684},[2181],[2061,10686,10688,10719],{"className":10687},[2185,2186],[2061,10689,10691,10716],{"className":10690},[2190],[2061,10692,10694,10705],{"className":10693,"style":10421},[2194],[2061,10695,10696,10699],{"style":4767},[2061,10697],{"className":10698,"style":2203},[2202],[2061,10700,10702],{"className":10701},[2207,2208,2209,2210],[2061,10703,2134],{"className":10704},[2169,2210],[2061,10706,10707,10710],{"style":4779},[2061,10708],{"className":10709,"style":2203},[2202],[2061,10711,10713],{"className":10712},[2207,2208,2209,2210],[2061,10714,10359],{"className":10715},[2984,2210],[2061,10717,2218],{"className":10718},[2217],[2061,10720,10722],{"className":10721},[2190],[2061,10723,10725],{"className":10724,"style":4802},[2194],[2061,10726],{},[2061,10728],{"className":10729,"style":2232},[2231],[2061,10731,2099],{"className":10732},[2236],[2061,10734],{"className":10735,"style":2232},[2231],[2061,10737,10739,10742,10782,10785,10825,10828,10831,10871,10874,10877,10880],{"className":10738},[2160],[2061,10740],{"className":10741,"style":4634},[2164],[2061,10743,10745,10748],{"className":10744},[2169],[2061,10746,2119],{"className":10747},[2169,2170],[2061,10749,10751],{"className":10750},[2181],[2061,10752,10754,10774],{"className":10753},[2185,2186],[2061,10755,10757,10771],{"className":10756},[2190],[2061,10758,10760],{"className":10759,"style":2370},[2194],[2061,10761,10762,10765],{"style":2302},[2061,10763],{"className":10764,"style":2203},[2202],[2061,10766,10768],{"className":10767},[2207,2208,2209,2210],[2061,10769,2134],{"className":10770},[2169,2210],[2061,10772,2218],{"className":10773},[2217],[2061,10775,10777],{"className":10776},[2190],[2061,10778,10780],{"className":10779,"style":2225},[2194],[2061,10781],{},[2061,10783,2114],{"className":10784},[2253],[2061,10786,10788,10791],{"className":10787},[2169],[2061,10789,1798],{"className":10790},[2169,2170],[2061,10792,10794],{"className":10793},[2181],[2061,10795,10797,10817],{"className":10796},[2185,2186],[2061,10798,10800,10814],{"className":10799},[2190],[2061,10801,10803],{"className":10802,"style":2370},[2194],[2061,10804,10805,10808],{"style":2302},[2061,10806],{"className":10807,"style":2203},[2202],[2061,10809,10811],{"className":10810},[2207,2208,2209,2210],[2061,10812,2123],{"className":10813},[2169,2210],[2061,10815,2218],{"className":10816},[2217],[2061,10818,10820],{"className":10819},[2190],[2061,10821,10823],{"className":10822,"style":2225},[2194],[2061,10824],{},[2061,10826,2127],{"className":10827},[2396],[2061,10829],{"className":10830,"style":2400},[2231],[2061,10832,10834,10837],{"className":10833},[2169],[2061,10835,1798],{"className":10836},[2169,2170],[2061,10838,10840],{"className":10839},[2181],[2061,10841,10843,10863],{"className":10842},[2185,2186],[2061,10844,10846,10860],{"className":10845},[2190],[2061,10847,10849],{"className":10848,"style":2370},[2194],[2061,10850,10851,10854],{"style":2302},[2061,10852],{"className":10853,"style":2203},[2202],[2061,10855,10857],{"className":10856},[2207,2208,2209,2210],[2061,10858,2134],{"className":10859},[2169,2210],[2061,10861,2218],{"className":10862},[2217],[2061,10864,10866],{"className":10865},[2190],[2061,10867,10869],{"className":10868,"style":2225},[2194],[2061,10870],{},[2061,10872,2127],{"className":10873},[2396],[2061,10875],{"className":10876,"style":2400},[2231],[2061,10878,7160],{"className":10879},[2169,2170],[2061,10881,2137],{"className":10882},[2444],[1798,10884,10885,10886,10889],{},"将最优解代回效用函数，得到",[1865,10887,10888],{},"间接效用函数 (Indirect Utility Function)","，它表示在给定价格和收入下，消费者能达到的最大效用水平：",[2061,10891,10893],{"className":10892},[2064],[2061,10894,10896,11002],{"className":10895},[2068],[2061,10897,10899],{"className":10898},[2072],[2074,10900,10901],{"xmlns":2076,"display":2077},[2079,10902,10903,10999],{},[2082,10904,10905,10907,10909,10915,10917,10923,10925,10927,10929,10931,10933,10935,10943,10945,10951,10953,10959,10961,10963,10965,10967,10975,10977,10983,10985,10991,10993,10995,10997],{},[2085,10906,6887],{},[2097,10908,2114],{"stretchy":2113},[2089,10910,10911,10913],{},[2085,10912,1798],{},[2121,10914,2123],{},[2097,10916,2127],{"separator":2126},[2089,10918,10919,10921],{},[2085,10920,1798],{},[2121,10922,2134],{},[2097,10924,2127],{"separator":2126},[2085,10926,7160],{},[2097,10928,2137],{"stretchy":2113},[2097,10930,2099],{},[2085,10932,2005],{},[2097,10934,2114],{"stretchy":2113},[2500,10936,10937,10939,10941],{},[2085,10938,2119],{},[2121,10940,2123],{},[2097,10942,10359],{},[2097,10944,2114],{"stretchy":2113},[2089,10946,10947,10949],{},[2085,10948,1798],{},[2121,10950,2123],{},[2097,10952,2127],{"separator":2126},[2089,10954,10955,10957],{},[2085,10956,1798],{},[2121,10958,2134],{},[2097,10960,2127],{"separator":2126},[2085,10962,7160],{},[2097,10964,2137],{"stretchy":2113},[2097,10966,2127],{"separator":2126},[2500,10968,10969,10971,10973],{},[2085,10970,2119],{},[2121,10972,2134],{},[2097,10974,10359],{},[2097,10976,2114],{"stretchy":2113},[2089,10978,10979,10981],{},[2085,10980,1798],{},[2121,10982,2123],{},[2097,10984,2127],{"separator":2126},[2089,10986,10987,10989],{},[2085,10988,1798],{},[2121,10990,2134],{},[2097,10992,2127],{"separator":2126},[2085,10994,7160],{},[2097,10996,2137],{"stretchy":2113},[2097,10998,2137],{"stretchy":2113},[2149,11000,11001],{"encoding":2151},"v(p_1, p_2, m) = U(x_1^*(p_1, p_2, m), x_2^*(p_1, p_2, m))",[2061,11003,11005,11124],{"className":11004,"ariaHidden":2126},[2156],[2061,11006,11008,11011,11014,11017,11057,11060,11063,11103,11106,11109,11112,11115,11118,11121],{"className":11007},[2160],[2061,11009],{"className":11010,"style":4634},[2164],[2061,11012,6887],{"className":11013,"style":6572},[2169,2170],[2061,11015,2114],{"className":11016},[2253],[2061,11018,11020,11023],{"className":11019},[2169],[2061,11021,1798],{"className":11022},[2169,2170],[2061,11024,11026],{"className":11025},[2181],[2061,11027,11029,11049],{"className":11028},[2185,2186],[2061,11030,11032,11046],{"className":11031},[2190],[2061,11033,11035],{"className":11034,"style":2370},[2194],[2061,11036,11037,11040],{"style":2302},[2061,11038],{"className":11039,"style":2203},[2202],[2061,11041,11043],{"className":11042},[2207,2208,2209,2210],[2061,11044,2123],{"className":11045},[2169,2210],[2061,11047,2218],{"className":11048},[2217],[2061,11050,11052],{"className":11051},[2190],[2061,11053,11055],{"className":11054,"style":2225},[2194],[2061,11056],{},[2061,11058,2127],{"className":11059},[2396],[2061,11061],{"className":11062,"style":2400},[2231],[2061,11064,11066,11069],{"className":11065},[2169],[2061,11067,1798],{"className":11068},[2169,2170],[2061,11070,11072],{"className":11071},[2181],[2061,11073,11075,11095],{"className":11074},[2185,2186],[2061,11076,11078,11092],{"className":11077},[2190],[2061,11079,11081],{"className":11080,"style":2370},[2194],[2061,11082,11083,11086],{"style":2302},[2061,11084],{"className":11085,"style":2203},[2202],[2061,11087,11089],{"className":11088},[2207,2208,2209,2210],[2061,11090,2134],{"className":11091},[2169,2210],[2061,11093,2218],{"className":11094},[2217],[2061,11096,11098],{"className":11097},[2190],[2061,11099,11101],{"className":11100,"style":2225},[2194],[2061,11102],{},[2061,11104,2127],{"className":11105},[2396],[2061,11107],{"className":11108,"style":2400},[2231],[2061,11110,7160],{"className":11111},[2169,2170],[2061,11113,2137],{"className":11114},[2444],[2061,11116],{"className":11117,"style":2232},[2231],[2061,11119,2099],{"className":11120},[2236],[2061,11122],{"className":11123,"style":2232},[2231],[2061,11125,11127,11130,11133,11136,11187,11190,11230,11233,11236,11276,11279,11282,11285,11288,11291,11294,11345,11348,11388,11391,11394,11434,11437,11440,11443],{"className":11126},[2160],[2061,11128],{"className":11129,"style":4634},[2164],[2061,11131,2005],{"className":11132,"style":2171},[2169,2170],[2061,11134,2114],{"className":11135},[2253],[2061,11137,11139,11142],{"className":11138},[2169],[2061,11140,2119],{"className":11141},[2169,2170],[2061,11143,11145],{"className":11144},[2181],[2061,11146,11148,11179],{"className":11147},[2185,2186],[2061,11149,11151,11176],{"className":11150},[2190],[2061,11152,11154,11165],{"className":11153,"style":10421},[2194],[2061,11155,11156,11159],{"style":4767},[2061,11157],{"className":11158,"style":2203},[2202],[2061,11160,11162],{"className":11161},[2207,2208,2209,2210],[2061,11163,2123],{"className":11164},[2169,2210],[2061,11166,11167,11170],{"style":4779},[2061,11168],{"className":11169,"style":2203},[2202],[2061,11171,11173],{"className":11172},[2207,2208,2209,2210],[2061,11174,10359],{"className":11175},[2984,2210],[2061,11177,2218],{"className":11178},[2217],[2061,11180,11182],{"className":11181},[2190],[2061,11183,11185],{"className":11184,"style":4802},[2194],[2061,11186],{},[2061,11188,2114],{"className":11189},[2253],[2061,11191,11193,11196],{"className":11192},[2169],[2061,11194,1798],{"className":11195},[2169,2170],[2061,11197,11199],{"className":11198},[2181],[2061,11200,11202,11222],{"className":11201},[2185,2186],[2061,11203,11205,11219],{"className":11204},[2190],[2061,11206,11208],{"className":11207,"style":2370},[2194],[2061,11209,11210,11213],{"style":2302},[2061,11211],{"className":11212,"style":2203},[2202],[2061,11214,11216],{"className":11215},[2207,2208,2209,2210],[2061,11217,2123],{"className":11218},[2169,2210],[2061,11220,2218],{"className":11221},[2217],[2061,11223,11225],{"className":11224},[2190],[2061,11226,11228],{"className":11227,"style":2225},[2194],[2061,11229],{},[2061,11231,2127],{"className":11232},[2396],[2061,11234],{"className":11235,"style":2400},[2231],[2061,11237,11239,11242],{"className":11238},[2169],[2061,11240,1798],{"className":11241},[2169,2170],[2061,11243,11245],{"className":11244},[2181],[2061,11246,11248,11268],{"className":11247},[2185,2186],[2061,11249,11251,11265],{"className":11250},[2190],[2061,11252,11254],{"className":11253,"style":2370},[2194],[2061,11255,11256,11259],{"style":2302},[2061,11257],{"className":11258,"style":2203},[2202],[2061,11260,11262],{"className":11261},[2207,2208,2209,2210],[2061,11263,2134],{"className":11264},[2169,2210],[2061,11266,2218],{"className":11267},[2217],[2061,11269,11271],{"className":11270},[2190],[2061,11272,11274],{"className":11273,"style":2225},[2194],[2061,11275],{},[2061,11277,2127],{"className":11278},[2396],[2061,11280],{"className":11281,"style":2400},[2231],[2061,11283,7160],{"className":11284},[2169,2170],[2061,11286,2137],{"className":11287},[2444],[2061,11289,2127],{"className":11290},[2396],[2061,11292],{"className":11293,"style":2400},[2231],[2061,11295,11297,11300],{"className":11296},[2169],[2061,11298,2119],{"className":11299},[2169,2170],[2061,11301,11303],{"className":11302},[2181],[2061,11304,11306,11337],{"className":11305},[2185,2186],[2061,11307,11309,11334],{"className":11308},[2190],[2061,11310,11312,11323],{"className":11311,"style":10421},[2194],[2061,11313,11314,11317],{"style":4767},[2061,11315],{"className":11316,"style":2203},[2202],[2061,11318,11320],{"className":11319},[2207,2208,2209,2210],[2061,11321,2134],{"className":11322},[2169,2210],[2061,11324,11325,11328],{"style":4779},[2061,11326],{"className":11327,"style":2203},[2202],[2061,11329,11331],{"className":11330},[2207,2208,2209,2210],[2061,11332,10359],{"className":11333},[2984,2210],[2061,11335,2218],{"className":11336},[2217],[2061,11338,11340],{"className":11339},[2190],[2061,11341,11343],{"className":11342,"style":4802},[2194],[2061,11344],{},[2061,11346,2114],{"className":11347},[2253],[2061,11349,11351,11354],{"className":11350},[2169],[2061,11352,1798],{"className":11353},[2169,2170],[2061,11355,11357],{"className":11356},[2181],[2061,11358,11360,11380],{"className":11359},[2185,2186],[2061,11361,11363,11377],{"className":11362},[2190],[2061,11364,11366],{"className":11365,"style":2370},[2194],[2061,11367,11368,11371],{"style":2302},[2061,11369],{"className":11370,"style":2203},[2202],[2061,11372,11374],{"className":11373},[2207,2208,2209,2210],[2061,11375,2123],{"className":11376},[2169,2210],[2061,11378,2218],{"className":11379},[2217],[2061,11381,11383],{"className":11382},[2190],[2061,11384,11386],{"className":11385,"style":2225},[2194],[2061,11387],{},[2061,11389,2127],{"className":11390},[2396],[2061,11392],{"className":11393,"style":2400},[2231],[2061,11395,11397,11400],{"className":11396},[2169],[2061,11398,1798],{"className":11399},[2169,2170],[2061,11401,11403],{"className":11402},[2181],[2061,11404,11406,11426],{"className":11405},[2185,2186],[2061,11407,11409,11423],{"className":11408},[2190],[2061,11410,11412],{"className":11411,"style":2370},[2194],[2061,11413,11414,11417],{"style":2302},[2061,11415],{"className":11416,"style":2203},[2202],[2061,11418,11420],{"className":11419},[2207,2208,2209,2210],[2061,11421,2134],{"className":11422},[2169,2210],[2061,11424,2218],{"className":11425},[2217],[2061,11427,11429],{"className":11428},[2190],[2061,11430,11432],{"className":11431,"style":2225},[2194],[2061,11433],{},[2061,11435,2127],{"className":11436},[2396],[2061,11438],{"className":11439,"style":2400},[2231],[2061,11441,7160],{"className":11442},[2169,2170],[2061,11444,11446],{"className":11445},[2444],"))",[1840,11448],{},[1794,11450,11452],{"id":11451},"_3-对偶问题与重要恒等式","3. 对偶问题与重要恒等式",[1847,11454,11456],{"id":11455},"_31-支出最小化问题-expenditure-minimization-problem-emp","3.1 支出最小化问题 (Expenditure Minimization Problem, EMP)",[1798,11458,11459,11460,11463],{},"这是效用最大化问题的对偶问题：为了达到一个给定的效用水平 ",[1855,11461,11462],{},"u","，消费者最少需要花费多少钱？",[2061,11465,11467],{"className":11466},[2064],[2061,11468,11470,11563],{"className":11469},[2068],[2061,11471,11473],{"className":11472},[2072],[2074,11474,11475],{"xmlns":2076,"display":2077},[2079,11476,11477,11560],{},[2082,11478,11479,11503,11509,11515,11517,11523,11529,11531,11533,11535,11537,11539,11545,11547,11553,11555,11558],{},[7453,11480,11481,11487],{},[2082,11482,11483,11485],{},[2085,11484,5777],{},[2097,11486,4951],{},[2082,11488,11489,11495,11497],{},[2089,11490,11491,11493],{},[2085,11492,2119],{},[2121,11494,2123],{},[2097,11496,2127],{"separator":2126},[2089,11498,11499,11501],{},[2085,11500,2119],{},[2121,11502,2134],{},[2089,11504,11505,11507],{},[2085,11506,1798],{},[2121,11508,2123],{},[2089,11510,11511,11513],{},[2085,11512,2119],{},[2121,11514,2123],{},[2097,11516,2762],{},[2089,11518,11519,11521],{},[2085,11520,1798],{},[2121,11522,2134],{},[2089,11524,11525,11527],{},[2085,11526,2119],{},[2121,11528,2134],{},[2231,11530],{"width":4610},[7501,11532,7503],{},[2231,11534],{"width":4610},[2085,11536,2005],{},[2097,11538,2114],{"stretchy":2113},[2089,11540,11541,11543],{},[2085,11542,2119],{},[2121,11544,2123],{},[2097,11546,2127],{"separator":2126},[2089,11548,11549,11551],{},[2085,11550,2119],{},[2121,11552,2134],{},[2097,11554,2137],{"stretchy":2113},[2097,11556,11557],{},"≥",[2085,11559,11462],{},[2149,11561,11562],{"encoding":2151},"\\min_{x_1, x_2} p_1 x_1 + p_2 x_2 \\quad \\text{s.t.} \\quad U(x_1, x_2) \\ge u",[2061,11564,11566,11793,11995],{"className":11565,"ariaHidden":2126},[2156],[2061,11567,11569,11573,11701,11704,11744,11784,11787,11790],{"className":11568},[2160],[2061,11570],{"className":11571,"style":11572},[2164],"height:1.504em;vertical-align:-0.8361em;",[2061,11574,11576],{"className":11575},[5104,7552],[2061,11577,11579,11693],{"className":11578},[2185,2186],[2061,11580,11582,11690],{"className":11581},[2190],[2061,11583,11586,11680],{"className":11584,"style":11585},[2194],"height:0.6679em;",[2061,11587,11588,11591],{"style":7564},[2061,11589],{"className":11590,"style":2274},[2202],[2061,11592,11594],{"className":11593},[2207,2208,2209,2210],[2061,11595,11597,11637,11640],{"className":11596},[2169,2210],[2061,11598,11600,11603],{"className":11599},[2169,2210],[2061,11601,2119],{"className":11602},[2169,2170,2210],[2061,11604,11606],{"className":11605},[2181],[2061,11607,11609,11629],{"className":11608},[2185,2186],[2061,11610,11612,11626],{"className":11611},[2190],[2061,11613,11615],{"className":11614,"style":5322},[2194],[2061,11616,11617,11620],{"style":5325},[2061,11618],{"className":11619,"style":5329},[2202],[2061,11621,11623],{"className":11622},[2207,5333,5334,2210],[2061,11624,2123],{"className":11625},[2169,2210],[2061,11627,2218],{"className":11628},[2217],[2061,11630,11632],{"className":11631},[2190],[2061,11633,11635],{"className":11634,"style":5347},[2194],[2061,11636],{},[2061,11638,2127],{"className":11639},[2396,2210],[2061,11641,11643,11646],{"className":11642},[2169,2210],[2061,11644,2119],{"className":11645},[2169,2170,2210],[2061,11647,11649],{"className":11648},[2181],[2061,11650,11652,11672],{"className":11651},[2185,2186],[2061,11653,11655,11669],{"className":11654},[2190],[2061,11656,11658],{"className":11657,"style":5322},[2194],[2061,11659,11660,11663],{"style":5325},[2061,11661],{"className":11662,"style":5329},[2202],[2061,11664,11666],{"className":11665},[2207,5333,5334,2210],[2061,11667,2134],{"className":11668},[2169,2210],[2061,11670,2218],{"className":11671},[2217],[2061,11673,11675],{"className":11674},[2190],[2061,11676,11678],{"className":11677,"style":5347},[2194],[2061,11679],{},[2061,11681,11682,11685],{"style":7659},[2061,11683],{"className":11684,"style":2274},[2202],[2061,11686,11687],{},[2061,11688,5777],{"className":11689},[5104],[2061,11691,2218],{"className":11692},[2217],[2061,11694,11696],{"className":11695},[2190],[2061,11697,11699],{"className":11698,"style":7677},[2194],[2061,11700],{},[2061,11702],{"className":11703,"style":2400},[2231],[2061,11705,11707,11710],{"className":11706},[2169],[2061,11708,1798],{"className":11709},[2169,2170],[2061,11711,11713],{"className":11712},[2181],[2061,11714,11716,11736],{"className":11715},[2185,2186],[2061,11717,11719,11733],{"className":11718},[2190],[2061,11720,11722],{"className":11721,"style":2370},[2194],[2061,11723,11724,11727],{"style":2302},[2061,11725],{"className":11726,"style":2203},[2202],[2061,11728,11730],{"className":11729},[2207,2208,2209,2210],[2061,11731,2123],{"className":11732},[2169,2210],[2061,11734,2218],{"className":11735},[2217],[2061,11737,11739],{"className":11738},[2190],[2061,11740,11742],{"className":11741,"style":2225},[2194],[2061,11743],{},[2061,11745,11747,11750],{"className":11746},[2169],[2061,11748,2119],{"className":11749},[2169,2170],[2061,11751,11753],{"className":11752},[2181],[2061,11754,11756,11776],{"className":11755},[2185,2186],[2061,11757,11759,11773],{"className":11758},[2190],[2061,11760,11762],{"className":11761,"style":2370},[2194],[2061,11763,11764,11767],{"style":2302},[2061,11765],{"className":11766,"style":2203},[2202],[2061,11768,11770],{"className":11769},[2207,2208,2209,2210],[2061,11771,2123],{"className":11772},[2169,2210],[2061,11774,2218],{"className":11775},[2217],[2061,11777,11779],{"className":11778},[2190],[2061,11780,11782],{"className":11781,"style":2225},[2194],[2061,11783],{},[2061,11785],{"className":11786,"style":2980},[2231],[2061,11788,2762],{"className":11789},[2984],[2061,11791],{"className":11792,"style":2980},[2231],[2061,11794,11796,11799,11839,11879,11882,11888,11891,11894,11897,11937,11940,11943,11983,11986,11989,11992],{"className":11795},[2160],[2061,11797],{"className":11798,"style":4634},[2164],[2061,11800,11802,11805],{"className":11801},[2169],[2061,11803,1798],{"className":11804},[2169,2170],[2061,11806,11808],{"className":11807},[2181],[2061,11809,11811,11831],{"className":11810},[2185,2186],[2061,11812,11814,11828],{"className":11813},[2190],[2061,11815,11817],{"className":11816,"style":2370},[2194],[2061,11818,11819,11822],{"style":2302},[2061,11820],{"className":11821,"style":2203},[2202],[2061,11823,11825],{"className":11824},[2207,2208,2209,2210],[2061,11826,2134],{"className":11827},[2169,2210],[2061,11829,2218],{"className":11830},[2217],[2061,11832,11834],{"className":11833},[2190],[2061,11835,11837],{"className":11836,"style":2225},[2194],[2061,11838],{},[2061,11840,11842,11845],{"className":11841},[2169],[2061,11843,2119],{"className":11844},[2169,2170],[2061,11846,11848],{"className":11847},[2181],[2061,11849,11851,11871],{"className":11850},[2185,2186],[2061,11852,11854,11868],{"className":11853},[2190],[2061,11855,11857],{"className":11856,"style":2370},[2194],[2061,11858,11859,11862],{"style":2302},[2061,11860],{"className":11861,"style":2203},[2202],[2061,11863,11865],{"className":11864},[2207,2208,2209,2210],[2061,11866,2134],{"className":11867},[2169,2210],[2061,11869,2218],{"className":11870},[2217],[2061,11872,11874],{"className":11873},[2190],[2061,11875,11877],{"className":11876,"style":2225},[2194],[2061,11878],{},[2061,11880],{"className":11881,"style":4870},[2231],[2061,11883,11885],{"className":11884},[2169,7784],[2061,11886,7503],{"className":11887},[2169],[2061,11889],{"className":11890,"style":4870},[2231],[2061,11892,2005],{"className":11893,"style":2171},[2169,2170],[2061,11895,2114],{"className":11896},[2253],[2061,11898,11900,11903],{"className":11899},[2169],[2061,11901,2119],{"className":11902},[2169,2170],[2061,11904,11906],{"className":11905},[2181],[2061,11907,11909,11929],{"className":11908},[2185,2186],[2061,11910,11912,11926],{"className":11911},[2190],[2061,11913,11915],{"className":11914,"style":2370},[2194],[2061,11916,11917,11920],{"style":2302},[2061,11918],{"className":11919,"style":2203},[2202],[2061,11921,11923],{"className":11922},[2207,2208,2209,2210],[2061,11924,2123],{"className":11925},[2169,2210],[2061,11927,2218],{"className":11928},[2217],[2061,11930,11932],{"className":11931},[2190],[2061,11933,11935],{"className":11934,"style":2225},[2194],[2061,11936],{},[2061,11938,2127],{"className":11939},[2396],[2061,11941],{"className":11942,"style":2400},[2231],[2061,11944,11946,11949],{"className":11945},[2169],[2061,11947,2119],{"className":11948},[2169,2170],[2061,11950,11952],{"className":11951},[2181],[2061,11953,11955,11975],{"className":11954},[2185,2186],[2061,11956,11958,11972],{"className":11957},[2190],[2061,11959,11961],{"className":11960,"style":2370},[2194],[2061,11962,11963,11966],{"style":2302},[2061,11964],{"className":11965,"style":2203},[2202],[2061,11967,11969],{"className":11968},[2207,2208,2209,2210],[2061,11970,2134],{"className":11971},[2169,2210],[2061,11973,2218],{"className":11974},[2217],[2061,11976,11978],{"className":11977},[2190],[2061,11979,11981],{"className":11980,"style":2225},[2194],[2061,11982],{},[2061,11984,2137],{"className":11985},[2444],[2061,11987],{"className":11988,"style":2232},[2231],[2061,11990,11557],{"className":11991},[2236],[2061,11993],{"className":11994,"style":2232},[2231],[2061,11996,11998,12001],{"className":11997},[2160],[2061,11999],{"className":12000,"style":6568},[2164],[2061,12002,11462],{"className":12003},[2169,2170],[1798,12005,12006,12007,10335],{},"同样使用拉格朗日法求解，可以得到",[1865,12008,12009],{},"希克斯需求函数 (Hicksian \u002F Compensated Demand Functions)",[2061,12011,12013],{"className":12012},[2064],[2061,12014,12016,12067],{"className":12015},[2068],[2061,12017,12019],{"className":12018},[2072],[2074,12020,12021],{"xmlns":2076,"display":2077},[2079,12022,12023,12064],{},[2082,12024,12025,12034,12036,12042,12044,12050,12052,12058,12060,12062],{},[2500,12026,12027,12030,12032],{},[2085,12028,12029],{},"h",[2121,12031,2123],{},[2097,12033,10359],{},[2097,12035,2099],{},[2089,12037,12038,12040],{},[2085,12039,12029],{},[2121,12041,2123],{},[2097,12043,2114],{"stretchy":2113},[2089,12045,12046,12048],{},[2085,12047,1798],{},[2121,12049,2123],{},[2097,12051,2127],{"separator":2126},[2089,12053,12054,12056],{},[2085,12055,1798],{},[2121,12057,2134],{},[2097,12059,2127],{"separator":2126},[2085,12061,11462],{},[2097,12063,2137],{"stretchy":2113},[2149,12065,12066],{"encoding":2151},"h_1^* = h_1(p_1, p_2, u)",[2061,12068,12070,12136],{"className":12069,"ariaHidden":2126},[2156],[2061,12071,12073,12076,12127,12130,12133],{"className":12072},[2160],[2061,12074],{"className":12075,"style":10402},[2164],[2061,12077,12079,12082],{"className":12078},[2169],[2061,12080,12029],{"className":12081},[2169,2170],[2061,12083,12085],{"className":12084},[2181],[2061,12086,12088,12119],{"className":12087},[2185,2186],[2061,12089,12091,12116],{"className":12090},[2190],[2061,12092,12094,12105],{"className":12093,"style":10421},[2194],[2061,12095,12096,12099],{"style":4767},[2061,12097],{"className":12098,"style":2203},[2202],[2061,12100,12102],{"className":12101},[2207,2208,2209,2210],[2061,12103,2123],{"className":12104},[2169,2210],[2061,12106,12107,12110],{"style":4779},[2061,12108],{"className":12109,"style":2203},[2202],[2061,12111,12113],{"className":12112},[2207,2208,2209,2210],[2061,12114,10359],{"className":12115},[2984,2210],[2061,12117,2218],{"className":12118},[2217],[2061,12120,12122],{"className":12121},[2190],[2061,12123,12125],{"className":12124,"style":4802},[2194],[2061,12126],{},[2061,12128],{"className":12129,"style":2232},[2231],[2061,12131,2099],{"className":12132},[2236],[2061,12134],{"className":12135,"style":2232},[2231],[2061,12137,12139,12142,12182,12185,12225,12228,12231,12271,12274,12277,12280],{"className":12138},[2160],[2061,12140],{"className":12141,"style":4634},[2164],[2061,12143,12145,12148],{"className":12144},[2169],[2061,12146,12029],{"className":12147},[2169,2170],[2061,12149,12151],{"className":12150},[2181],[2061,12152,12154,12174],{"className":12153},[2185,2186],[2061,12155,12157,12171],{"className":12156},[2190],[2061,12158,12160],{"className":12159,"style":2370},[2194],[2061,12161,12162,12165],{"style":2302},[2061,12163],{"className":12164,"style":2203},[2202],[2061,12166,12168],{"className":12167},[2207,2208,2209,2210],[2061,12169,2123],{"className":12170},[2169,2210],[2061,12172,2218],{"className":12173},[2217],[2061,12175,12177],{"className":12176},[2190],[2061,12178,12180],{"className":12179,"style":2225},[2194],[2061,12181],{},[2061,12183,2114],{"className":12184},[2253],[2061,12186,12188,12191],{"className":12187},[2169],[2061,12189,1798],{"className":12190},[2169,2170],[2061,12192,12194],{"className":12193},[2181],[2061,12195,12197,12217],{"className":12196},[2185,2186],[2061,12198,12200,12214],{"className":12199},[2190],[2061,12201,12203],{"className":12202,"style":2370},[2194],[2061,12204,12205,12208],{"style":2302},[2061,12206],{"className":12207,"style":2203},[2202],[2061,12209,12211],{"className":12210},[2207,2208,2209,2210],[2061,12212,2123],{"className":12213},[2169,2210],[2061,12215,2218],{"className":12216},[2217],[2061,12218,12220],{"className":12219},[2190],[2061,12221,12223],{"className":12222,"style":2225},[2194],[2061,12224],{},[2061,12226,2127],{"className":12227},[2396],[2061,12229],{"className":12230,"style":2400},[2231],[2061,12232,12234,12237],{"className":12233},[2169],[2061,12235,1798],{"className":12236},[2169,2170],[2061,12238,12240],{"className":12239},[2181],[2061,12241,12243,12263],{"className":12242},[2185,2186],[2061,12244,12246,12260],{"className":12245},[2190],[2061,12247,12249],{"className":12248,"style":2370},[2194],[2061,12250,12251,12254],{"style":2302},[2061,12252],{"className":12253,"style":2203},[2202],[2061,12255,12257],{"className":12256},[2207,2208,2209,2210],[2061,12258,2134],{"className":12259},[2169,2210],[2061,12261,2218],{"className":12262},[2217],[2061,12264,12266],{"className":12265},[2190],[2061,12267,12269],{"className":12268,"style":2225},[2194],[2061,12270],{},[2061,12272,2127],{"className":12273},[2396],[2061,12275],{"className":12276,"style":2400},[2231],[2061,12278,11462],{"className":12279},[2169,2170],[2061,12281,2137],{"className":12282},[2444],[2061,12284,12286],{"className":12285},[2064],[2061,12287,12289,12339],{"className":12288},[2068],[2061,12290,12292],{"className":12291},[2072],[2074,12293,12294],{"xmlns":2076,"display":2077},[2079,12295,12296,12336],{},[2082,12297,12298,12306,12308,12314,12316,12322,12324,12330,12332,12334],{},[2500,12299,12300,12302,12304],{},[2085,12301,12029],{},[2121,12303,2134],{},[2097,12305,10359],{},[2097,12307,2099],{},[2089,12309,12310,12312],{},[2085,12311,12029],{},[2121,12313,2134],{},[2097,12315,2114],{"stretchy":2113},[2089,12317,12318,12320],{},[2085,12319,1798],{},[2121,12321,2123],{},[2097,12323,2127],{"separator":2126},[2089,12325,12326,12328],{},[2085,12327,1798],{},[2121,12329,2134],{},[2097,12331,2127],{"separator":2126},[2085,12333,11462],{},[2097,12335,2137],{"stretchy":2113},[2149,12337,12338],{"encoding":2151},"h_2^* = h_2(p_1, p_2, u)",[2061,12340,12342,12408],{"className":12341,"ariaHidden":2126},[2156],[2061,12343,12345,12348,12399,12402,12405],{"className":12344},[2160],[2061,12346],{"className":12347,"style":10402},[2164],[2061,12349,12351,12354],{"className":12350},[2169],[2061,12352,12029],{"className":12353},[2169,2170],[2061,12355,12357],{"className":12356},[2181],[2061,12358,12360,12391],{"className":12359},[2185,2186],[2061,12361,12363,12388],{"className":12362},[2190],[2061,12364,12366,12377],{"className":12365,"style":10421},[2194],[2061,12367,12368,12371],{"style":4767},[2061,12369],{"className":12370,"style":2203},[2202],[2061,12372,12374],{"className":12373},[2207,2208,2209,2210],[2061,12375,2134],{"className":12376},[2169,2210],[2061,12378,12379,12382],{"style":4779},[2061,12380],{"className":12381,"style":2203},[2202],[2061,12383,12385],{"className":12384},[2207,2208,2209,2210],[2061,12386,10359],{"className":12387},[2984,2210],[2061,12389,2218],{"className":12390},[2217],[2061,12392,12394],{"className":12393},[2190],[2061,12395,12397],{"className":12396,"style":4802},[2194],[2061,12398],{},[2061,12400],{"className":12401,"style":2232},[2231],[2061,12403,2099],{"className":12404},[2236],[2061,12406],{"className":12407,"style":2232},[2231],[2061,12409,12411,12414,12454,12457,12497,12500,12503,12543,12546,12549,12552],{"className":12410},[2160],[2061,12412],{"className":12413,"style":4634},[2164],[2061,12415,12417,12420],{"className":12416},[2169],[2061,12418,12029],{"className":12419},[2169,2170],[2061,12421,12423],{"className":12422},[2181],[2061,12424,12426,12446],{"className":12425},[2185,2186],[2061,12427,12429,12443],{"className":12428},[2190],[2061,12430,12432],{"className":12431,"style":2370},[2194],[2061,12433,12434,12437],{"style":2302},[2061,12435],{"className":12436,"style":2203},[2202],[2061,12438,12440],{"className":12439},[2207,2208,2209,2210],[2061,12441,2134],{"className":12442},[2169,2210],[2061,12444,2218],{"className":12445},[2217],[2061,12447,12449],{"className":12448},[2190],[2061,12450,12452],{"className":12451,"style":2225},[2194],[2061,12453],{},[2061,12455,2114],{"className":12456},[2253],[2061,12458,12460,12463],{"className":12459},[2169],[2061,12461,1798],{"className":12462},[2169,2170],[2061,12464,12466],{"className":12465},[2181],[2061,12467,12469,12489],{"className":12468},[2185,2186],[2061,12470,12472,12486],{"className":12471},[2190],[2061,12473,12475],{"className":12474,"style":2370},[2194],[2061,12476,12477,12480],{"style":2302},[2061,12478],{"className":12479,"style":2203},[2202],[2061,12481,12483],{"className":12482},[2207,2208,2209,2210],[2061,12484,2123],{"className":12485},[2169,2210],[2061,12487,2218],{"className":12488},[2217],[2061,12490,12492],{"className":12491},[2190],[2061,12493,12495],{"className":12494,"style":2225},[2194],[2061,12496],{},[2061,12498,2127],{"className":12499},[2396],[2061,12501],{"className":12502,"style":2400},[2231],[2061,12504,12506,12509],{"className":12505},[2169],[2061,12507,1798],{"className":12508},[2169,2170],[2061,12510,12512],{"className":12511},[2181],[2061,12513,12515,12535],{"className":12514},[2185,2186],[2061,12516,12518,12532],{"className":12517},[2190],[2061,12519,12521],{"className":12520,"style":2370},[2194],[2061,12522,12523,12526],{"style":2302},[2061,12524],{"className":12525,"style":2203},[2202],[2061,12527,12529],{"className":12528},[2207,2208,2209,2210],[2061,12530,2134],{"className":12531},[2169,2210],[2061,12533,2218],{"className":12534},[2217],[2061,12536,12538],{"className":12537},[2190],[2061,12539,12541],{"className":12540,"style":2225},[2194],[2061,12542],{},[2061,12544,2127],{"className":12545},[2396],[2061,12547],{"className":12548,"style":2400},[2231],[2061,12550,11462],{"className":12551},[2169,2170],[2061,12553,2137],{"className":12554},[2444],[1798,12556,12557],{},"希克斯需求函数表示在价格变化后，为了保持效用不变，消费者的需求如何调整（“补偿”了收入效应）。",[1798,12559,12560,12561,12564,12565,12567],{},"将最优解代回目标函数，得到",[1865,12562,12563],{},"支出函数 (Expenditure Function)","，它表示为了达到效用水平 ",[1855,12566,11462],{}," 所需的最小支出：",[2061,12569,12571],{"className":12570},[2064],[2061,12572,12574,12687],{"className":12573},[2068],[2061,12575,12577],{"className":12576},[2072],[2074,12578,12579],{"xmlns":2076,"display":2077},[2079,12580,12581,12684],{},[2082,12582,12583,12586,12588,12594,12596,12602,12604,12606,12608,12610,12616,12624,12626,12632,12634,12640,12642,12644,12646,12648,12654,12662,12664,12670,12672,12678,12680,12682],{},[2085,12584,12585],{},"e",[2097,12587,2114],{"stretchy":2113},[2089,12589,12590,12592],{},[2085,12591,1798],{},[2121,12593,2123],{},[2097,12595,2127],{"separator":2126},[2089,12597,12598,12600],{},[2085,12599,1798],{},[2121,12601,2134],{},[2097,12603,2127],{"separator":2126},[2085,12605,11462],{},[2097,12607,2137],{"stretchy":2113},[2097,12609,2099],{},[2089,12611,12612,12614],{},[2085,12613,1798],{},[2121,12615,2123],{},[2500,12617,12618,12620,12622],{},[2085,12619,12029],{},[2121,12621,2123],{},[2097,12623,10359],{},[2097,12625,2114],{"stretchy":2113},[2089,12627,12628,12630],{},[2085,12629,1798],{},[2121,12631,2123],{},[2097,12633,2127],{"separator":2126},[2089,12635,12636,12638],{},[2085,12637,1798],{},[2121,12639,2134],{},[2097,12641,2127],{"separator":2126},[2085,12643,11462],{},[2097,12645,2137],{"stretchy":2113},[2097,12647,2762],{},[2089,12649,12650,12652],{},[2085,12651,1798],{},[2121,12653,2134],{},[2500,12655,12656,12658,12660],{},[2085,12657,12029],{},[2121,12659,2134],{},[2097,12661,10359],{},[2097,12663,2114],{"stretchy":2113},[2089,12665,12666,12668],{},[2085,12667,1798],{},[2121,12669,2123],{},[2097,12671,2127],{"separator":2126},[2089,12673,12674,12676],{},[2085,12675,1798],{},[2121,12677,2134],{},[2097,12679,2127],{"separator":2126},[2085,12681,11462],{},[2097,12683,2137],{"stretchy":2113},[2149,12685,12686],{"encoding":2151},"e(p_1, p_2, u) = p_1 h_1^*(p_1, p_2, u) + p_2 h_2^*(p_1, p_2, u)",[2061,12688,12690,12809,13016],{"className":12689,"ariaHidden":2126},[2156],[2061,12691,12693,12696,12699,12702,12742,12745,12748,12788,12791,12794,12797,12800,12803,12806],{"className":12692},[2160],[2061,12694],{"className":12695,"style":4634},[2164],[2061,12697,12585],{"className":12698},[2169,2170],[2061,12700,2114],{"className":12701},[2253],[2061,12703,12705,12708],{"className":12704},[2169],[2061,12706,1798],{"className":12707},[2169,2170],[2061,12709,12711],{"className":12710},[2181],[2061,12712,12714,12734],{"className":12713},[2185,2186],[2061,12715,12717,12731],{"className":12716},[2190],[2061,12718,12720],{"className":12719,"style":2370},[2194],[2061,12721,12722,12725],{"style":2302},[2061,12723],{"className":12724,"style":2203},[2202],[2061,12726,12728],{"className":12727},[2207,2208,2209,2210],[2061,12729,2123],{"className":12730},[2169,2210],[2061,12732,2218],{"className":12733},[2217],[2061,12735,12737],{"className":12736},[2190],[2061,12738,12740],{"className":12739,"style":2225},[2194],[2061,12741],{},[2061,12743,2127],{"className":12744},[2396],[2061,12746],{"className":12747,"style":2400},[2231],[2061,12749,12751,12754],{"className":12750},[2169],[2061,12752,1798],{"className":12753},[2169,2170],[2061,12755,12757],{"className":12756},[2181],[2061,12758,12760,12780],{"className":12759},[2185,2186],[2061,12761,12763,12777],{"className":12762},[2190],[2061,12764,12766],{"className":12765,"style":2370},[2194],[2061,12767,12768,12771],{"style":2302},[2061,12769],{"className":12770,"style":2203},[2202],[2061,12772,12774],{"className":12773},[2207,2208,2209,2210],[2061,12775,2134],{"className":12776},[2169,2210],[2061,12778,2218],{"className":12779},[2217],[2061,12781,12783],{"className":12782},[2190],[2061,12784,12786],{"className":12785,"style":2225},[2194],[2061,12787],{},[2061,12789,2127],{"className":12790},[2396],[2061,12792],{"className":12793,"style":2400},[2231],[2061,12795,11462],{"className":12796},[2169,2170],[2061,12798,2137],{"className":12799},[2444],[2061,12801],{"className":12802,"style":2232},[2231],[2061,12804,2099],{"className":12805},[2236],[2061,12807],{"className":12808,"style":2232},[2231],[2061,12810,12812,12815,12855,12906,12909,12949,12952,12955,12995,12998,13001,13004,13007,13010,13013],{"className":12811},[2160],[2061,12813],{"className":12814,"style":4634},[2164],[2061,12816,12818,12821],{"className":12817},[2169],[2061,12819,1798],{"className":12820},[2169,2170],[2061,12822,12824],{"className":12823},[2181],[2061,12825,12827,12847],{"className":12826},[2185,2186],[2061,12828,12830,12844],{"className":12829},[2190],[2061,12831,12833],{"className":12832,"style":2370},[2194],[2061,12834,12835,12838],{"style":2302},[2061,12836],{"className":12837,"style":2203},[2202],[2061,12839,12841],{"className":12840},[2207,2208,2209,2210],[2061,12842,2123],{"className":12843},[2169,2210],[2061,12845,2218],{"className":12846},[2217],[2061,12848,12850],{"className":12849},[2190],[2061,12851,12853],{"className":12852,"style":2225},[2194],[2061,12854],{},[2061,12856,12858,12861],{"className":12857},[2169],[2061,12859,12029],{"className":12860},[2169,2170],[2061,12862,12864],{"className":12863},[2181],[2061,12865,12867,12898],{"className":12866},[2185,2186],[2061,12868,12870,12895],{"className":12869},[2190],[2061,12871,12873,12884],{"className":12872,"style":10421},[2194],[2061,12874,12875,12878],{"style":4767},[2061,12876],{"className":12877,"style":2203},[2202],[2061,12879,12881],{"className":12880},[2207,2208,2209,2210],[2061,12882,2123],{"className":12883},[2169,2210],[2061,12885,12886,12889],{"style":4779},[2061,12887],{"className":12888,"style":2203},[2202],[2061,12890,12892],{"className":12891},[2207,2208,2209,2210],[2061,12893,10359],{"className":12894},[2984,2210],[2061,12896,2218],{"className":12897},[2217],[2061,12899,12901],{"className":12900},[2190],[2061,12902,12904],{"className":12903,"style":4802},[2194],[2061,12905],{},[2061,12907,2114],{"className":12908},[2253],[2061,12910,12912,12915],{"className":12911},[2169],[2061,12913,1798],{"className":12914},[2169,2170],[2061,12916,12918],{"className":12917},[2181],[2061,12919,12921,12941],{"className":12920},[2185,2186],[2061,12922,12924,12938],{"className":12923},[2190],[2061,12925,12927],{"className":12926,"style":2370},[2194],[2061,12928,12929,12932],{"style":2302},[2061,12930],{"className":12931,"style":2203},[2202],[2061,12933,12935],{"className":12934},[2207,2208,2209,2210],[2061,12936,2123],{"className":12937},[2169,2210],[2061,12939,2218],{"className":12940},[2217],[2061,12942,12944],{"className":12943},[2190],[2061,12945,12947],{"className":12946,"style":2225},[2194],[2061,12948],{},[2061,12950,2127],{"className":12951},[2396],[2061,12953],{"className":12954,"style":2400},[2231],[2061,12956,12958,12961],{"className":12957},[2169],[2061,12959,1798],{"className":12960},[2169,2170],[2061,12962,12964],{"className":12963},[2181],[2061,12965,12967,12987],{"className":12966},[2185,2186],[2061,12968,12970,12984],{"className":12969},[2190],[2061,12971,12973],{"className":12972,"style":2370},[2194],[2061,12974,12975,12978],{"style":2302},[2061,12976],{"className":12977,"style":2203},[2202],[2061,12979,12981],{"className":12980},[2207,2208,2209,2210],[2061,12982,2134],{"className":12983},[2169,2210],[2061,12985,2218],{"className":12986},[2217],[2061,12988,12990],{"className":12989},[2190],[2061,12991,12993],{"className":12992,"style":2225},[2194],[2061,12994],{},[2061,12996,2127],{"className":12997},[2396],[2061,12999],{"className":13000,"style":2400},[2231],[2061,13002,11462],{"className":13003},[2169,2170],[2061,13005,2137],{"className":13006},[2444],[2061,13008],{"className":13009,"style":2980},[2231],[2061,13011,2762],{"className":13012},[2984],[2061,13014],{"className":13015,"style":2980},[2231],[2061,13017,13019,13022,13062,13113,13116,13156,13159,13162,13202,13205,13208,13211],{"className":13018},[2160],[2061,13020],{"className":13021,"style":4634},[2164],[2061,13023,13025,13028],{"className":13024},[2169],[2061,13026,1798],{"className":13027},[2169,2170],[2061,13029,13031],{"className":13030},[2181],[2061,13032,13034,13054],{"className":13033},[2185,2186],[2061,13035,13037,13051],{"className":13036},[2190],[2061,13038,13040],{"className":13039,"style":2370},[2194],[2061,13041,13042,13045],{"style":2302},[2061,13043],{"className":13044,"style":2203},[2202],[2061,13046,13048],{"className":13047},[2207,2208,2209,2210],[2061,13049,2134],{"className":13050},[2169,2210],[2061,13052,2218],{"className":13053},[2217],[2061,13055,13057],{"className":13056},[2190],[2061,13058,13060],{"className":13059,"style":2225},[2194],[2061,13061],{},[2061,13063,13065,13068],{"className":13064},[2169],[2061,13066,12029],{"className":13067},[2169,2170],[2061,13069,13071],{"className":13070},[2181],[2061,13072,13074,13105],{"className":13073},[2185,2186],[2061,13075,13077,13102],{"className":13076},[2190],[2061,13078,13080,13091],{"className":13079,"style":10421},[2194],[2061,13081,13082,13085],{"style":4767},[2061,13083],{"className":13084,"style":2203},[2202],[2061,13086,13088],{"className":13087},[2207,2208,2209,2210],[2061,13089,2134],{"className":13090},[2169,2210],[2061,13092,13093,13096],{"style":4779},[2061,13094],{"className":13095,"style":2203},[2202],[2061,13097,13099],{"className":13098},[2207,2208,2209,2210],[2061,13100,10359],{"className":13101},[2984,2210],[2061,13103,2218],{"className":13104},[2217],[2061,13106,13108],{"className":13107},[2190],[2061,13109,13111],{"className":13110,"style":4802},[2194],[2061,13112],{},[2061,13114,2114],{"className":13115},[2253],[2061,13117,13119,13122],{"className":13118},[2169],[2061,13120,1798],{"className":13121},[2169,2170],[2061,13123,13125],{"className":13124},[2181],[2061,13126,13128,13148],{"className":13127},[2185,2186],[2061,13129,13131,13145],{"className":13130},[2190],[2061,13132,13134],{"className":13133,"style":2370},[2194],[2061,13135,13136,13139],{"style":2302},[2061,13137],{"className":13138,"style":2203},[2202],[2061,13140,13142],{"className":13141},[2207,2208,2209,2210],[2061,13143,2123],{"className":13144},[2169,2210],[2061,13146,2218],{"className":13147},[2217],[2061,13149,13151],{"className":13150},[2190],[2061,13152,13154],{"className":13153,"style":2225},[2194],[2061,13155],{},[2061,13157,2127],{"className":13158},[2396],[2061,13160],{"className":13161,"style":2400},[2231],[2061,13163,13165,13168],{"className":13164},[2169],[2061,13166,1798],{"className":13167},[2169,2170],[2061,13169,13171],{"className":13170},[2181],[2061,13172,13174,13194],{"className":13173},[2185,2186],[2061,13175,13177,13191],{"className":13176},[2190],[2061,13178,13180],{"className":13179,"style":2370},[2194],[2061,13181,13182,13185],{"style":2302},[2061,13183],{"className":13184,"style":2203},[2202],[2061,13186,13188],{"className":13187},[2207,2208,2209,2210],[2061,13189,2134],{"className":13190},[2169,2210],[2061,13192,2218],{"className":13193},[2217],[2061,13195,13197],{"className":13196},[2190],[2061,13198,13200],{"className":13199,"style":2225},[2194],[2061,13201],{},[2061,13203,2127],{"className":13204},[2396],[2061,13206],{"className":13207,"style":2400},[2231],[2061,13209,11462],{"className":13210},[2169,2170],[2061,13212,2137],{"className":13213},[2444],[1847,13215,13217],{"id":13216},"_32-谢泼德引理-shephards-lemma","3.2 谢泼德引理 (Shephard's Lemma)",[1798,13219,13220],{},"支出函数对商品价格的偏导数等于该商品的希克斯需求量。",[2061,13222,13224],{"className":13223},[2064],[2061,13225,13227,13309],{"className":13226},[2068],[2061,13228,13230],{"className":13229},[2072],[2074,13231,13232],{"xmlns":2076,"display":2077},[2079,13233,13234,13306],{},[2082,13235,13236,13276,13278,13284,13286,13292,13294,13300,13302,13304],{},[2101,13237,13238,13266],{},[2082,13239,13240,13242,13244,13246,13252,13254,13260,13262,13264],{},[2085,13241,2108],{"mathvariant":2107},[2085,13243,12585],{},[2097,13245,2114],{"stretchy":2113},[2089,13247,13248,13250],{},[2085,13249,1798],{},[2121,13251,2123],{},[2097,13253,2127],{"separator":2126},[2089,13255,13256,13258],{},[2085,13257,1798],{},[2121,13259,2134],{},[2097,13261,2127],{"separator":2126},[2085,13263,11462],{},[2097,13265,2137],{"stretchy":2113},[2082,13267,13268,13270],{},[2085,13269,2108],{"mathvariant":2107},[2089,13271,13272,13274],{},[2085,13273,1798],{},[2085,13275,2095],{},[2097,13277,2099],{},[2089,13279,13280,13282],{},[2085,13281,12029],{},[2085,13283,2095],{},[2097,13285,2114],{"stretchy":2113},[2089,13287,13288,13290],{},[2085,13289,1798],{},[2121,13291,2123],{},[2097,13293,2127],{"separator":2126},[2089,13295,13296,13298],{},[2085,13297,1798],{},[2121,13299,2134],{},[2097,13301,2127],{"separator":2126},[2085,13303,11462],{},[2097,13305,2137],{"stretchy":2113},[2149,13307,13308],{"encoding":2151},"\\frac{\\partial e(p_1, p_2, u)}{\\partial p_i} = h_i(p_1, p_2, u)",[2061,13310,13312,13534],{"className":13311,"ariaHidden":2126},[2156],[2061,13313,13315,13319,13525,13528,13531],{"className":13314},[2160],[2061,13316],{"className":13317,"style":13318},[2164],"height:2.3074em;vertical-align:-0.8804em;",[2061,13320,13322,13325,13522],{"className":13321},[2169],[2061,13323],{"className":13324},[2253,2254],[2061,13326,13328],{"className":13327},[2101],[2061,13329,13331,13514],{"className":13330},[2185,2186],[2061,13332,13334,13511],{"className":13333},[2190],[2061,13335,13337,13388,13396],{"className":13336,"style":2267},[2194],[2061,13338,13339,13342],{"style":2270},[2061,13340],{"className":13341,"style":2274},[2202],[2061,13343,13345,13348],{"className":13344},[2169],[2061,13346,2108],{"className":13347,"style":2281},[2169],[2061,13349,13351,13354],{"className":13350},[2169],[2061,13352,1798],{"className":13353},[2169,2170],[2061,13355,13357],{"className":13356},[2181],[2061,13358,13360,13380],{"className":13359},[2185,2186],[2061,13361,13363,13377],{"className":13362},[2190],[2061,13364,13366],{"className":13365,"style":2195},[2194],[2061,13367,13368,13371],{"style":2302},[2061,13369],{"className":13370,"style":2203},[2202],[2061,13372,13374],{"className":13373},[2207,2208,2209,2210],[2061,13375,2095],{"className":13376},[2169,2170,2210],[2061,13378,2218],{"className":13379},[2217],[2061,13381,13383],{"className":13382},[2190],[2061,13384,13386],{"className":13385,"style":2225},[2194],[2061,13387],{},[2061,13389,13390,13393],{"style":2325},[2061,13391],{"className":13392,"style":2274},[2202],[2061,13394],{"className":13395,"style":2333},[2332],[2061,13397,13398,13401],{"style":2336},[2061,13399],{"className":13400,"style":2274},[2202],[2061,13402,13404,13407,13410,13413,13453,13456,13459,13499,13502,13505,13508],{"className":13403},[2169],[2061,13405,2108],{"className":13406,"style":2281},[2169],[2061,13408,12585],{"className":13409},[2169,2170],[2061,13411,2114],{"className":13412},[2253],[2061,13414,13416,13419],{"className":13415},[2169],[2061,13417,1798],{"className":13418},[2169,2170],[2061,13420,13422],{"className":13421},[2181],[2061,13423,13425,13445],{"className":13424},[2185,2186],[2061,13426,13428,13442],{"className":13427},[2190],[2061,13429,13431],{"className":13430,"style":2370},[2194],[2061,13432,13433,13436],{"style":2302},[2061,13434],{"className":13435,"style":2203},[2202],[2061,13437,13439],{"className":13438},[2207,2208,2209,2210],[2061,13440,2123],{"className":13441},[2169,2210],[2061,13443,2218],{"className":13444},[2217],[2061,13446,13448],{"className":13447},[2190],[2061,13449,13451],{"className":13450,"style":2225},[2194],[2061,13452],{},[2061,13454,2127],{"className":13455},[2396],[2061,13457],{"className":13458,"style":2400},[2231],[2061,13460,13462,13465],{"className":13461},[2169],[2061,13463,1798],{"className":13464},[2169,2170],[2061,13466,13468],{"className":13467},[2181],[2061,13469,13471,13491],{"className":13470},[2185,2186],[2061,13472,13474,13488],{"className":13473},[2190],[2061,13475,13477],{"className":13476,"style":2370},[2194],[2061,13478,13479,13482],{"style":2302},[2061,13480],{"className":13481,"style":2203},[2202],[2061,13483,13485],{"className":13484},[2207,2208,2209,2210],[2061,13486,2134],{"className":13487},[2169,2210],[2061,13489,2218],{"className":13490},[2217],[2061,13492,13494],{"className":13493},[2190],[2061,13495,13497],{"className":13496,"style":2225},[2194],[2061,13498],{},[2061,13500,2127],{"className":13501},[2396],[2061,13503],{"className":13504,"style":2400},[2231],[2061,13506,11462],{"className":13507},[2169,2170],[2061,13509,2137],{"className":13510},[2444],[2061,13512,2218],{"className":13513},[2217],[2061,13515,13517],{"className":13516},[2190],[2061,13518,13520],{"className":13519,"style":8254},[2194],[2061,13521],{},[2061,13523],{"className":13524},[2444,2254],[2061,13526],{"className":13527,"style":2232},[2231],[2061,13529,2099],{"className":13530},[2236],[2061,13532],{"className":13533,"style":2232},[2231],[2061,13535,13537,13540,13580,13583,13623,13626,13629,13669,13672,13675,13678],{"className":13536},[2160],[2061,13538],{"className":13539,"style":4634},[2164],[2061,13541,13543,13546],{"className":13542},[2169],[2061,13544,12029],{"className":13545},[2169,2170],[2061,13547,13549],{"className":13548},[2181],[2061,13550,13552,13572],{"className":13551},[2185,2186],[2061,13553,13555,13569],{"className":13554},[2190],[2061,13556,13558],{"className":13557,"style":2195},[2194],[2061,13559,13560,13563],{"style":2302},[2061,13561],{"className":13562,"style":2203},[2202],[2061,13564,13566],{"className":13565},[2207,2208,2209,2210],[2061,13567,2095],{"className":13568},[2169,2170,2210],[2061,13570,2218],{"className":13571},[2217],[2061,13573,13575],{"className":13574},[2190],[2061,13576,13578],{"className":13577,"style":2225},[2194],[2061,13579],{},[2061,13581,2114],{"className":13582},[2253],[2061,13584,13586,13589],{"className":13585},[2169],[2061,13587,1798],{"className":13588},[2169,2170],[2061,13590,13592],{"className":13591},[2181],[2061,13593,13595,13615],{"className":13594},[2185,2186],[2061,13596,13598,13612],{"className":13597},[2190],[2061,13599,13601],{"className":13600,"style":2370},[2194],[2061,13602,13603,13606],{"style":2302},[2061,13604],{"className":13605,"style":2203},[2202],[2061,13607,13609],{"className":13608},[2207,2208,2209,2210],[2061,13610,2123],{"className":13611},[2169,2210],[2061,13613,2218],{"className":13614},[2217],[2061,13616,13618],{"className":13617},[2190],[2061,13619,13621],{"className":13620,"style":2225},[2194],[2061,13622],{},[2061,13624,2127],{"className":13625},[2396],[2061,13627],{"className":13628,"style":2400},[2231],[2061,13630,13632,13635],{"className":13631},[2169],[2061,13633,1798],{"className":13634},[2169,2170],[2061,13636,13638],{"className":13637},[2181],[2061,13639,13641,13661],{"className":13640},[2185,2186],[2061,13642,13644,13658],{"className":13643},[2190],[2061,13645,13647],{"className":13646,"style":2370},[2194],[2061,13648,13649,13652],{"style":2302},[2061,13650],{"className":13651,"style":2203},[2202],[2061,13653,13655],{"className":13654},[2207,2208,2209,2210],[2061,13656,2134],{"className":13657},[2169,2210],[2061,13659,2218],{"className":13660},[2217],[2061,13662,13664],{"className":13663},[2190],[2061,13665,13667],{"className":13666,"style":2225},[2194],[2061,13668],{},[2061,13670,2127],{"className":13671},[2396],[2061,13673],{"className":13674,"style":2400},[2231],[2061,13676,11462],{"className":13677},[2169,2170],[2061,13679,2137],{"className":13680},[2444],[1798,13682,13683,13686,13687,13689,13690,13693],{},[1865,13684,13685],{},"直觉",": 如果商品 ",[1855,13688,2095],{}," 的价格上涨1美元，为了保持效用不变，你需要增加的最小支出，正好就是你原本需要购买的 ",[1855,13691,13692],{},"h_i"," 单位商品的价格上涨部分。",[1847,13695,13697],{"id":13696},"_33-罗伊恒等式-roys-identity","3.3 罗伊恒等式 (Roy's Identity)",[1798,13699,13700],{},"通过间接效用函数，可以求得马歇尔需求函数。",[2061,13702,13704],{"className":13703},[2064],[2061,13705,13707,13781],{"className":13706},[2068],[2061,13708,13710],{"className":13709},[2072],[2074,13711,13712],{"xmlns":2076,"display":2077},[2079,13713,13714,13778],{},[2082,13715,13716,13722,13724,13730,13732,13738,13740,13742,13744,13746,13748],{},[2089,13717,13718,13720],{},[2085,13719,2119],{},[2085,13721,2095],{},[2097,13723,2114],{"stretchy":2113},[2089,13725,13726,13728],{},[2085,13727,1798],{},[2121,13729,2123],{},[2097,13731,2127],{"separator":2126},[2089,13733,13734,13736],{},[2085,13735,1798],{},[2121,13737,2134],{},[2097,13739,2127],{"separator":2126},[2085,13741,7160],{},[2097,13743,2137],{"stretchy":2113},[2097,13745,2099],{},[2097,13747,3204],{},[2101,13749,13750,13766],{},[2082,13751,13752,13754,13756,13758,13760],{},[2085,13753,2108],{"mathvariant":2107},[2085,13755,6887],{},[2085,13757,3215],{"mathvariant":2107},[2085,13759,2108],{"mathvariant":2107},[2089,13761,13762,13764],{},[2085,13763,1798],{},[2085,13765,2095],{},[2082,13767,13768,13770,13772,13774,13776],{},[2085,13769,2108],{"mathvariant":2107},[2085,13771,6887],{},[2085,13773,3215],{"mathvariant":2107},[2085,13775,2108],{"mathvariant":2107},[2085,13777,7160],{},[2149,13779,13780],{"encoding":2151},"x_i(p_1, p_2, m) = - \\frac{\\partial v \u002F \\partial p_i}{\\partial v \u002F \\partial m}",[2061,13782,13784,13940],{"className":13783,"ariaHidden":2126},[2156],[2061,13785,13787,13790,13830,13833,13873,13876,13879,13919,13922,13925,13928,13931,13934,13937],{"className":13786},[2160],[2061,13788],{"className":13789,"style":4634},[2164],[2061,13791,13793,13796],{"className":13792},[2169],[2061,13794,2119],{"className":13795},[2169,2170],[2061,13797,13799],{"className":13798},[2181],[2061,13800,13802,13822],{"className":13801},[2185,2186],[2061,13803,13805,13819],{"className":13804},[2190],[2061,13806,13808],{"className":13807,"style":2195},[2194],[2061,13809,13810,13813],{"style":2302},[2061,13811],{"className":13812,"style":2203},[2202],[2061,13814,13816],{"className":13815},[2207,2208,2209,2210],[2061,13817,2095],{"className":13818},[2169,2170,2210],[2061,13820,2218],{"className":13821},[2217],[2061,13823,13825],{"className":13824},[2190],[2061,13826,13828],{"className":13827,"style":2225},[2194],[2061,13829],{},[2061,13831,2114],{"className":13832},[2253],[2061,13834,13836,13839],{"className":13835},[2169],[2061,13837,1798],{"className":13838},[2169,2170],[2061,13840,13842],{"className":13841},[2181],[2061,13843,13845,13865],{"className":13844},[2185,2186],[2061,13846,13848,13862],{"className":13847},[2190],[2061,13849,13851],{"className":13850,"style":2370},[2194],[2061,13852,13853,13856],{"style":2302},[2061,13854],{"className":13855,"style":2203},[2202],[2061,13857,13859],{"className":13858},[2207,2208,2209,2210],[2061,13860,2123],{"className":13861},[2169,2210],[2061,13863,2218],{"className":13864},[2217],[2061,13866,13868],{"className":13867},[2190],[2061,13869,13871],{"className":13870,"style":2225},[2194],[2061,13872],{},[2061,13874,2127],{"className":13875},[2396],[2061,13877],{"className":13878,"style":2400},[2231],[2061,13880,13882,13885],{"className":13881},[2169],[2061,13883,1798],{"className":13884},[2169,2170],[2061,13886,13888],{"className":13887},[2181],[2061,13889,13891,13911],{"className":13890},[2185,2186],[2061,13892,13894,13908],{"className":13893},[2190],[2061,13895,13897],{"className":13896,"style":2370},[2194],[2061,13898,13899,13902],{"style":2302},[2061,13900],{"className":13901,"style":2203},[2202],[2061,13903,13905],{"className":13904},[2207,2208,2209,2210],[2061,13906,2134],{"className":13907},[2169,2210],[2061,13909,2218],{"className":13910},[2217],[2061,13912,13914],{"className":13913},[2190],[2061,13915,13917],{"className":13916,"style":2225},[2194],[2061,13918],{},[2061,13920,2127],{"className":13921},[2396],[2061,13923],{"className":13924,"style":2400},[2231],[2061,13926,7160],{"className":13927},[2169,2170],[2061,13929,2137],{"className":13930},[2444],[2061,13932],{"className":13933,"style":2232},[2231],[2061,13935,2099],{"className":13936},[2236],[2061,13938],{"className":13939,"style":2232},[2231],[2061,13941,13943,13946,13949],{"className":13942},[2160],[2061,13944],{"className":13945,"style":3435},[2164],[2061,13947,3204],{"className":13948},[2169],[2061,13950,13952,13955,14069],{"className":13951},[2169],[2061,13953],{"className":13954},[2253,2254],[2061,13956,13958],{"className":13957},[2101],[2061,13959,13961,14061],{"className":13960},[2185,2186],[2061,13962,13964,14058],{"className":13963},[2190],[2061,13965,13967,13990,13998],{"className":13966,"style":2267},[2194],[2061,13968,13969,13972],{"style":2270},[2061,13970],{"className":13971,"style":2274},[2202],[2061,13973,13975,13978,13981,13984,13987],{"className":13974},[2169],[2061,13976,2108],{"className":13977,"style":2281},[2169],[2061,13979,6887],{"className":13980,"style":6572},[2169,2170],[2061,13982,3215],{"className":13983},[2169],[2061,13985,2108],{"className":13986,"style":2281},[2169],[2061,13988,7160],{"className":13989},[2169,2170],[2061,13991,13992,13995],{"style":2325},[2061,13993],{"className":13994,"style":2274},[2202],[2061,13996],{"className":13997,"style":2333},[2332],[2061,13999,14000,14003],{"style":2336},[2061,14001],{"className":14002,"style":2274},[2202],[2061,14004,14006,14009,14012,14015,14018],{"className":14005},[2169],[2061,14007,2108],{"className":14008,"style":2281},[2169],[2061,14010,6887],{"className":14011,"style":6572},[2169,2170],[2061,14013,3215],{"className":14014},[2169],[2061,14016,2108],{"className":14017,"style":2281},[2169],[2061,14019,14021,14024],{"className":14020},[2169],[2061,14022,1798],{"className":14023},[2169,2170],[2061,14025,14027],{"className":14026},[2181],[2061,14028,14030,14050],{"className":14029},[2185,2186],[2061,14031,14033,14047],{"className":14032},[2190],[2061,14034,14036],{"className":14035,"style":2195},[2194],[2061,14037,14038,14041],{"style":2302},[2061,14039],{"className":14040,"style":2203},[2202],[2061,14042,14044],{"className":14043},[2207,2208,2209,2210],[2061,14045,2095],{"className":14046},[2169,2170,2210],[2061,14048,2218],{"className":14049},[2217],[2061,14051,14053],{"className":14052},[2190],[2061,14054,14056],{"className":14055,"style":2225},[2194],[2061,14057],{},[2061,14059,2218],{"className":14060},[2217],[2061,14062,14064],{"className":14063},[2190],[2061,14065,14067],{"className":14066,"style":3594},[2194],[2061,14068],{},[2061,14070],{"className":14071},[2444,2254],[1798,14073,14074],{},"这个恒等式不那么直观，但它建立了从价值函数到需求函数的另一条关键路径，在理论研究中非常有用。",[1847,14076,14078],{"id":14077},"_34-对偶关系总结","3.4 对偶关系总结",[1798,14080,14081],{},"UMP 和 EMP 之间存在深刻的对偶关系，它们是同一问题的两种不同表述。",[1965,14083],{"code64":14084,"locale":7},"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",[1840,14086],{},[1794,14088,14089],{"id":14089},"直觉与应用",[1805,14091,14092,14102,14108],{},[1808,14093,14094,14097,14098,14101],{},[1865,14095,14096],{},"核心思想",": 消费者的最优选择发生在",[1865,14099,14100],{},"主观交换意愿 (MRS) 等于市场客观交换率 (价格比)"," 的地方。",[1808,14103,14104,14107],{},[1865,14105,14106],{},"对偶性",": \"在给定收入下最大化快乐\"和\"为了达到一定快乐程度而最小化花费\"是等价的。",[1808,14109,14110,14112,14113],{},[1865,14111,5432],{},": 这些看似抽象的理论是分析几乎所有经济问题的基础，例如：\n",[1805,14114,14115,14121,14127],{},[1808,14116,14117,14120],{},[1865,14118,14119],{},"政策分析",": 预测税收或补贴对消费者行为和福利的影响。",[1808,14122,14123,14126],{},[1865,14124,14125],{},"劳动经济学",": 分析工资变化如何影响劳动供给决策（休闲与工作的权衡）。",[1808,14128,14129,14132],{},[1865,14130,14131],{},"金融学",": 分析投资者如何在风险和回报之间进行资产组合选择。",[1840,14134],{},[1794,14136,14138],{"id":14137},"_4-完整例题求解","4. 完整例题求解",[1847,14140,14142],{"id":14141},"例题-1-柯布-道格拉斯效用函数的需求推导","例题 1: 柯布-道格拉斯效用函数的需求推导",[1798,14144,14145,14148,14149,14434,14435,14527,14528,14621,14622,14674],{},[1865,14146,14147],{},"题目",": 假设消费者的效用函数为 ",[2061,14150,14152,14204],{"className":14151},[2068],[2061,14153,14155],{"className":14154},[2072],[2074,14156,14157],{"xmlns":2076},[2079,14158,14159,14201],{},[2082,14160,14161,14163,14165,14171,14173,14179,14181,14183,14192],{},[2085,14162,2005],{},[2097,14164,2114],{"stretchy":2113},[2089,14166,14167,14169],{},[2085,14168,2119],{},[2121,14170,2123],{},[2097,14172,2127],{"separator":2126},[2089,14174,14175,14177],{},[2085,14176,2119],{},[2121,14178,2134],{},[2097,14180,2137],{"stretchy":2113},[2097,14182,2099],{},[2500,14184,14185,14187,14189],{},[2085,14186,2119],{},[2121,14188,2123],{},[2121,14190,14191],{},"0.4",[2500,14193,14194,14196,14198],{},[2085,14195,2119],{},[2121,14197,2134],{},[2121,14199,14200],{},"0.6",[2149,14202,14203],{"encoding":2151},"U(x_1, x_2) = x_1^{0.4} x_2^{0.6}",[2061,14205,14207,14317],{"className":14206,"ariaHidden":2126},[2156],[2061,14208,14210,14213,14216,14219,14259,14262,14265,14305,14308,14311,14314],{"className":14209},[2160],[2061,14211],{"className":14212,"style":4634},[2164],[2061,14214,2005],{"className":14215,"style":2171},[2169,2170],[2061,14217,2114],{"className":14218},[2253],[2061,14220,14222,14225],{"className":14221},[2169],[2061,14223,2119],{"className":14224},[2169,2170],[2061,14226,14228],{"className":14227},[2181],[2061,14229,14231,14251],{"className":14230},[2185,2186],[2061,14232,14234,14248],{"className":14233},[2190],[2061,14235,14237],{"className":14236,"style":2370},[2194],[2061,14238,14239,14242],{"style":2302},[2061,14240],{"className":14241,"style":2203},[2202],[2061,14243,14245],{"className":14244},[2207,2208,2209,2210],[2061,14246,2123],{"className":14247},[2169,2210],[2061,14249,2218],{"className":14250},[2217],[2061,14252,14254],{"className":14253},[2190],[2061,14255,14257],{"className":14256,"style":2225},[2194],[2061,14258],{},[2061,14260,2127],{"className":14261},[2396],[2061,14263],{"className":14264,"style":2400},[2231],[2061,14266,14268,14271],{"className":14267},[2169],[2061,14269,2119],{"className":14270},[2169,2170],[2061,14272,14274],{"className":14273},[2181],[2061,14275,14277,14297],{"className":14276},[2185,2186],[2061,14278,14280,14294],{"className":14279},[2190],[2061,14281,14283],{"className":14282,"style":2370},[2194],[2061,14284,14285,14288],{"style":2302},[2061,14286],{"className":14287,"style":2203},[2202],[2061,14289,14291],{"className":14290},[2207,2208,2209,2210],[2061,14292,2134],{"className":14293},[2169,2210],[2061,14295,2218],{"className":14296},[2217],[2061,14298,14300],{"className":14299},[2190],[2061,14301,14303],{"className":14302,"style":2225},[2194],[2061,14304],{},[2061,14306,2137],{"className":14307},[2444],[2061,14309],{"className":14310,"style":2232},[2231],[2061,14312,2099],{"className":14313},[2236],[2061,14315],{"className":14316,"style":2232},[2231],[2061,14318,14320,14324,14380],{"className":14319},[2160],[2061,14321],{"className":14322,"style":14323},[2164],"height:1.0622em;vertical-align:-0.2481em;",[2061,14325,14327,14330],{"className":14326},[2169],[2061,14328,2119],{"className":14329},[2169,2170],[2061,14331,14333],{"className":14332},[2181],[2061,14334,14336,14371],{"className":14335},[2185,2186],[2061,14337,14339,14368],{"className":14338},[2190],[2061,14340,14342,14354],{"className":14341,"style":2646},[2194],[2061,14343,14345,14348],{"style":14344},"top:-2.4519em;margin-left:0em;margin-right:0.05em;",[2061,14346],{"className":14347,"style":2203},[2202],[2061,14349,14351],{"className":14350},[2207,2208,2209,2210],[2061,14352,2123],{"className":14353},[2169,2210],[2061,14355,14356,14359],{"style":2649},[2061,14357],{"className":14358,"style":2203},[2202],[2061,14360,14362],{"className":14361},[2207,2208,2209,2210],[2061,14363,14365],{"className":14364},[2169,2210],[2061,14366,14191],{"className":14367},[2169,2210],[2061,14369,2218],{"className":14370},[2217],[2061,14372,14374],{"className":14373},[2190],[2061,14375,14378],{"className":14376,"style":14377},[2194],"height:0.2481em;",[2061,14379],{},[2061,14381,14383,14386],{"className":14382},[2169],[2061,14384,2119],{"className":14385},[2169,2170],[2061,14387,14389],{"className":14388},[2181],[2061,14390,14392,14426],{"className":14391},[2185,2186],[2061,14393,14395,14423],{"className":14394},[2190],[2061,14396,14398,14409],{"className":14397,"style":2646},[2194],[2061,14399,14400,14403],{"style":14344},[2061,14401],{"className":14402,"style":2203},[2202],[2061,14404,14406],{"className":14405},[2207,2208,2209,2210],[2061,14407,2134],{"className":14408},[2169,2210],[2061,14410,14411,14414],{"style":2649},[2061,14412],{"className":14413,"style":2203},[2202],[2061,14415,14417],{"className":14416},[2207,2208,2209,2210],[2061,14418,14420],{"className":14419},[2169,2210],[2061,14421,14200],{"className":14422},[2169,2210],[2061,14424,2218],{"className":14425},[2217],[2061,14427,14429],{"className":14428},[2190],[2061,14430,14432],{"className":14431,"style":14377},[2194],[2061,14433],{},"，价格为 ",[2061,14436,14438,14460],{"className":14437},[2068],[2061,14439,14441],{"className":14440},[2072],[2074,14442,14443],{"xmlns":2076},[2079,14444,14445,14457],{},[2082,14446,14447,14453,14455],{},[2089,14448,14449,14451],{},[2085,14450,1798],{},[2121,14452,2123],{},[2097,14454,2099],{},[2121,14456,2134],{},[2149,14458,14459],{"encoding":2151},"p_1 = 2",[2061,14461,14463,14518],{"className":14462,"ariaHidden":2126},[2156],[2061,14464,14466,14469,14509,14512,14515],{"className":14465},[2160],[2061,14467],{"className":14468,"style":6705},[2164],[2061,14470,14472,14475],{"className":14471},[2169],[2061,14473,1798],{"className":14474},[2169,2170],[2061,14476,14478],{"className":14477},[2181],[2061,14479,14481,14501],{"className":14480},[2185,2186],[2061,14482,14484,14498],{"className":14483},[2190],[2061,14485,14487],{"className":14486,"style":2370},[2194],[2061,14488,14489,14492],{"style":2302},[2061,14490],{"className":14491,"style":2203},[2202],[2061,14493,14495],{"className":14494},[2207,2208,2209,2210],[2061,14496,2123],{"className":14497},[2169,2210],[2061,14499,2218],{"className":14500},[2217],[2061,14502,14504],{"className":14503},[2190],[2061,14505,14507],{"className":14506,"style":2225},[2194],[2061,14508],{},[2061,14510],{"className":14511,"style":2232},[2231],[2061,14513,2099],{"className":14514},[2236],[2061,14516],{"className":14517,"style":2232},[2231],[2061,14519,14521,14524],{"className":14520},[2160],[2061,14522],{"className":14523,"style":2692},[2164],[2061,14525,2134],{"className":14526},[2169],", ",[2061,14529,14531,14554],{"className":14530},[2068],[2061,14532,14534],{"className":14533},[2072],[2074,14535,14536],{"xmlns":2076},[2079,14537,14538,14551],{},[2082,14539,14540,14546,14548],{},[2089,14541,14542,14544],{},[2085,14543,1798],{},[2121,14545,2134],{},[2097,14547,2099],{},[2121,14549,14550],{},"3",[2149,14552,14553],{"encoding":2151},"p_2 = 3",[2061,14555,14557,14612],{"className":14556,"ariaHidden":2126},[2156],[2061,14558,14560,14563,14603,14606,14609],{"className":14559},[2160],[2061,14561],{"className":14562,"style":6705},[2164],[2061,14564,14566,14569],{"className":14565},[2169],[2061,14567,1798],{"className":14568},[2169,2170],[2061,14570,14572],{"className":14571},[2181],[2061,14573,14575,14595],{"className":14574},[2185,2186],[2061,14576,14578,14592],{"className":14577},[2190],[2061,14579,14581],{"className":14580,"style":2370},[2194],[2061,14582,14583,14586],{"style":2302},[2061,14584],{"className":14585,"style":2203},[2202],[2061,14587,14589],{"className":14588},[2207,2208,2209,2210],[2061,14590,2134],{"className":14591},[2169,2210],[2061,14593,2218],{"className":14594},[2217],[2061,14596,14598],{"className":14597},[2190],[2061,14599,14601],{"className":14600,"style":2225},[2194],[2061,14602],{},[2061,14604],{"className":14605,"style":2232},[2231],[2061,14607,2099],{"className":14608},[2236],[2061,14610],{"className":14611,"style":2232},[2231],[2061,14613,14615,14618],{"className":14614},[2160],[2061,14616],{"className":14617,"style":2692},[2164],[2061,14619,14550],{"className":14620},[2169],"，收入为 ",[2061,14623,14625,14644],{"className":14624},[2068],[2061,14626,14628],{"className":14627},[2072],[2074,14629,14630],{"xmlns":2076},[2079,14631,14632,14641],{},[2082,14633,14634,14636,14638],{},[2085,14635,7160],{},[2097,14637,2099],{},[2121,14639,14640],{},"120",[2149,14642,14643],{"encoding":2151},"m = 120",[2061,14645,14647,14665],{"className":14646,"ariaHidden":2126},[2156],[2061,14648,14650,14653,14656,14659,14662],{"className":14649},[2160],[2061,14651],{"className":14652,"style":6568},[2164],[2061,14654,7160],{"className":14655},[2169,2170],[2061,14657],{"className":14658,"style":2232},[2231],[2061,14660,2099],{"className":14661},[2236],[2061,14663],{"className":14664,"style":2232},[2231],[2061,14666,14668,14671],{"className":14667},[2160],[2061,14669],{"className":14670,"style":2692},[2164],[2061,14672,14640],{"className":14673},[2169],"。求：",[1860,14676,14677,14680,14683],{},[1808,14678,14679],{},"马歇尔需求函数",[1808,14681,14682],{},"间接效用函数",[1808,14684,14685],{},"希克斯需求函数和支出函数",[1798,14687,14688,4550],{},[1865,14689,14690],{},"解答",[1798,14692,14693],{},[1865,14694,14695],{},"(1) 马歇尔需求函数",[1798,14697,14698],{},"建立拉格朗日函数：",[2061,14700,14702],{"className":14701},[2064],[2061,14703,14705,14767],{"className":14704},[2068],[2061,14706,14708],{"className":14707},[2072],[2074,14709,14710],{"xmlns":2076,"display":2077},[2079,14711,14712,14764],{},[2082,14713,14714,14716,14718,14726,14734,14736,14738,14740,14742,14744,14746,14752,14754,14756,14762],{},[2085,14715,8609],{"mathvariant":8608},[2097,14717,2099],{},[2500,14719,14720,14722,14724],{},[2085,14721,2119],{},[2121,14723,2123],{},[2121,14725,14191],{},[2500,14727,14728,14730,14732],{},[2085,14729,2119],{},[2121,14731,2134],{},[2121,14733,14200],{},[2097,14735,2762],{},[2085,14737,8630],{},[2097,14739,2114],{"stretchy":2113},[2121,14741,14640],{},[2097,14743,3204],{},[2121,14745,2134],{},[2089,14747,14748,14750],{},[2085,14749,2119],{},[2121,14751,2123],{},[2097,14753,3204],{},[2121,14755,14550],{},[2089,14757,14758,14760],{},[2085,14759,2119],{},[2121,14761,2134],{},[2097,14763,2137],{"stretchy":2113},[2149,14765,14766],{"encoding":2151},"\\mathcal{L} = x_1^{0.4} x_2^{0.6} + \\lambda(120 - 2x_1 - 3x_2)",[2061,14768,14770,14788,14913,14937,14996],{"className":14769,"ariaHidden":2126},[2156],[2061,14771,14773,14776,14779,14782,14785],{"className":14772},[2160],[2061,14774],{"className":14775,"style":8096},[2164],[2061,14777,8609],{"className":14778},[2169,8708],[2061,14780],{"className":14781,"style":2232},[2231],[2061,14783,2099],{"className":14784},[2236],[2061,14786],{"className":14787,"style":2232},[2231],[2061,14789,14791,14795,14850,14904,14907,14910],{"className":14790},[2160],[2061,14792],{"className":14793,"style":14794},[2164],"height:1.1111em;vertical-align:-0.247em;",[2061,14796,14798,14801],{"className":14797},[2169],[2061,14799,2119],{"className":14800},[2169,2170],[2061,14802,14804],{"className":14803},[2181],[2061,14805,14807,14842],{"className":14806},[2185,2186],[2061,14808,14810,14839],{"className":14809},[2190],[2061,14811,14814,14825],{"className":14812,"style":14813},[2194],"height:0.8641em;",[2061,14815,14816,14819],{"style":4767},[2061,14817],{"className":14818,"style":2203},[2202],[2061,14820,14822],{"className":14821},[2207,2208,2209,2210],[2061,14823,2123],{"className":14824},[2169,2210],[2061,14826,14827,14830],{"style":4779},[2061,14828],{"className":14829,"style":2203},[2202],[2061,14831,14833],{"className":14832},[2207,2208,2209,2210],[2061,14834,14836],{"className":14835},[2169,2210],[2061,14837,14191],{"className":14838},[2169,2210],[2061,14840,2218],{"className":14841},[2217],[2061,14843,14845],{"className":14844},[2190],[2061,14846,14848],{"className":14847,"style":4802},[2194],[2061,14849],{},[2061,14851,14853,14856],{"className":14852},[2169],[2061,14854,2119],{"className":14855},[2169,2170],[2061,14857,14859],{"className":14858},[2181],[2061,14860,14862,14896],{"className":14861},[2185,2186],[2061,14863,14865,14893],{"className":14864},[2190],[2061,14866,14868,14879],{"className":14867,"style":14813},[2194],[2061,14869,14870,14873],{"style":4767},[2061,14871],{"className":14872,"style":2203},[2202],[2061,14874,14876],{"className":14875},[2207,2208,2209,2210],[2061,14877,2134],{"className":14878},[2169,2210],[2061,14880,14881,14884],{"style":4779},[2061,14882],{"className":14883,"style":2203},[2202],[2061,14885,14887],{"className":14886},[2207,2208,2209,2210],[2061,14888,14890],{"className":14889},[2169,2210],[2061,14891,14200],{"className":14892},[2169,2210],[2061,14894,2218],{"className":14895},[2217],[2061,14897,14899],{"className":14898},[2190],[2061,14900,14902],{"className":14901,"style":4802},[2194],[2061,14903],{},[2061,14905],{"className":14906,"style":2980},[2231],[2061,14908,2762],{"className":14909},[2984],[2061,14911],{"className":14912,"style":2980},[2231],[2061,14914,14916,14919,14922,14925,14928,14931,14934],{"className":14915},[2160],[2061,14917],{"className":14918,"style":4634},[2164],[2061,14920,8630],{"className":14921},[2169,2170],[2061,14923,2114],{"className":14924},[2253],[2061,14926,14640],{"className":14927},[2169],[2061,14929],{"className":14930,"style":2980},[2231],[2061,14932,3204],{"className":14933},[2984],[2061,14935],{"className":14936,"style":2980},[2231],[2061,14938,14940,14944,14947,14987,14990,14993],{"className":14939},[2160],[2061,14941],{"className":14942,"style":14943},[2164],"height:0.7944em;vertical-align:-0.15em;",[2061,14945,2134],{"className":14946},[2169],[2061,14948,14950,14953],{"className":14949},[2169],[2061,14951,2119],{"className":14952},[2169,2170],[2061,14954,14956],{"className":14955},[2181],[2061,14957,14959,14979],{"className":14958},[2185,2186],[2061,14960,14962,14976],{"className":14961},[2190],[2061,14963,14965],{"className":14964,"style":2370},[2194],[2061,14966,14967,14970],{"style":2302},[2061,14968],{"className":14969,"style":2203},[2202],[2061,14971,14973],{"className":14972},[2207,2208,2209,2210],[2061,14974,2123],{"className":14975},[2169,2210],[2061,14977,2218],{"className":14978},[2217],[2061,14980,14982],{"className":14981},[2190],[2061,14983,14985],{"className":14984,"style":2225},[2194],[2061,14986],{},[2061,14988],{"className":14989,"style":2980},[2231],[2061,14991,3204],{"className":14992},[2984],[2061,14994],{"className":14995,"style":2980},[2231],[2061,14997,14999,15002,15005,15045],{"className":14998},[2160],[2061,15000],{"className":15001,"style":4634},[2164],[2061,15003,14550],{"className":15004},[2169],[2061,15006,15008,15011],{"className":15007},[2169],[2061,15009,2119],{"className":15010},[2169,2170],[2061,15012,15014],{"className":15013},[2181],[2061,15015,15017,15037],{"className":15016},[2185,2186],[2061,15018,15020,15034],{"className":15019},[2190],[2061,15021,15023],{"className":15022,"style":2370},[2194],[2061,15024,15025,15028],{"style":2302},[2061,15026],{"className":15027,"style":2203},[2202],[2061,15029,15031],{"className":15030},[2207,2208,2209,2210],[2061,15032,2134],{"className":15033},[2169,2210],[2061,15035,2218],{"className":15036},[2217],[2061,15038,15040],{"className":15039},[2190],[2061,15041,15043],{"className":15042,"style":2225},[2194],[2061,15044],{},[2061,15046,2137],{"className":15047},[2444],[1798,15049,15050],{},"一阶条件：",[2061,15052,15054],{"className":15053},[2064],[2061,15055,15057,15257],{"className":15056},[2068],[2061,15058,15060],{"className":15059},[2072],[2074,15061,15062],{"xmlns":2076,"display":2077},[2079,15063,15064,15254],{},[9154,15065,15066,15132,15198],{"rowspacing":9156,"columnalign":9157,"columnspacing":9158},[9160,15067,15068,15090],{},[9163,15069,15070],{},[9166,15071,15072],{"scriptlevel":2513,"displaystyle":2126},[2101,15073,15074,15080],{},[2082,15075,15076,15078],{},[2085,15077,2108],{"mathvariant":2107},[2085,15079,8609],{"mathvariant":8608},[2082,15081,15082,15084],{},[2085,15083,2108],{"mathvariant":2107},[2089,15085,15086,15088],{},[2085,15087,2119],{},[2121,15089,2123],{},[9163,15091,15092],{},[9166,15093,15094],{"scriptlevel":2513,"displaystyle":2126},[2082,15095,15096,15098,15100,15102,15114,15122,15124,15126,15128,15130],{},[2082,15097],{},[2097,15099,2099],{},[2121,15101,14191],{},[2500,15103,15104,15106,15108],{},[2085,15105,2119],{},[2121,15107,2123],{},[2082,15109,15110,15112],{},[2097,15111,3204],{},[2121,15113,14200],{},[2500,15115,15116,15118,15120],{},[2085,15117,2119],{},[2121,15119,2134],{},[2121,15121,14200],{},[2097,15123,3204],{},[2121,15125,2134],{},[2085,15127,8630],{},[2097,15129,2099],{},[2121,15131,2513],{},[9160,15133,15134,15156],{},[9163,15135,15136],{},[9166,15137,15138],{"scriptlevel":2513,"displaystyle":2126},[2101,15139,15140,15146],{},[2082,15141,15142,15144],{},[2085,15143,2108],{"mathvariant":2107},[2085,15145,8609],{"mathvariant":8608},[2082,15147,15148,15150],{},[2085,15149,2108],{"mathvariant":2107},[2089,15151,15152,15154],{},[2085,15153,2119],{},[2121,15155,2134],{},[9163,15157,15158],{},[9166,15159,15160],{"scriptlevel":2513,"displaystyle":2126},[2082,15161,15162,15164,15166,15168,15176,15188,15190,15192,15194,15196],{},[2082,15163],{},[2097,15165,2099],{},[2121,15167,14200],{},[2500,15169,15170,15172,15174],{},[2085,15171,2119],{},[2121,15173,2123],{},[2121,15175,14191],{},[2500,15177,15178,15180,15182],{},[2085,15179,2119],{},[2121,15181,2134],{},[2082,15183,15184,15186],{},[2097,15185,3204],{},[2121,15187,14191],{},[2097,15189,3204],{},[2121,15191,14550],{},[2085,15193,8630],{},[2097,15195,2099],{},[2121,15197,2513],{},[9160,15199,15200,15218],{},[9163,15201,15202],{},[9166,15203,15204],{"scriptlevel":2513,"displaystyle":2126},[2101,15205,15206,15212],{},[2082,15207,15208,15210],{},[2085,15209,2108],{"mathvariant":2107},[2085,15211,8609],{"mathvariant":8608},[2082,15213,15214,15216],{},[2085,15215,2108],{"mathvariant":2107},[2085,15217,8630],{},[9163,15219,15220],{},[9166,15221,15222],{"scriptlevel":2513,"displaystyle":2126},[2082,15223,15224,15226,15228,15230,15232,15234,15240,15242,15244,15250,15252],{},[2082,15225],{},[2097,15227,2099],{},[2121,15229,14640],{},[2097,15231,3204],{},[2121,15233,2134],{},[2089,15235,15236,15238],{},[2085,15237,2119],{},[2121,15239,2123],{},[2097,15241,3204],{},[2121,15243,14550],{},[2089,15245,15246,15248],{},[2085,15247,2119],{},[2121,15249,2134],{},[2097,15251,2099],{},[2121,15253,2513],{},[2149,15255,15256],{"encoding":2151},"\\begin{align*}\n\\frac{\\partial \\mathcal{L}}{\\partial x_1} &= 0.4 x_1^{-0.6} x_2^{0.6} - 2\\lambda = 0 \\\\\n\\frac{\\partial \\mathcal{L}}{\\partial x_2} &= 0.6 x_1^{0.4} x_2^{-0.4} - 3\\lambda = 0 \\\\\n\\frac{\\partial \\mathcal{L}}{\\partial \\lambda} &= 120 - 2x_1 - 3x_2 = 0\n\\end{align*}",[2061,15258,15260],{"className":15259,"ariaHidden":2126},[2156],[2061,15261,15263,15266],{"className":15262},[2160],[2061,15264],{"className":15265,"style":9370},[2164],[2061,15267,15269],{"className":15268},[2169],[2061,15270,15272,15597],{"className":15271},[9154],[2061,15273,15275],{"className":15274},[9380],[2061,15276,15278,15589],{"className":15277},[2185,2186],[2061,15279,15281,15586],{"className":15280},[2190],[2061,15282,15284,15397,15510],{"className":15283,"style":9390},[2194],[2061,15285,15286,15289],{"style":9393},[2061,15287],{"className":15288,"style":9397},[2202],[2061,15290,15292],{"className":15291},[2169],[2061,15293,15295,15298,15394],{"className":15294},[2169],[2061,15296],{"className":15297},[2253,2254],[2061,15299,15301],{"className":15300},[2101],[2061,15302,15304,15386],{"className":15303},[2185,2186],[2061,15305,15307,15383],{"className":15306},[2190],[2061,15308,15310,15361,15369],{"className":15309,"style":2846},[2194],[2061,15311,15312,15315],{"style":2270},[2061,15313],{"className":15314,"style":2274},[2202],[2061,15316,15318,15321],{"className":15317},[2169],[2061,15319,2108],{"className":15320,"style":2281},[2169],[2061,15322,15324,15327],{"className":15323},[2169],[2061,15325,2119],{"className":15326},[2169,2170],[2061,15328,15330],{"className":15329},[2181],[2061,15331,15333,15353],{"className":15332},[2185,2186],[2061,15334,15336,15350],{"className":15335},[2190],[2061,15337,15339],{"className":15338,"style":2370},[2194],[2061,15340,15341,15344],{"style":2302},[2061,15342],{"className":15343,"style":2203},[2202],[2061,15345,15347],{"className":15346},[2207,2208,2209,2210],[2061,15348,2123],{"className":15349},[2169,2210],[2061,15351,2218],{"className":15352},[2217],[2061,15354,15356],{"className":15355},[2190],[2061,15357,15359],{"className":15358,"style":2225},[2194],[2061,15360],{},[2061,15362,15363,15366],{"style":2325},[2061,15364],{"className":15365,"style":2274},[2202],[2061,15367],{"className":15368,"style":2333},[2332],[2061,15370,15371,15374],{"style":2336},[2061,15372],{"className":15373,"style":2274},[2202],[2061,15375,15377,15380],{"className":15376},[2169],[2061,15378,2108],{"className":15379,"style":2281},[2169],[2061,15381,8609],{"className":15382},[2169,8708],[2061,15384,2218],{"className":15385},[2217],[2061,15387,15389],{"className":15388},[2190],[2061,15390,15392],{"className":15391,"style":2454},[2194],[2061,15393],{},[2061,15395],{"className":15396},[2444,2254],[2061,15398,15399,15402],{"style":9508},[2061,15400],{"className":15401,"style":9397},[2202],[2061,15403,15405],{"className":15404},[2169],[2061,15406,15408,15411,15507],{"className":15407},[2169],[2061,15409],{"className":15410},[2253,2254],[2061,15412,15414],{"className":15413},[2101],[2061,15415,15417,15499],{"className":15416},[2185,2186],[2061,15418,15420,15496],{"className":15419},[2190],[2061,15421,15423,15474,15482],{"className":15422,"style":2846},[2194],[2061,15424,15425,15428],{"style":2270},[2061,15426],{"className":15427,"style":2274},[2202],[2061,15429,15431,15434],{"className":15430},[2169],[2061,15432,2108],{"className":15433,"style":2281},[2169],[2061,15435,15437,15440],{"className":15436},[2169],[2061,15438,2119],{"className":15439},[2169,2170],[2061,15441,15443],{"className":15442},[2181],[2061,15444,15446,15466],{"className":15445},[2185,2186],[2061,15447,15449,15463],{"className":15448},[2190],[2061,15450,15452],{"className":15451,"style":2370},[2194],[2061,15453,15454,15457],{"style":2302},[2061,15455],{"className":15456,"style":2203},[2202],[2061,15458,15460],{"className":15459},[2207,2208,2209,2210],[2061,15461,2134],{"className":15462},[2169,2210],[2061,15464,2218],{"className":15465},[2217],[2061,15467,15469],{"className":15468},[2190],[2061,15470,15472],{"className":15471,"style":2225},[2194],[2061,15473],{},[2061,15475,15476,15479],{"style":2325},[2061,15477],{"className":15478,"style":2274},[2202],[2061,15480],{"className":15481,"style":2333},[2332],[2061,15483,15484,15487],{"style":2336},[2061,15485],{"className":15486,"style":2274},[2202],[2061,15488,15490,15493],{"className":15489},[2169],[2061,15491,2108],{"className":15492,"style":2281},[2169],[2061,15494,8609],{"className":15495},[2169,8708],[2061,15497,2218],{"className":15498},[2217],[2061,15500,15502],{"className":15501},[2190],[2061,15503,15505],{"className":15504,"style":2454},[2194],[2061,15506],{},[2061,15508],{"className":15509},[2444,2254],[2061,15511,15512,15515],{"style":9622},[2061,15513],{"className":15514,"style":9397},[2202],[2061,15516,15518],{"className":15517},[2169],[2061,15519,15521,15524,15583],{"className":15520},[2169],[2061,15522],{"className":15523},[2253,2254],[2061,15525,15527],{"className":15526},[2101],[2061,15528,15530,15575],{"className":15529},[2185,2186],[2061,15531,15533,15572],{"className":15532},[2190],[2061,15534,15536,15550,15558],{"className":15535,"style":2846},[2194],[2061,15537,15538,15541],{"style":2270},[2061,15539],{"className":15540,"style":2274},[2202],[2061,15542,15544,15547],{"className":15543},[2169],[2061,15545,2108],{"className":15546,"style":2281},[2169],[2061,15548,8630],{"className":15549},[2169,2170],[2061,15551,15552,15555],{"style":2325},[2061,15553],{"className":15554,"style":2274},[2202],[2061,15556],{"className":15557,"style":2333},[2332],[2061,15559,15560,15563],{"style":2336},[2061,15561],{"className":15562,"style":2274},[2202],[2061,15564,15566,15569],{"className":15565},[2169],[2061,15567,2108],{"className":15568,"style":2281},[2169],[2061,15570,8609],{"className":15571},[2169,8708],[2061,15573,2218],{"className":15574},[2217],[2061,15576,15578],{"className":15577},[2190],[2061,15579,15581],{"className":15580,"style":9692},[2194],[2061,15582],{},[2061,15584],{"className":15585},[2444,2254],[2061,15587,2218],{"className":15588},[2217],[2061,15590,15592],{"className":15591},[2190],[2061,15593,15595],{"className":15594,"style":9707},[2194],[2061,15596],{},[2061,15598,15600],{"className":15599},[9713],[2061,15601,15603,16075],{"className":15602},[2185,2186],[2061,15604,15606,16072],{"className":15605},[2190],[2061,15607,15609,15772,15933],{"className":15608,"style":9390},[2194],[2061,15610,15611,15614],{"style":9393},[2061,15612],{"className":15613,"style":9397},[2202],[2061,15615,15617,15620,15623,15626,15629,15632,15691,15745,15748,15751,15754,15757,15760,15763,15766,15769],{"className":15616},[2169],[2061,15618],{"className":15619},[2169],[2061,15621],{"className":15622,"style":2232},[2231],[2061,15624,2099],{"className":15625},[2236],[2061,15627],{"className":15628,"style":2232},[2231],[2061,15630,14191],{"className":15631},[2169],[2061,15633,15635,15638],{"className":15634},[2169],[2061,15636,2119],{"className":15637},[2169,2170],[2061,15639,15641],{"className":15640},[2181],[2061,15642,15644,15682],{"className":15643},[2185,2186],[2061,15645,15647,15679],{"className":15646},[2190],[2061,15648,15650,15662],{"className":15649,"style":14813},[2194],[2061,15651,15653,15656],{"style":15652},"top:-2.4436em;margin-left:0em;margin-right:0.05em;",[2061,15654],{"className":15655,"style":2203},[2202],[2061,15657,15659],{"className":15658},[2207,2208,2209,2210],[2061,15660,2123],{"className":15661},[2169,2210],[2061,15663,15664,15667],{"style":4779},[2061,15665],{"className":15666,"style":2203},[2202],[2061,15668,15670],{"className":15669},[2207,2208,2209,2210],[2061,15671,15673,15676],{"className":15672},[2169,2210],[2061,15674,3204],{"className":15675},[2169,2210],[2061,15677,14200],{"className":15678},[2169,2210],[2061,15680,2218],{"className":15681},[2217],[2061,15683,15685],{"className":15684},[2190],[2061,15686,15689],{"className":15687,"style":15688},[2194],"height:0.2564em;",[2061,15690],{},[2061,15692,15694,15697],{"className":15693},[2169],[2061,15695,2119],{"className":15696},[2169,2170],[2061,15698,15700],{"className":15699},[2181],[2061,15701,15703,15737],{"className":15702},[2185,2186],[2061,15704,15706,15734],{"className":15705},[2190],[2061,15707,15709,15720],{"className":15708,"style":14813},[2194],[2061,15710,15711,15714],{"style":4767},[2061,15712],{"className":15713,"style":2203},[2202],[2061,15715,15717],{"className":15716},[2207,2208,2209,2210],[2061,15718,2134],{"className":15719},[2169,2210],[2061,15721,15722,15725],{"style":4779},[2061,15723],{"className":15724,"style":2203},[2202],[2061,15726,15728],{"className":15727},[2207,2208,2209,2210],[2061,15729,15731],{"className":15730},[2169,2210],[2061,15732,14200],{"className":15733},[2169,2210],[2061,15735,2218],{"className":15736},[2217],[2061,15738,15740],{"className":15739},[2190],[2061,15741,15743],{"className":15742,"style":4802},[2194],[2061,15744],{},[2061,15746],{"className":15747,"style":2980},[2231],[2061,15749,3204],{"className":15750},[2984],[2061,15752],{"className":15753,"style":2980},[2231],[2061,15755,2134],{"className":15756},[2169],[2061,15758,8630],{"className":15759},[2169,2170],[2061,15761],{"className":15762,"style":2232},[2231],[2061,15764,2099],{"className":15765},[2236],[2061,15767],{"className":15768,"style":2232},[2231],[2061,15770,2513],{"className":15771},[2169],[2061,15773,15774,15777],{"style":9508},[2061,15775],{"className":15776,"style":9397},[2202],[2061,15778,15780,15783,15786,15789,15792,15795,15849,15906,15909,15912,15915,15918,15921,15924,15927,15930],{"className":15779},[2169],[2061,15781],{"className":15782},[2169],[2061,15784],{"className":15785,"style":2232},[2231],[2061,15787,2099],{"className":15788},[2236],[2061,15790],{"className":15791,"style":2232},[2231],[2061,15793,14200],{"className":15794},[2169],[2061,15796,15798,15801],{"className":15797},[2169],[2061,15799,2119],{"className":15800},[2169,2170],[2061,15802,15804],{"className":15803},[2181],[2061,15805,15807,15841],{"className":15806},[2185,2186],[2061,15808,15810,15838],{"className":15809},[2190],[2061,15811,15813,15824],{"className":15812,"style":14813},[2194],[2061,15814,15815,15818],{"style":4767},[2061,15816],{"className":15817,"style":2203},[2202],[2061,15819,15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x_1^{-0.6} x_2^{0.6}}{0.6 x_1^{0.4} x_2^{-0.4}} = \\frac{2}{3}",[2061,16163,16165,16470],{"className":16164,"ariaHidden":2126},[2156],[2061,16166,16168,16172,16461,16464,16467],{"className":16167},[2160],[2061,16169],{"className":16170,"style":16171},[2164],"height:2.5418em;vertical-align:-1.0105em;",[2061,16173,16175,16178,16458],{"className":16174},[2169],[2061,16176],{"className":16177},[2253,2254],[2061,16179,16181],{"className":16180},[2101],[2061,16182,16184,16449],{"className":16183},[2185,2186],[2061,16185,16187,16446],{"className":16186},[2190],[2061,16188,16191,16316,16324],{"className":16189,"style":16190},[2194],"height:1.5312em;",[2061,16192,16194,16197],{"style":16193},"top:-2.2558em;",[2061,16195],{"className":16196,"style":2274},[2202],[2061,16198,16200,16203,16257],{"className":16199},[2169],[2061,16201,14200],{"className":16202},[2169],[2061,16204,16206,16209],{"className":16205},[2169],[2061,16207,2119],{"className":16208},[2169,2170],[2061,16210,16212],{"className":16211},[2181],[2061,16213,16215,16249],{"className":16214},[2185,2186],[2061,16216,16218,16246],{"className":16217},[2190],[2061,16219,16221,16232],{"className":16220,"style":2575},[2194],[2061,16222,16223,16226],{"style":4826},[2061,16224],{"className":16225,"style":2203},[2202],[2061,16227,16229],{"className":16228},[2207,2208,2209,2210],[2061,16230,2123],{"className":16231},[2169,2210],[2061,16233,16234,16237],{"style":2590},[2061,16235],{"className":16236,"style":2203},[2202],[2061,16238,16240],{"className":16239},[2207,2208,2209,2210],[2061,16241,16243],{"className":16242},[2169,2210],[2061,16244,14191],{"className":16245},[2169,2210],[2061,16247,2218],{"className":16248},[2217],[2061,16250,16252],{"className":16251},[2190],[2061,16253,16255],{"className":16254,"style":4861},[2194],[2061,16256],{},[2061,16258,16260,16263],{"className":16259},[2169],[2061,16261,2119],{"className":16262},[2169,2170],[2061,16264,16266],{"className":16265},[2181],[2061,16267,16269,16308],{"className":16268},[2185,2186],[2061,16270,16272,16305],{"className":16271},[2190],[2061,16273,16276,16287],{"className":16274,"style":16275},[2194],"height:0.8542em;",[2061,16277,16278,16281],{"style":4826},[2061,16279],{"className":16280,"style":2203},[2202],[2061,16282,16284],{"className":16283},[2207,2208,2209,2210],[2061,16285,2134],{"className":16286},[2169,2210],[2061,16288,16290,16293],{"style":16289},"top:-3.1031em;margin-right:0.05em;",[2061,16291],{"className":16292,"style":2203},[2202],[2061,16294,16296],{"className":16295},[2207,2208,2209,2210],[2061,16297,16299,16302],{"className":16298},[2169,2210],[2061,16300,3204],{"className":16301},[2169,2210],[2061,16303,14191],{"className":16304},[2169,2210],[2061,16306,2218],{"className":16307},[2217],[2061,16309,16311],{"className":16310},[2190],[2061,16312,16314],{"className":16313,"style":4861},[2194],[2061,16315],{},[2061,16317,16318,16321],{"style":2325},[2061,16319],{"className":16320,"style":2274},[2202],[2061,16322],{"className":16323,"style":2333},[2332],[2061,16325,16326,16329],{"style":2336},[2061,16327],{"className":16328,"style":2274},[2202],[2061,16330,16332,16335,16392],{"className":16331},[2169],[2061,16333,14191],{"className":16334},[2169],[2061,16336,16338,16341],{"className":16337},[2169],[2061,16339,2119],{"className":16340},[2169,2170],[2061,16342,16344],{"className":16343},[2181],[2061,16345,16347,16384],{"className":16346},[2185,2186],[2061,16348,16350,16381],{"className":16349},[2190],[2061,16351,16353,16364],{"className":16352,"style":16275},[2194],[2061,16354,16355,16358],{"style":4826},[2061,16356],{"className":16357,"style":2203},[2202],[2061,16359,16361],{"className":16360},[2207,2208,2209,2210],[2061,16362,2123],{"className":16363},[2169,2210],[2061,16365,16366,16369],{"style":16289},[2061,16367],{"className":16368,"style":2203},[2202],[2061,16370,16372],{"className":16371},[2207,2208,2209,2210],[2061,16373,16375,16378],{"className":16374},[2169,2210],[2061,16376,3204],{"className":16377},[2169,2210],[2061,16379,14200],{"className":16380},[2169,2210],[2061,16382,2218],{"className":16383},[2217],[2061,16385,16387],{"className":16386},[2190],[2061,16388,16390],{"className":16389,"style":4861},[2194],[2061,16391],{},[2061,16393,16395,16398],{"className":16394},[2169],[2061,16396,2119],{"className":16397},[2169,2170],[2061,16399,16401],{"className":16400},[2181],[2061,16402,16404,16438],{"className":16403},[2185,2186],[2061,16405,16407,16435],{"className":16406},[2190],[2061,16408,16410,16421],{"className":16409,"style":2646},[2194],[2061,16411,16412,16415],{"style":14344},[2061,16413],{"className":16414,"style":2203},[2202],[2061,16416,16418],{"className":16417},[2207,2208,2209,2210],[2061,16419,2134],{"className":16420},[2169,2210],[2061,16422,16423,16426],{"style":2649},[2061,16424],{"className":16425,"style":2203},[2202],[2061,16427,16429],{"className":16428},[2207,2208,2209,2210],[2061,16430,16432],{"className":16431},[2169,2210],[2061,16433,14200],{"className":16434},[2169,2210],[2061,16436,2218],{"className":16437},[2217],[2061,16439,16441],{"className":16440},[2190],[2061,16442,16444],{"className":16443,"style":14377},[2194],[2061,16445],{},[2061,16447,2218],{"className":16448},[2217],[2061,16450,16452],{"className":16451},[2190],[2061,16453,16456],{"className":16454,"style":16455},[2194],"height:1.0105em;",[2061,16457],{},[2061,16459],{"className":16460},[2444,2254],[2061,16462],{"className":16463,"style":2232},[2231],[2061,16465,2099],{"className":16466},[2236],[2061,16468],{"className":16469,"style":2232},[2231],[2061,16471,16473,16477],{"className":16472},[2160],[2061,16474],{"className":16475,"style":16476},[2164],"height:2.0074em;vertical-align:-0.686em;",[2061,16478,16480,16483,16537],{"className":16479},[2169],[2061,16481],{"className":16482},[2253,2254],[2061,16484,16486],{"className":16485},[2101],[2061,16487,16489,16529],{"className":16488},[2185,2186],[2061,16490,16492,16526],{"className":16491},[2190],[2061,16493,16496,16507,16515],{"className":16494,"style":16495},[2194],"height:1.3214em;",[2061,16497,16498,16501],{"style":2270},[2061,16499],{"className":16500,"style":2274},[2202],[2061,16502,16504],{"className":16503},[2169],[2061,16505,14550],{"className":16506},[2169],[2061,16508,16509,16512],{"style":2325},[2061,16510],{"className":16511,"style":2274},[2202],[2061,16513],{"className":16514,"style":2333},[2332],[2061,16516,16517,16520],{"style":2336},[2061,16518],{"className":16519,"style":2274},[2202],[2061,16521,16523],{"className":16522},[2169],[2061,16524,2134],{"className":16525},[2169],[2061,16527,2218],{"className":16528},[2217],[2061,16530,16532],{"className":16531},[2190],[2061,16533,16535],{"className":16534,"style":9692},[2194],[2061,16536],{},[2061,16538],{"className":16539},[2444,2254],[1798,16541,16542],{},"简化得：",[2061,16544,16546],{"className":16545},[2064],[2061,16547,16549,16592],{"className":16548},[2068],[2061,16550,16552],{"className":16551},[2072],[2074,16553,16554],{"xmlns":2076,"display":2077},[2079,16555,16556,16589],{},[2082,16557,16558,16564,16567,16581,16583],{},[2101,16559,16560,16562],{},[2121,16561,14191],{},[2121,16563,14200],{},[2097,16565,16566],{},"⋅",[2101,16568,16569,16575],{},[2089,16570,16571,16573],{},[2085,16572,2119],{},[2121,16574,2134],{},[2089,16576,16577,16579],{},[2085,16578,2119],{},[2121,16580,2123],{},[2097,16582,2099],{},[2101,16584,16585,16587],{},[2121,16586,2134],{},[2121,16588,14550],{},[2149,16590,16591],{"encoding":2151},"\\frac{0.4}{0.6} \\cdot \\frac{x_2}{x_1} = \\frac{2}{3}",[2061,16593,16595,16672,16824],{"className":16594,"ariaHidden":2126},[2156],[2061,16596,16598,16601,16663,16666,16669],{"className":16597},[2160],[2061,16599],{"className":16600,"style":16476},[2164],[2061,16602,16604,16607,16660],{"className":16603},[2169],[2061,16605],{"className":16606},[2253,2254],[2061,16608,16610],{"className":16609},[2101],[2061,16611,16613,16652],{"className":16612},[2185,2186],[2061,16614,16616,16649],{"className":16615},[2190],[2061,16617,16619,16630,16638],{"className":16618,"style":16495},[2194],[2061,16620,16621,16624],{"style":2270},[2061,16622],{"className":16623,"style":2274},[2202],[2061,16625,16627],{"className":16626},[2169],[2061,16628,14200],{"className":16629},[2169],[2061,16631,16632,16635],{"style":2325},[2061,16633],{"className":16634,"style":2274},[2202],[2061,16636],{"className":16637,"style":2333},[2332],[2061,16639,16640,16643],{"style":2336},[2061,16641],{"className":16642,"style":2274},[2202],[2061,16644,16646],{"className":16645},[2169],[2061,16647,14191],{"className":16648},[2169],[2061,16650,2218],{"className":16651},[2217],[2061,16653,16655],{"className":16654},[2190],[2061,16656,16658],{"className":16657,"style":9692},[2194],[2061,16659],{},[2061,16661],{"className":16662},[2444,2254],[2061,16664],{"className":16665,"style":2980},[2231],[2061,16667,16566],{"className":16668},[2984],[2061,16670],{"className":16671,"style":2980},[2231],[2061,16673,16675,16679,16815,16818,16821],{"className":16674},[2160],[2061,16676],{"className":16677,"style":16678},[2164],"height:1.9436em;vertical-align:-0.836em;",[2061,16680,16682,16685,16812],{"className":16681},[2169],[2061,16683],{"className":16684},[2253,2254],[2061,16686,16688],{"className":16687},[2101],[2061,16689,16691,16804],{"className":16690},[2185,2186],[2061,16692,16694,16801],{"className":16693},[2190],[2061,16695,16697,16745,16753],{"className":16696,"style":8140},[2194],[2061,16698,16699,16702],{"style":2270},[2061,16700],{"className":16701,"style":2274},[2202],[2061,16703,16705],{"className":16704},[2169],[2061,16706,16708,16711],{"className":16707},[2169],[2061,16709,2119],{"className":16710},[2169,2170],[2061,16712,16714],{"className":16713},[2181],[2061,16715,16717,16737],{"className":16716},[2185,2186],[2061,16718,16720,16734],{"className":16719},[2190],[2061,16721,16723],{"className":16722,"style":2370},[2194],[2061,16724,16725,16728],{"style":2302},[2061,16726],{"className":16727,"style":2203},[2202],[2061,16729,16731],{"className":16730},[2207,2208,2209,2210],[2061,16732,2123],{"className":16733},[2169,2210],[2061,16735,2218],{"className":16736},[2217],[2061,16738,16740],{"className":16739},[2190],[2061,16741,16743],{"className":16742,"style":2225},[2194],[2061,16744],{},[2061,16746,16747,16750],{"style":2325},[2061,16748],{"className":16749,"style":2274},[2202],[2061,16751],{"className":16752,"style":2333},[2332],[2061,16754,16755,16758],{"style":2336},[2061,16756],{"className":16757,"style":2274},[2202],[2061,16759,16761],{"className":16760},[2169],[2061,16762,16764,16767],{"className":16763},[2169],[2061,16765,2119],{"className":16766},[2169,2170],[2061,16768,16770],{"className":16769},[2181],[2061,16771,16773,16793],{"className":16772},[2185,2186],[2061,16774,16776,16790],{"className":16775},[2190],[2061,16777,16779],{"className":16778,"style":2370},[2194],[2061,16780,16781,16784],{"style":2302},[2061,16782],{"className":16783,"style":2203},[2202],[2061,16785,16787],{"className":16786},[2207,2208,2209,2210],[2061,16788,2134],{"className":16789},[2169,2210],[2061,16791,2218],{"className":16792},[2217],[2061,16794,16796],{"className":16795},[2190],[2061,16797,16799],{"className":16798,"style":2225},[2194],[2061,16800],{},[2061,16802,2218],{"className":16803},[2217],[2061,16805,16807],{"className":16806},[2190],[2061,16808,16810],{"className":16809,"style":2454},[2194],[2061,16811],{},[2061,16813],{"className":16814},[2444,2254],[2061,16816],{"className":16817,"style":2232},[2231],[2061,16819,2099],{"className":16820},[2236],[2061,16822],{"className":16823,"style":2232},[2231],[2061,16825,16827,16830],{"className":16826},[2160],[2061,16828],{"className":16829,"style":16476},[2164],[2061,16831,16833,16836,16889],{"className":16832},[2169],[2061,16834],{"className":16835},[2253,2254],[2061,16837,16839],{"className":16838},[2101],[2061,16840,16842,16881],{"className":16841},[2185,2186],[2061,16843,16845,16878],{"className":16844},[2190],[2061,16846,16848,16859,16867],{"className":16847,"style":16495},[2194],[2061,16849,16850,16853],{"style":2270},[2061,16851],{"className":16852,"style":2274},[2202],[2061,16854,16856],{"className":16855},[2169],[2061,16857,14550],{"className":16858},[2169],[2061,16860,16861,16864],{"style":2325},[2061,16862],{"className":16863,"style":2274},[2202],[2061,16865],{"className":16866,"style":2333},[2332],[2061,16868,16869,16872],{"style":2336},[2061,16870],{"className":16871,"style":2274},[2202],[2061,16873,16875],{"className":16874},[2169],[2061,16876,2134],{"className":16877},[2169],[2061,16879,2218],{"className":16880},[2217],[2061,16882,16884],{"className":16883},[2190],[2061,16885,16887],{"className":16886,"style":9692},[2194],[2061,16888],{},[2061,16890],{"className":16891},[2444,2254],[2061,16893,16895],{"className":16894},[2064],[2061,16896,16898,16940],{"className":16897},[2068],[2061,16899,16901],{"className":16900},[2072],[2074,16902,16903],{"xmlns":2076,"display":2077},[2079,16904,16905,16937],{},[2082,16906,16907,16929,16931],{},[2101,16908,16909,16919],{},[2082,16910,16911,16913],{},[2121,16912,2134],{},[2089,16914,16915,16917],{},[2085,16916,2119],{},[2121,16918,2134],{},[2082,16920,16921,16923],{},[2121,16922,14550],{},[2089,16924,16925,16927],{},[2085,16926,2119],{},[2121,16928,2123],{},[2097,16930,2099],{},[2101,16932,16933,16935],{},[2121,16934,2134],{},[2121,16936,14550],{},[2149,16938,16939],{"encoding":2151},"\\frac{2x_2}{3x_1} = \\frac{2}{3}",[2061,16941,16943,17101],{"className":16942,"ariaHidden":2126},[2156],[2061,16944,16946,16950,17092,17095,17098],{"className":16945},[2160],[2061,16947],{"className":16948,"style":16949},[2164],"height:2.1574em;vertical-align:-0.836em;",[2061,16951,16953,16956,17089],{"className":16952},[2169],[2061,16954],{"className":16955},[2253,2254],[2061,16957,16959],{"className":16958},[2101],[2061,16960,16962,17081],{"className":16961},[2185,2186],[2061,16963,16965,17078],{"className":16964},[2190],[2061,16966,16968,17019,17027],{"className":16967,"style":16495},[2194],[2061,16969,16970,16973],{"style":2270},[2061,16971],{"className":16972,"style":2274},[2202],[2061,16974,16976,16979],{"className":16975},[2169],[2061,16977,14550],{"className":16978},[2169],[2061,16980,16982,16985],{"className":16981},[2169],[2061,16983,2119],{"className":16984},[2169,2170],[2061,16986,16988],{"className":16987},[2181],[2061,16989,16991,17011],{"className":16990},[2185,2186],[2061,16992,16994,17008],{"className":16993},[2190],[2061,16995,16997],{"className":16996,"style":2370},[2194],[2061,16998,16999,17002],{"style":2302},[2061,17000],{"className":17001,"style":2203},[2202],[2061,17003,17005],{"className":17004},[2207,2208,2209,2210],[2061,17006,2123],{"className":17007},[2169,2210],[2061,17009,2218],{"className":17010},[2217],[2061,17012,17014],{"className":17013},[2190],[2061,17015,17017],{"className":17016,"style":2225},[2194],[2061,17018],{},[2061,17020,17021,17024],{"style":2325},[2061,17022],{"className":17023,"style":2274},[2202],[2061,17025],{"className":17026,"style":2333},[2332],[2061,17028,17029,17032],{"style":2336},[2061,17030],{"className":17031,"style":2274},[2202],[2061,17033,17035,17038],{"className":17034},[2169],[2061,17036,2134],{"className":17037},[2169],[2061,17039,17041,17044],{"className":17040},[2169],[2061,17042,2119],{"className":17043},[2169,2170],[2061,17045,17047],{"className":17046},[2181],[2061,17048,17050,17070],{"className":17049},[2185,2186],[2061,17051,17053,17067],{"className":17052},[2190],[2061,17054,17056],{"className":17055,"style":2370},[2194],[2061,17057,17058,17061],{"style":2302},[2061,17059],{"className":17060,"style":2203},[2202],[2061,17062,17064],{"className":17063},[2207,2208,2209,2210],[2061,17065,2134],{"className":17066},[2169,2210],[2061,17068,2218],{"className":17069},[2217],[2061,17071,17073],{"className":17072},[2190],[2061,17074,17076],{"className":17075,"style":2225},[2194],[2061,17077],{},[2061,17079,2218],{"className":17080},[2217],[2061,17082,17084],{"className":17083},[2190],[2061,17085,17087],{"className":17086,"style":2454},[2194],[2061,17088],{},[2061,17090],{"className":17091},[2444,2254],[2061,17093],{"className":17094,"style":2232},[2231],[2061,17096,2099],{"className":17097},[2236],[2061,17099],{"className":17100,"style":2232},[2231],[2061,17102,17104,17107],{"className":17103},[2160],[2061,17105],{"className":17106,"style":16476},[2164],[2061,17108,17110,17113,17166],{"className":17109},[2169],[2061,17111],{"className":17112},[2253,2254],[2061,17114,17116],{"className":17115},[2101],[2061,17117,17119,17158],{"className":17118},[2185,2186],[2061,17120,17122,17155],{"className":17121},[2190],[2061,17123,17125,17136,17144],{"className":17124,"style":16495},[2194],[2061,17126,17127,17130],{"style":2270},[2061,17128],{"className":17129,"style":2274},[2202],[2061,17131,17133],{"className":17132},[2169],[2061,17134,14550],{"className":17135},[2169],[2061,17137,17138,17141],{"style":2325},[2061,17139],{"className":17140,"style":2274},[2202],[2061,17142],{"className":17143,"style":2333},[2332],[2061,17145,17146,17149],{"style":2336},[2061,17147],{"className":17148,"style":2274},[2202],[2061,17150,17152],{"className":17151},[2169],[2061,17153,2134],{"className":17154},[2169],[2061,17156,2218],{"className":17157},[2217],[2061,17159,17161],{"className":17160},[2190],[2061,17162,17164],{"className":17163,"style":9692},[2194],[2061,17165],{},[2061,17167],{"className":17168},[2444,2254],[2061,17170,17172],{"className":17171},[2064],[2061,17173,17175,17201],{"className":17174},[2068],[2061,17176,17178],{"className":17177},[2072],[2074,17179,17180],{"xmlns":2076,"display":2077},[2079,17181,17182,17198],{},[2082,17183,17184,17190,17192],{},[2089,17185,17186,17188],{},[2085,17187,2119],{},[2121,17189,2134],{},[2097,17191,2099],{},[2089,17193,17194,17196],{},[2085,17195,2119],{},[2121,17197,2123],{},[2149,17199,17200],{"encoding":2151},"x_2 = x_1",[2061,17202,17204,17259],{"className":17203,"ariaHidden":2126},[2156],[2061,17205,17207,17210,17250,17253,17256],{"className":17206},[2160],[2061,17208],{"className":17209,"style":7092},[2164],[2061,17211,17213,17216],{"className":17212},[2169],[2061,17214,2119],{"className":17215},[2169,2170],[2061,17217,17219],{"className":17218},[2181],[2061,17220,17222,17242],{"className":17221},[2185,2186],[2061,17223,17225,17239],{"className":17224},[2190],[2061,17226,17228],{"className":17227,"style":2370},[2194],[2061,17229,17230,17233],{"style":2302},[2061,17231],{"className":17232,"style":2203},[2202],[2061,17234,17236],{"className":17235},[2207,2208,2209,2210],[2061,17237,2134],{"className":17238},[2169,2210],[2061,17240,2218],{"className":17241},[2217],[2061,17243,17245],{"className":17244},[2190],[2061,17246,17248],{"className":17247,"style":2225},[2194],[2061,17249],{},[2061,17251],{"className":17252,"style":2232},[2231],[2061,17254,2099],{"className":17255},[2236],[2061,17257],{"className":17258,"style":2232},[2231],[2061,17260,17262,17265],{"className":17261},[2160],[2061,17263],{"className":17264,"style":7092},[2164],[2061,17266,17268,17271],{"className":17267},[2169],[2061,17269,2119],{"className":17270},[2169,2170],[2061,17272,17274],{"className":17273},[2181],[2061,17275,17277,17297],{"className":17276},[2185,2186],[2061,17278,17280,17294],{"className":17279},[2190],[2061,17281,17283],{"className":17282,"style":2370},[2194],[2061,17284,17285,17288],{"style":2302},[2061,17286],{"className":17287,"style":2203},[2202],[2061,17289,17291],{"className":17290},[2207,2208,2209,2210],[2061,17292,2123],{"className":17293},[2169,2210],[2061,17295,2218],{"className":17296},[2217],[2061,17298,17300],{"className":17299},[2190],[2061,17301,17303],{"className":17302,"style":2225},[2194],[2061,17304],{},[1798,17306,17307],{},"代入预算约束：",[2061,17309,17311],{"className":17310},[2064],[2061,17312,17314,17348],{"className":17313},[2068],[2061,17315,17317],{"className":17316},[2072],[2074,17318,17319],{"xmlns":2076,"display":2077},[2079,17320,17321,17345],{},[2082,17322,17323,17325,17331,17333,17335,17341,17343],{},[2121,17324,2134],{},[2089,17326,17327,17329],{},[2085,17328,2119],{},[2121,17330,2123],{},[2097,17332,2762],{},[2121,17334,14550],{},[2089,17336,17337,17339],{},[2085,17338,2119],{},[2121,17340,2123],{},[2097,17342,2099],{},[2121,17344,14640],{},[2149,17346,17347],{"encoding":2151},"2x_1 + 3x_1 = 120",[2061,17349,17351,17409,17467],{"className":17350,"ariaHidden":2126},[2156],[2061,17352,17354,17357,17360,17400,17403,17406],{"className":17353},[2160],[2061,17355],{"className":17356,"style":14943},[2164],[2061,17358,2134],{"className":17359},[2169],[2061,17361,17363,17366],{"className":17362},[2169],[2061,17364,2119],{"className":17365},[2169,2170],[2061,17367,17369],{"className":17368},[2181],[2061,17370,17372,17392],{"className":17371},[2185,2186],[2061,17373,17375,17389],{"className":17374},[2190],[2061,17376,17378],{"className":17377,"style":2370},[2194],[2061,17379,17380,17383],{"style":2302},[2061,17381],{"className":17382,"style":2203},[2202],[2061,17384,17386],{"className":17385},[2207,2208,2209,2210],[2061,17387,2123],{"className":17388},[2169,2210],[2061,17390,2218],{"className":17391},[2217],[2061,17393,17395],{"className":17394},[2190],[2061,17396,17398],{"className":17397,"style":2225},[2194],[2061,17399],{},[2061,17401],{"className":17402,"style":2980},[2231],[2061,17404,2762],{"className":17405},[2984],[2061,17407],{"className":17408,"style":2980},[2231],[2061,17410,17412,17415,17418,17458,17461,17464],{"className":17411},[2160],[2061,17413],{"className":17414,"style":14943},[2164],[2061,17416,14550],{"className":17417},[2169],[2061,17419,17421,17424],{"className":17420},[2169],[2061,17422,2119],{"className":17423},[2169,2170],[2061,17425,17427],{"className":17426},[2181],[2061,17428,17430,17450],{"className":17429},[2185,2186],[2061,17431,17433,17447],{"className":17432},[2190],[2061,17434,17436],{"className":17435,"style":2370},[2194],[2061,17437,17438,17441],{"style":2302},[2061,17439],{"className":17440,"style":2203},[2202],[2061,17442,17444],{"className":17443},[2207,2208,2209,2210],[2061,17445,2123],{"className":17446},[2169,2210],[2061,17448,2218],{"className":17449},[2217],[2061,17451,17453],{"className":17452},[2190],[2061,17454,17456],{"className":17455,"style":2225},[2194],[2061,17457],{},[2061,17459],{"className":17460,"style":2232},[2231],[2061,17462,2099],{"className":17463},[2236],[2061,17465],{"className":17466,"style":2232},[2231],[2061,17468,17470,17473],{"className":17469},[2160],[2061,17471],{"className":17472,"style":2692},[2164],[2061,17474,14640],{"className":17475},[2169],[2061,17477,17479],{"className":17478},[2064],[2061,17480,17482,17523],{"className":17481},[2068],[2061,17483,17485],{"className":17484},[2072],[2074,17486,17487],{"xmlns":2076,"display":2077},[2079,17488,17489,17520],{},[2082,17490,17491,17499,17501,17504,17506,17508,17516,17518],{},[2500,17492,17493,17495,17497],{},[2085,17494,2119],{},[2121,17496,2123],{},[2097,17498,10359],{},[2097,17500,2099],{},[2121,17502,17503],{},"24",[2097,17505,2127],{"separator":2126},[2231,17507],{"width":4610},[2500,17509,17510,17512,17514],{},[2085,17511,2119],{},[2121,17513,2134],{},[2097,17515,10359],{},[2097,17517,2099],{},[2121,17519,17503],{},[2149,17521,17522],{"encoding":2151},"x_1^* = 24, \\quad x_2^* = 24",[2061,17524,17526,17592,17670],{"className":17525,"ariaHidden":2126},[2156],[2061,17527,17529,17532,17583,17586,17589],{"className":17528},[2160],[2061,17530],{"className":17531,"style":10402},[2164],[2061,17533,17535,17538],{"className":17534},[2169],[2061,17536,2119],{"className":17537},[2169,2170],[2061,17539,17541],{"className":17540},[2181],[2061,17542,17544,17575],{"className":17543},[2185,2186],[2061,17545,17547,17572],{"className":17546},[2190],[2061,17548,17550,17561],{"className":17549,"style":10421},[2194],[2061,17551,17552,17555],{"style":4767},[2061,17553],{"className":17554,"style":2203},[2202],[2061,17556,17558],{"className":17557},[2207,2208,2209,2210],[2061,17559,2123],{"className":17560},[2169,2210],[2061,17562,17563,17566],{"style":4779},[2061,17564],{"className":17565,"style":2203},[2202],[2061,17567,17569],{"className":17568},[2207,2208,2209,2210],[2061,17570,10359],{"className":17571},[2984,2210],[2061,17573,2218],{"className":17574},[2217],[2061,17576,17578],{"className":17577},[2190],[2061,17579,17581],{"className":17580,"style":4802},[2194],[2061,17582],{},[2061,17584],{"className":17585,"style":2232},[2231],[2061,17587,2099],{"className":17588},[2236],[2061,17590],{"className":17591,"style":2232},[2231],[2061,17593,17595,17598,17601,17604,17607,17610,17661,17664,17667],{"className":17594},[2160],[2061,17596],{"className":17597,"style":10402},[2164],[2061,17599,17503],{"className":17600},[2169],[2061,17602,2127],{"className":17603},[2396],[2061,17605],{"className":17606,"style":4870},[2231],[2061,17608],{"className":17609,"style":2400},[2231],[2061,17611,17613,17616],{"className":17612},[2169],[2061,17614,2119],{"className":17615},[2169,2170],[2061,17617,17619],{"className":17618},[2181],[2061,17620,17622,17653],{"className":17621},[2185,2186],[2061,17623,17625,17650],{"className":17624},[2190],[2061,17626,17628,17639],{"className":17627,"style":10421},[2194],[2061,17629,17630,17633],{"style":4767},[2061,17631],{"className":17632,"style":2203},[2202],[2061,17634,17636],{"className":17635},[2207,2208,2209,2210],[2061,17637,2134],{"className":17638},[2169,2210],[2061,17640,17641,17644],{"style":4779},[2061,17642],{"className":17643,"style":2203},[2202],[2061,17645,17647],{"className":17646},[2207,2208,2209,2210],[2061,17648,10359],{"className":17649},[2984,2210],[2061,17651,2218],{"className":17652},[2217],[2061,17654,17656],{"className":17655},[2190],[2061,17657,17659],{"className":17658,"style":4802},[2194],[2061,17660],{},[2061,17662],{"className":17663,"style":2232},[2231],[2061,17665,2099],{"className":17666},[2236],[2061,17668],{"className":17669,"style":2232},[2231],[2061,17671,17673,17676],{"className":17672},[2160],[2061,17674],{"className":17675,"style":2692},[2164],[2061,17677,17503],{"className":17678},[2169],[1798,17680,17681,17684],{},[1865,17682,17683],{},"一般形式的马歇尔需求函数","（柯布-道格拉斯的重要性质）：",[2061,17686,17688],{"className":17687},[2064],[2061,17689,17691,17765],{"className":17690},[2068],[2061,17692,17694],{"className":17693},[2072],[2074,17695,17696],{"xmlns":2076,"display":2077},[2079,17697,17698,17762],{},[2082,17699,17700,17706,17708,17714,17716,17722,17724,17726,17728,17730,17744,17746,17758,17760],{},[2089,17701,17702,17704],{},[2085,17703,2119],{},[2121,17705,2123],{},[2097,17707,2114],{"stretchy":2113},[2089,17709,17710,17712],{},[2085,17711,1798],{},[2121,17713,2123],{},[2097,17715,2127],{"separator":2126},[2089,17717,17718,17720],{},[2085,17719,1798],{},[2121,17721,2134],{},[2097,17723,2127],{"separator":2126},[2085,17725,7160],{},[2097,17727,2137],{"stretchy":2113},[2097,17729,2099],{},[2101,17731,17732,17738],{},[2082,17733,17734,17736],{},[2121,17735,14191],{},[2085,17737,7160],{},[2089,17739,17740,17742],{},[2085,17741,1798],{},[2121,17743,2123],{},[2097,17745,2099],{},[2101,17747,17748,17756],{},[2082,17749,17750,17752,17754],{},[2121,17751,14191],{},[2097,17753,16566],{},[2121,17755,14640],{},[2121,17757,2134],{},[2097,17759,2099],{},[2121,17761,17503],{},[2149,17763,17764],{"encoding":2151},"x_1(p_1, p_2, m) = \\frac{0.4m}{p_1} = \\frac{0.4 \\cdot 120}{2} = 24",[2061,17766,17768,17924,18042,18131],{"className":17767,"ariaHidden":2126},[2156],[2061,17769,17771,17774,17814,17817,17857,17860,17863,17903,17906,17909,17912,17915,17918,17921],{"className":17770},[2160],[2061,17772],{"className":17773,"style":4634},[2164],[2061,17775,17777,17780],{"className":17776},[2169],[2061,17778,2119],{"className":17779},[2169,2170],[2061,17781,17783],{"className":17782},[2181],[2061,17784,17786,17806],{"className":17785},[2185,2186],[2061,17787,17789,17803],{"className":17788},[2190],[2061,17790,17792],{"className":17791,"style":2370},[2194],[2061,17793,17794,17797],{"style":2302},[2061,17795],{"className":17796,"style":2203},[2202],[2061,17798,17800],{"className":17799},[2207,2208,2209,2210],[2061,17801,2123],{"className":17802},[2169,2210],[2061,17804,2218],{"className":17805},[2217],[2061,17807,17809],{"className":17808},[2190],[2061,17810,17812],{"className":17811,"style":2225},[2194],[2061,17813],{},[2061,17815,2114],{"className":17816},[2253],[2061,17818,17820,17823],{"className":17819},[2169],[2061,17821,1798],{"className":17822},[2169,2170],[2061,17824,17826],{"className":17825},[2181],[2061,17827,17829,17849],{"className":17828},[2185,2186],[2061,17830,17832,17846],{"className":17831},[2190],[2061,17833,17835],{"className":17834,"style":2370},[2194],[2061,17836,17837,17840],{"style":2302},[2061,17838],{"className":17839,"style":2203},[2202],[2061,17841,17843],{"className":17842},[2207,2208,2209,2210],[2061,17844,2123],{"className":17845},[2169,2210],[2061,17847,2218],{"className":17848},[2217],[2061,17850,17852],{"className":17851},[2190],[2061,17853,17855],{"className":17854,"style":2225},[2194],[2061,17856],{},[2061,17858,2127],{"className":17859},[2396],[2061,17861],{"className":17862,"style":2400},[2231],[2061,17864,17866,17869],{"className":17865},[2169],[2061,17867,1798],{"className":17868},[2169,2170],[2061,17870,17872],{"className":17871},[2181],[2061,17873,17875,17895],{"className":17874},[2185,2186],[2061,17876,17878,17892],{"className":17877},[2190],[2061,17879,17881],{"className":17880,"style":2370},[2194],[2061,17882,17883,17886],{"style":2302},[2061,17884],{"className":17885,"style":2203},[2202],[2061,17887,17889],{"className":17888},[2207,2208,2209,2210],[2061,17890,2134],{"className":17891},[2169,2210],[2061,17893,2218],{"className":17894},[2217],[2061,17896,17898],{"className":17897},[2190],[2061,17899,17901],{"className":17900,"style":2225},[2194],[2061,17902],{},[2061,17904,2127],{"className":17905},[2396],[2061,17907],{"className":17908,"style":2400},[2231],[2061,17910,7160],{"className":17911},[2169,2170],[2061,17913,2137],{"className":17914},[2444],[2061,17916],{"className":17917,"style":2232},[2231],[2061,17919,2099],{"className":17920},[2236],[2061,17922],{"className":17923,"style":2232},[2231],[2061,17925,17927,17931,18033,18036,18039],{"className":17926},[2160],[2061,17928],{"className":17929,"style":17930},[2164],"height:2.2019em;vertical-align:-0.8804em;",[2061,17932,17934,17937,18030],{"className":17933},[2169],[2061,17935],{"className":17936},[2253,2254],[2061,17938,17940],{"className":17939},[2101],[2061,17941,17943,18022],{"className":17942},[2185,2186],[2061,17944,17946,18019],{"className":17945},[2190],[2061,17947,17949,17997,18005],{"className":17948,"style":16495},[2194],[2061,17950,17951,17954],{"style":2270},[2061,17952],{"className":17953,"style":2274},[2202],[2061,17955,17957],{"className":17956},[2169],[2061,17958,17960,17963],{"className":17959},[2169],[2061,17961,1798],{"className":17962},[2169,2170],[2061,17964,17966],{"className":17965},[2181],[2061,17967,17969,17989],{"className":17968},[2185,2186],[2061,17970,17972,17986],{"className":17971},[2190],[2061,17973,17975],{"className":17974,"style":2370},[2194],[2061,17976,17977,17980],{"style":2302},[2061,17978],{"className":17979,"style":2203},[2202],[2061,17981,17983],{"className":17982},[2207,2208,2209,2210],[2061,17984,2123],{"className":17985},[2169,2210],[2061,17987,2218],{"className":17988},[2217],[2061,17990,17992],{"className":17991},[2190],[2061,17993,17995],{"className":17994,"style":2225},[2194],[2061,17996],{},[2061,17998,17999,18002],{"style":2325},[2061,18000],{"className":18001,"style":2274},[2202],[2061,18003],{"className":18004,"style":2333},[2332],[2061,18006,18007,18010],{"style":2336},[2061,18008],{"className":18009,"style":2274},[2202],[2061,18011,18013,18016],{"className":18012},[2169],[2061,18014,14191],{"className":18015},[2169],[2061,18017,7160],{"className":18018},[2169,2170],[2061,18020,2218],{"className":18021},[2217],[2061,18023,18025],{"className":18024},[2190],[2061,18026,18028],{"className":18027,"style":8254},[2194],[2061,18029],{},[2061,18031],{"className":18032},[2444,2254],[2061,18034],{"className":18035,"style":2232},[2231],[2061,18037,2099],{"className":18038},[2236],[2061,18040],{"className":18041,"style":2232},[2231],[2061,18043,18045,18048,18122,18125,18128],{"className":18044},[2160],[2061,18046],{"className":18047,"style":16476},[2164],[2061,18049,18051,18054,18119],{"className":18050},[2169],[2061,18052],{"className":18053},[2253,2254],[2061,18055,18057],{"className":18056},[2101],[2061,18058,18060,18111],{"className":18059},[2185,2186],[2061,18061,18063,18108],{"className":18062},[2190],[2061,18064,18066,18077,18085],{"className":18065,"style":16495},[2194],[2061,18067,18068,18071],{"style":2270},[2061,18069],{"className":18070,"style":2274},[2202],[2061,18072,18074],{"className":18073},[2169],[2061,18075,2134],{"className":18076},[2169],[2061,18078,18079,18082],{"style":2325},[2061,18080],{"className":18081,"style":2274},[2202],[2061,18083],{"className":18084,"style":2333},[2332],[2061,18086,18087,18090],{"style":2336},[2061,18088],{"className":18089,"style":2274},[2202],[2061,18091,18093,18096,18099,18102,18105],{"className":18092},[2169],[2061,18094,14191],{"className":18095},[2169],[2061,18097],{"className":18098,"style":2980},[2231],[2061,18100,16566],{"className":18101},[2984],[2061,18103],{"className":18104,"style":2980},[2231],[2061,18106,14640],{"className":18107},[2169],[2061,18109,2218],{"className":18110},[2217],[2061,18112,18114],{"className":18113},[2190],[2061,18115,18117],{"className":18116,"style":9692},[2194],[2061,18118],{},[2061,18120],{"className":18121},[2444,2254],[2061,18123],{"className":18124,"style":2232},[2231],[2061,18126,2099],{"className":18127},[2236],[2061,18129],{"className":18130,"style":2232},[2231],[2061,18132,18134,18137],{"className":18133},[2160],[2061,18135],{"className":18136,"style":2692},[2164],[2061,18138,17503],{"className":18139},[2169],[2061,18141,18143],{"className":18142},[2064],[2061,18144,18146,18220],{"className":18145},[2068],[2061,18147,18149],{"className":18148},[2072],[2074,18150,18151],{"xmlns":2076,"display":2077},[2079,18152,18153,18217],{},[2082,18154,18155,18161,18163,18169,18171,18177,18179,18181,18183,18185,18199,18201,18213,18215],{},[2089,18156,18157,18159],{},[2085,18158,2119],{},[2121,18160,2134],{},[2097,18162,2114],{"stretchy":2113},[2089,18164,18165,18167],{},[2085,18166,1798],{},[2121,18168,2123],{},[2097,18170,2127],{"separator":2126},[2089,18172,18173,18175],{},[2085,18174,1798],{},[2121,18176,2134],{},[2097,18178,2127],{"separator":2126},[2085,18180,7160],{},[2097,18182,2137],{"stretchy":2113},[2097,18184,2099],{},[2101,18186,18187,18193],{},[2082,18188,18189,18191],{},[2121,18190,14200],{},[2085,18192,7160],{},[2089,18194,18195,18197],{},[2085,18196,1798],{},[2121,18198,2134],{},[2097,18200,2099],{},[2101,18202,18203,18211],{},[2082,18204,18205,18207,18209],{},[2121,18206,14200],{},[2097,18208,16566],{},[2121,18210,14640],{},[2121,18212,14550],{},[2097,18214,2099],{},[2121,18216,17503],{},[2149,18218,18219],{"encoding":2151},"x_2(p_1, p_2, m) = \\frac{0.6m}{p_2} = \\frac{0.6 \\cdot 120}{3} = 24",[2061,18221,18223,18379,18496,18585],{"className":18222,"ariaHidden":2126},[2156],[2061,18224,18226,18229,18269,18272,18312,18315,18318,18358,18361,18364,18367,18370,18373,18376],{"className":18225},[2160],[2061,18227],{"className":18228,"style":4634},[2164],[2061,18230,18232,18235],{"className":18231},[2169],[2061,18233,2119],{"className":18234},[2169,2170],[2061,18236,18238],{"className":18237},[2181],[2061,18239,18241,18261],{"className":18240},[2185,2186],[2061,18242,18244,18258],{"className":18243},[2190],[2061,18245,18247],{"className":18246,"style":2370},[2194],[2061,18248,18249,18252],{"style":2302},[2061,18250],{"className":18251,"style":2203},[2202],[2061,18253,18255],{"className":18254},[2207,2208,2209,2210],[2061,18256,2134],{"className":18257},[2169,2210],[2061,18259,2218],{"className":18260},[2217],[2061,18262,18264],{"className":18263},[2190],[2061,18265,18267],{"className":18266,"style":2225},[2194],[2061,18268],{},[2061,18270,2114],{"className":18271},[2253],[2061,18273,18275,18278],{"className":18274},[2169],[2061,18276,1798],{"className":18277},[2169,2170],[2061,18279,18281],{"className":18280},[2181],[2061,18282,18284,18304],{"className":18283},[2185,2186],[2061,18285,18287,18301],{"className":18286},[2190],[2061,18288,18290],{"className":18289,"style":2370},[2194],[2061,18291,18292,18295],{"style":2302},[2061,18293],{"className":18294,"style":2203},[2202],[2061,18296,18298],{"className":18297},[2207,2208,2209,2210],[2061,18299,2123],{"className":18300},[2169,2210],[2061,18302,2218],{"className":18303},[2217],[2061,18305,18307],{"className":18306},[2190],[2061,18308,18310],{"className":18309,"style":2225},[2194],[2061,18311],{},[2061,18313,2127],{"className":18314},[2396],[2061,18316],{"className":18317,"style":2400},[2231],[2061,18319,18321,18324],{"className":18320},[2169],[2061,18322,1798],{"className":18323},[2169,2170],[2061,18325,18327],{"className":18326},[2181],[2061,18328,18330,18350],{"className":18329},[2185,2186],[2061,18331,18333,18347],{"className":18332},[2190],[2061,18334,18336],{"className":18335,"style":2370},[2194],[2061,18337,18338,18341],{"style":2302},[2061,18339],{"className":18340,"style":2203},[2202],[2061,18342,18344],{"className":18343},[2207,2208,2209,2210],[2061,18345,2134],{"className":18346},[2169,2210],[2061,18348,2218],{"className":18349},[2217],[2061,18351,18353],{"className":18352},[2190],[2061,18354,18356],{"className":18355,"style":2225},[2194],[2061,18357],{},[2061,18359,2127],{"className":18360},[2396],[2061,18362],{"className":18363,"style":2400},[2231],[2061,18365,7160],{"className":18366},[2169,2170],[2061,18368,2137],{"className":18369},[2444],[2061,18371],{"className":18372,"style":2232},[2231],[2061,18374,2099],{"className":18375},[2236],[2061,18377],{"className":18378,"style":2232},[2231],[2061,18380,18382,18385,18487,18490,18493],{"className":18381},[2160],[2061,18383],{"className":18384,"style":17930},[2164],[2061,18386,18388,18391,18484],{"className":18387},[2169],[2061,18389],{"className":18390},[2253,2254],[2061,18392,18394],{"className":18393},[2101],[2061,18395,18397,18476],{"className":18396},[2185,2186],[2061,18398,18400,18473],{"className":18399},[2190],[2061,18401,18403,18451,18459],{"className":18402,"style":16495},[2194],[2061,18404,18405,18408],{"style":2270},[2061,18406],{"className":18407,"style":2274},[2202],[2061,18409,18411],{"className":18410},[2169],[2061,18412,18414,18417],{"className":18413},[2169],[2061,18415,1798],{"className":18416},[2169,2170],[2061,18418,18420],{"className":18419},[2181],[2061,18421,18423,18443],{"className":18422},[2185,2186],[2061,18424,18426,18440],{"className":18425},[2190],[2061,18427,18429],{"className":18428,"style":2370},[2194],[2061,18430,18431,18434],{"style":2302},[2061,18432],{"className":18433,"style":2203},[2202],[2061,18435,18437],{"className":18436},[2207,2208,2209,2210],[2061,18438,2134],{"className":18439},[2169,2210],[2061,18441,2218],{"className":18442},[2217],[2061,18444,18446],{"className":18445},[2190],[2061,18447,18449],{"className":18448,"style":2225},[2194],[2061,18450],{},[2061,18452,18453,18456],{"style":2325},[2061,18454],{"className":18455,"style":2274},[2202],[2061,18457],{"className":18458,"style":2333},[2332],[2061,18460,18461,18464],{"style":2336},[2061,18462],{"className":18463,"style":2274},[2202],[2061,18465,18467,18470],{"className":18466},[2169],[2061,18468,14200],{"className":18469},[2169],[2061,18471,7160],{"className":18472},[2169,2170],[2061,18474,2218],{"className":18475},[2217],[2061,18477,18479],{"className":18478},[2190],[2061,18480,18482],{"className":18481,"style":8254},[2194],[2061,18483],{},[2061,18485],{"className":18486},[2444,2254],[2061,18488],{"className":18489,"style":2232},[2231],[2061,18491,2099],{"className":18492},[2236],[2061,18494],{"className":18495,"style":2232},[2231],[2061,18497,18499,18502,18576,18579,18582],{"className":18498},[2160],[2061,18500],{"className":18501,"style":16476},[2164],[2061,18503,18505,18508,18573],{"className":18504},[2169],[2061,18506],{"className":18507},[2253,2254],[2061,18509,18511],{"className":18510},[2101],[2061,18512,18514,18565],{"className":18513},[2185,2186],[2061,18515,18517,18562],{"className":18516},[2190],[2061,18518,18520,18531,18539],{"className":18519,"style":16495},[2194],[2061,18521,18522,18525],{"style":2270},[2061,18523],{"className":18524,"style":2274},[2202],[2061,18526,18528],{"className":18527},[2169],[2061,18529,14550],{"className":18530},[2169],[2061,18532,18533,18536],{"style":2325},[2061,18534],{"className":18535,"style":2274},[2202],[2061,18537],{"className":18538,"style":2333},[2332],[2061,18540,18541,18544],{"style":2336},[2061,18542],{"className":18543,"style":2274},[2202],[2061,18545,18547,18550,18553,18556,18559],{"className":18546},[2169],[2061,18548,14200],{"className":18549},[2169],[2061,18551],{"className":18552,"style":2980},[2231],[2061,18554,16566],{"className":18555},[2984],[2061,18557],{"className":18558,"style":2980},[2231],[2061,18560,14640],{"className":18561},[2169],[2061,18563,2218],{"className":18564},[2217],[2061,18566,18568],{"className":18567},[2190],[2061,18569,18571],{"className":18570,"style":9692},[2194],[2061,18572],{},[2061,18574],{"className":18575},[2444,2254],[2061,18577],{"className":18578,"style":2232},[2231],[2061,18580,2099],{"className":18581},[2236],[2061,18583],{"className":18584,"style":2232},[2231],[2061,18586,18588,18591],{"className":18587},[2160],[2061,18589],{"className":18590,"style":2692},[2164],[2061,18592,17503],{"className":18593},[2169],[1798,18595,18596,18599,18600,18771,18772,18884,18885,18998],{},[1865,18597,18598],{},"关键洞见",": 对于柯布-道格拉斯效用函数 ",[2061,18601,18603,18635],{"className":18602},[2068],[2061,18604,18606],{"className":18605},[2072],[2074,18607,18608],{"xmlns":2076},[2079,18609,18610,18632],{},[2082,18611,18612,18614,18616,18624],{},[2085,18613,2005],{},[2097,18615,2099],{},[2500,18617,18618,18620,18622],{},[2085,18619,2119],{},[2121,18621,2123],{},[2085,18623,4596],{},[2500,18625,18626,18628,18630],{},[2085,18627,2119],{},[2121,18629,2134],{},[2085,18631,4605],{},[2149,18633,18634],{"encoding":2151},"U = x_1^{\\alpha} x_2^{\\beta}",[2061,18636,18638,18656],{"className":18637,"ariaHidden":2126},[2156],[2061,18639,18641,18644,18647,18650,18653],{"className":18640},[2160],[2061,18642],{"className":18643,"style":8096},[2164],[2061,18645,2005],{"className":18646,"style":2171},[2169,2170],[2061,18648],{"className":18649,"style":2232},[2231],[2061,18651,2099],{"className":18652},[2236],[2061,18654],{"className":18655,"style":2232},[2231],[2061,18657,18659,18662,18717],{"className":18658},[2160],[2061,18660],{"className":18661,"style":4745},[2164],[2061,18663,18665,18668],{"className":18664},[2169],[2061,18666,2119],{"className":18667},[2169,2170],[2061,18669,18671],{"className":18670},[2181],[2061,18672,18674,18709],{"className":18673},[2185,2186],[2061,18675,18677,18706],{"className":18676},[2190],[2061,18678,18681,18692],{"className":18679,"style":18680},[2194],"height:0.6644em;",[2061,18682,18683,18686],{"style":14344},[2061,18684],{"className":18685,"style":2203},[2202],[2061,18687,18689],{"className":18688},[2207,2208,2209,2210],[2061,18690,2123],{"className":18691},[2169,2210],[2061,18693,18694,18697],{"style":2649},[2061,18695],{"className":18696,"style":2203},[2202],[2061,18698,18700],{"className":18699},[2207,2208,2209,2210],[2061,18701,18703],{"className":18702},[2169,2210],[2061,18704,4596],{"className":18705,"style":4792},[2169,2170,2210],[2061,18707,2218],{"className":18708},[2217],[2061,18710,18712],{"className":18711},[2190],[2061,18713,18715],{"className":18714,"style":14377},[2194],[2061,18716],{},[2061,18718,18720,18723],{"className":18719},[2169],[2061,18721,2119],{"className":18722},[2169,2170],[2061,18724,18726],{"className":18725},[2181],[2061,18727,18729,18763],{"className":18728},[2185,2186],[2061,18730,18732,18760],{"className":18731},[2190],[2061,18733,18735,18746],{"className":18734,"style":4823},[2194],[2061,18736,18737,18740],{"style":4826},[2061,18738],{"className":18739,"style":2203},[2202],[2061,18741,18743],{"className":18742},[2207,2208,2209,2210],[2061,18744,2134],{"className":18745},[2169,2210],[2061,18747,18748,18751],{"style":4838},[2061,18749],{"className":18750,"style":2203},[2202],[2061,18752,18754],{"className":18753},[2207,2208,2209,2210],[2061,18755,18757],{"className":18756},[2169,2210],[2061,18758,4605],{"className":18759,"style":4851},[2169,2170,2210],[2061,18761,2218],{"className":18762},[2217],[2061,18764,18766],{"className":18765},[2190],[2061,18767,18769],{"className":18768,"style":4861},[2194],[2061,18770],{},"，消费者将收入的 ",[2061,18773,18775,18799],{"className":18774},[2068],[2061,18776,18778],{"className":18777},[2072],[2074,18779,18780],{"xmlns":2076},[2079,18781,18782,18796],{},[2082,18783,18784],{},[2101,18785,18786,18788],{},[2085,18787,4596],{},[2082,18789,18790,18792,18794],{},[2085,18791,4596],{},[2097,18793,2762],{},[2085,18795,4605],{},[2149,18797,18798],{"encoding":2151},"\\frac{\\alpha}{\\alpha+\\beta}",[2061,18800,18802],{"className":18801,"ariaHidden":2126},[2156],[2061,18803,18805,18809],{"className":18804},[2160],[2061,18806],{"className":18807,"style":18808},[2164],"height:1.1765em;vertical-align:-0.4811em;",[2061,18810,18812,18815,18881],{"className":18811},[2169],[2061,18813],{"className":18814},[2253,2254],[2061,18816,18818],{"className":18817},[2101],[2061,18819,18821,18873],{"className":18820},[2185,2186],[2061,18822,18824,18870],{"className":18823},[2190],[2061,18825,18828,18848,18856],{"className":18826,"style":18827},[2194],"height:0.6954em;",[2061,18829,18830,18833],{"style":5291},[2061,18831],{"className":18832,"style":2274},[2202],[2061,18834,18836],{"className":18835},[2207,2208,2209,2210],[2061,18837,18839,18842,18845],{"className":18838},[2169,2210],[2061,18840,4596],{"className":18841,"style":4792},[2169,2170,2210],[2061,18843,2762],{"className":18844},[2984,2210],[2061,18846,4605],{"className":18847,"style":4851},[2169,2170,2210],[2061,18849,18850,18853],{"style":2325},[2061,18851],{"className":18852,"style":2274},[2202],[2061,18854],{"className":18855,"style":2333},[2332],[2061,18857,18858,18861],{"style":6638},[2061,18859],{"className":18860,"style":2274},[2202],[2061,18862,18864],{"className":18863},[2207,2208,2209,2210],[2061,18865,18867],{"className":18866},[2169,2210],[2061,18868,4596],{"className":18869,"style":4792},[2169,2170,2210],[2061,18871,2218],{"className":18872},[2217],[2061,18874,18876],{"className":18875},[2190],[2061,18877,18879],{"className":18878,"style":5422},[2194],[2061,18880],{},[2061,18882],{"className":18883},[2444,2254]," 花在商品1上，",[2061,18886,18888,18912],{"className":18887},[2068],[2061,18889,18891],{"className":18890},[2072],[2074,18892,18893],{"xmlns":2076},[2079,18894,18895,18909],{},[2082,18896,18897],{},[2101,18898,18899,18901],{},[2085,18900,4605],{},[2082,18902,18903,18905,18907],{},[2085,18904,4596],{},[2097,18906,2762],{},[2085,18908,4605],{},[2149,18910,18911],{"encoding":2151},"\\frac{\\beta}{\\alpha+\\beta}",[2061,18913,18915],{"className":18914,"ariaHidden":2126},[2156],[2061,18916,18918,18922],{"className":18917},[2160],[2061,18919],{"className":18920,"style":18921},[2164],"height:1.4133em;vertical-align:-0.4811em;",[2061,18923,18925,18928,18995],{"className":18924},[2169],[2061,18926],{"className":18927},[2253,2254],[2061,18929,18931],{"className":18930},[2101],[2061,18932,18934,18987],{"className":18933},[2185,2186],[2061,18935,18937,18984],{"className":18936},[2190],[2061,18938,18941,18961,18969],{"className":18939,"style":18940},[2194],"height:0.9322em;",[2061,18942,18943,18946],{"style":5291},[2061,18944],{"className":18945,"style":2274},[2202],[2061,18947,18949],{"className":18948},[2207,2208,2209,2210],[2061,18950,18952,18955,18958],{"className":18951},[2169,2210],[2061,18953,4596],{"className":18954,"style":4792},[2169,2170,2210],[2061,18956,2762],{"className":18957},[2984,2210],[2061,18959,4605],{"className":18960,"style":4851},[2169,2170,2210],[2061,18962,18963,18966],{"style":2325},[2061,18964],{"className":18965,"style":2274},[2202],[2061,18967],{"className":18968,"style":2333},[2332],[2061,18970,18972,18975],{"style":18971},"top:-3.4461em;",[2061,18973],{"className":18974,"style":2274},[2202],[2061,18976,18978],{"className":18977},[2207,2208,2209,2210],[2061,18979,18981],{"className":18980},[2169,2210],[2061,18982,4605],{"className":18983,"style":4851},[2169,2170,2210],[2061,18985,2218],{"className":18986},[2217],[2061,18988,18990],{"className":18989},[2190],[2061,18991,18993],{"className":18992,"style":5422},[2194],[2061,18994],{},[2061,18996],{"className":18997},[2444,2254]," 花在商品2上。",[1798,19000,19001],{},[1865,19002,19003],{},"(2) 间接效用函数",[2061,19005,19007],{"className":19006},[2064],[2061,19008,19010,19092],{"className":19009},[2068],[2061,19011,19013],{"className":19012},[2072],[2074,19014,19015],{"xmlns":2076,"display":2077},[2079,19016,19017,19089],{},[2082,19018,19019,19021,19023,19029,19031,19037,19039,19041,19043,19045,19047,19049,19057,19059,19067,19069,19071,19077,19079,19085,19087],{},[2085,19020,6887],{},[2097,19022,2114],{"stretchy":2113},[2089,19024,19025,19027],{},[2085,19026,1798],{},[2121,19028,2123],{},[2097,19030,2127],{"separator":2126},[2089,19032,19033,19035],{},[2085,19034,1798],{},[2121,19036,2134],{},[2097,19038,2127],{"separator":2126},[2085,19040,7160],{},[2097,19042,2137],{"stretchy":2113},[2097,19044,2099],{},[2085,19046,2005],{},[2097,19048,2114],{"stretchy":2113},[2500,19050,19051,19053,19055],{},[2085,19052,2119],{},[2121,19054,2123],{},[2097,19056,10359],{},[2097,19058,2127],{"separator":2126},[2500,19060,19061,19063,19065],{},[2085,19062,2119],{},[2121,19064,2134],{},[2097,19066,10359],{},[2097,19068,2137],{"stretchy":2113},[2097,19070,2099],{},[2487,19072,19073,19075],{},[2121,19074,17503],{},[2121,19076,14191],{},[2097,19078,16566],{},[2487,19080,19081,19083],{},[2121,19082,17503],{},[2121,19084,14200],{},[2097,19086,2099],{},[2121,19088,17503],{},[2149,19090,19091],{"encoding":2151},"v(p_1, p_2, m) = U(x_1^*, x_2^*) = 24^{0.4} \\cdot 24^{0.6} = 24",[2061,19093,19095,19214,19346,19397,19447],{"className":19094,"ariaHidden":2126},[2156],[2061,19096,19098,19101,19104,19107,19147,19150,19153,19193,19196,19199,19202,19205,19208,19211],{"className":19097},[2160],[2061,19099],{"className":19100,"style":4634},[2164],[2061,19102,6887],{"className":19103,"style":6572},[2169,2170],[2061,19105,2114],{"className":19106},[2253],[2061,19108,19110,19113],{"className":19109},[2169],[2061,19111,1798],{"className":19112},[2169,2170],[2061,19114,19116],{"className":19115},[2181],[2061,19117,19119,19139],{"className":19118},[2185,2186],[2061,19120,19122,19136],{"className":19121},[2190],[2061,19123,19125],{"className":19124,"style":2370},[2194],[2061,19126,19127,19130],{"style":2302},[2061,19128],{"className":19129,"style":2203},[2202],[2061,19131,19133],{"className":19132},[2207,2208,2209,2210],[2061,19134,2123],{"className":19135},[2169,2210],[2061,19137,2218],{"className":19138},[2217],[2061,19140,19142],{"className":19141},[2190],[2061,19143,19145],{"className":19144,"style":2225},[2194],[2061,19146],{},[2061,19148,2127],{"className":19149},[2396],[2061,19151],{"className":19152,"style":2400},[2231],[2061,19154,19156,19159],{"className":19155},[2169],[2061,19157,1798],{"className":19158},[2169,2170],[2061,19160,19162],{"className":19161},[2181],[2061,19163,19165,19185],{"className":19164},[2185,2186],[2061,19166,19168,19182],{"className":19167},[2190],[2061,19169,19171],{"className":19170,"style":2370},[2194],[2061,19172,19173,19176],{"style":2302},[2061,19174],{"className":19175,"style":2203},[2202],[2061,19177,19179],{"className":19178},[2207,2208,2209,2210],[2061,19180,2134],{"className":19181},[2169,2210],[2061,19183,2218],{"className":19184},[2217],[2061,19186,19188],{"className":19187},[2190],[2061,19189,19191],{"className":19190,"style":2225},[2194],[2061,19192],{},[2061,19194,2127],{"className":19195},[2396],[2061,19197],{"className":19198,"style":2400},[2231],[2061,19200,7160],{"className":19201},[2169,2170],[2061,19203,2137],{"className":19204},[2444],[2061,19206],{"className":19207,"style":2232},[2231],[2061,19209,2099],{"className":19210},[2236],[2061,19212],{"className":19213,"style":2232},[2231],[2061,19215,19217,19220,19223,19226,19277,19280,19283,19334,19337,19340,19343],{"className":19216},[2160],[2061,19218],{"className":19219,"style":4634},[2164],[2061,19221,2005],{"className":19222,"style":2171},[2169,2170],[2061,19224,2114],{"className":19225},[2253],[2061,19227,19229,19232],{"className":19228},[2169],[2061,19230,2119],{"className":19231},[2169,2170],[2061,19233,19235],{"className":19234},[2181],[2061,19236,19238,19269],{"className":19237},[2185,2186],[2061,19239,19241,19266],{"className":19240},[2190],[2061,19242,19244,19255],{"className":19243,"style":10421},[2194],[2061,19245,19246,19249],{"style":4767},[2061,19247],{"className":19248,"style":2203},[2202],[2061,19250,19252],{"className":19251},[2207,2208,2209,2210],[2061,19253,2123],{"className":19254},[2169,2210],[2061,19256,19257,19260],{"style":4779},[2061,19258],{"className":19259,"style":2203},[2202],[2061,19261,19263],{"className":19262},[2207,2208,2209,2210],[2061,19264,10359],{"className":19265},[2984,2210],[2061,19267,2218],{"className":19268},[2217],[2061,19270,19272],{"className":19271},[2190],[2061,19273,19275],{"className":19274,"style":4802},[2194],[2061,19276],{},[2061,19278,2127],{"className":19279},[2396],[2061,19281],{"className":19282,"style":2400},[2231],[2061,19284,19286,19289],{"className":19285},[2169],[2061,19287,2119],{"className":19288},[2169,2170],[2061,19290,19292],{"className":19291},[2181],[2061,19293,19295,19326],{"className":19294},[2185,2186],[2061,19296,19298,19323],{"className":19297},[2190],[2061,19299,19301,19312],{"className":19300,"style":10421},[2194],[2061,19302,19303,19306],{"style":4767},[2061,19304],{"className":19305,"style":2203},[2202],[2061,19307,19309],{"className":19308},[2207,2208,2209,2210],[2061,19310,2134],{"className":19311},[2169,2210],[2061,19313,19314,19317],{"style":4779},[2061,19315],{"className":19316,"style":2203},[2202],[2061,19318,19320],{"className":19319},[2207,2208,2209,2210],[2061,19321,10359],{"className":19322},[2984,2210],[2061,19324,2218],{"className":19325},[2217],[2061,19327,19329],{"className":19328},[2190],[2061,19330,19332],{"className":19331,"style":4802},[2194],[2061,19333],{},[2061,19335,2137],{"className":19336},[2444],[2061,19338],{"className":19339,"style":2232},[2231],[2061,19341,2099],{"className":19342},[2236],[2061,19344],{"className":19345,"style":2232},[2231],[2061,19347,19349,19352,19355,19388,19391,19394],{"className":19348},[2160],[2061,19350],{"className":19351,"style":14813},[2164],[2061,19353,2134],{"className":19354},[2169],[2061,19356,19358,19362],{"className":19357},[2169],[2061,19359,19361],{"className":19360},[2169],"4",[2061,19363,19365],{"className":19364},[2181],[2061,19366,19368],{"className":19367},[2185],[2061,19369,19371],{"className":19370},[2190],[2061,19372,19374],{"className":19373,"style":14813},[2194],[2061,19375,19376,19379],{"style":4779},[2061,19377],{"className":19378,"style":2203},[2202],[2061,19380,19382],{"className":19381},[2207,2208,2209,2210],[2061,19383,19385],{"className":19384},[2169,2210],[2061,19386,14191],{"className":19387},[2169,2210],[2061,19389],{"className":19390,"style":2980},[2231],[2061,19392,16566],{"className":19393},[2984],[2061,19395],{"className":19396,"style":2980},[2231],[2061,19398,19400,19403,19406,19438,19441,19444],{"className":19399},[2160],[2061,19401],{"className":19402,"style":14813},[2164],[2061,19404,2134],{"className":19405},[2169],[2061,19407,19409,19412],{"className":19408},[2169],[2061,19410,19361],{"className":19411},[2169],[2061,19413,19415],{"className":19414},[2181],[2061,19416,19418],{"className":19417},[2185],[2061,19419,19421],{"className":19420},[2190],[2061,19422,19424],{"className":19423,"style":14813},[2194],[2061,19425,19426,19429],{"style":4779},[2061,19427],{"className":19428,"style":2203},[2202],[2061,19430,19432],{"className":19431},[2207,2208,2209,2210],[2061,19433,19435],{"className":19434},[2169,2210],[2061,19436,14200],{"className":19437},[2169,2210],[2061,19439],{"className":19440,"style":2232},[2231],[2061,19442,2099],{"className":19443},[2236],[2061,19445],{"className":19446,"style":2232},[2231],[2061,19448,19450,19453],{"className":19449},[2160],[2061,19451],{"className":19452,"style":2692},[2164],[2061,19454,17503],{"className":19455},[2169],[1798,19457,19458],{},"一般形式：",[2061,19460,19462],{"className":19461},[2064],[2061,19463,19465,19551],{"className":19464},[2068],[2061,19466,19468],{"className":19467},[2072],[2074,19469,19470],{"xmlns":2076,"display":2077},[2079,19471,19472,19548],{},[2082,19473,19474,19476,19478,19484,19486,19492,19494,19496,19498,19500,19524],{},[2085,19475,6887],{},[2097,19477,2114],{"stretchy":2113},[2089,19479,19480,19482],{},[2085,19481,1798],{},[2121,19483,2123],{},[2097,19485,2127],{"separator":2126},[2089,19487,19488,19490],{},[2085,19489,1798],{},[2121,19491,2134],{},[2097,19493,2127],{"separator":2126},[2085,19495,7160],{},[2097,19497,2137],{"stretchy":2113},[2097,19499,2099],{},[2487,19501,19502,19522],{},[2082,19503,19504,19506,19520],{},[2097,19505,2114],{"fence":2126},[2101,19507,19508,19514],{},[2082,19509,19510,19512],{},[2121,19511,14191],{},[2085,19513,7160],{},[2089,19515,19516,19518],{},[2085,19517,1798],{},[2121,19519,2123],{},[2097,19521,2137],{"fence":2126},[2121,19523,14191],{},[2487,19525,19526,19546],{},[2082,19527,19528,19530,19544],{},[2097,19529,2114],{"fence":2126},[2101,19531,19532,19538],{},[2082,19533,19534,19536],{},[2121,19535,14200],{},[2085,19537,7160],{},[2089,19539,19540,19542],{},[2085,19541,1798],{},[2121,19543,2134],{},[2097,19545,2137],{"fence":2126},[2121,19547,14200],{},[2149,19549,19550],{"encoding":2151},"v(p_1, p_2, m) = \\left(\\frac{0.4m}{p_1}\\right)^{0.4} \\left(\\frac{0.6m}{p_2}\\right)^{0.6}",[2061,19552,19554,19673],{"className":19553,"ariaHidden":2126},[2156],[2061,19555,19557,19560,19563,19566,19606,19609,19612,19652,19655,19658,19661,19664,19667,19670],{"className":19556},[2160],[2061,19558],{"className":19559,"style":4634},[2164],[2061,19561,6887],{"className":19562,"style":6572},[2169,2170],[2061,19564,2114],{"className":19565},[2253],[2061,19567,19569,19572],{"className":19568},[2169],[2061,19570,1798],{"className":19571},[2169,2170],[2061,19573,19575],{"className":19574},[2181],[2061,19576,19578,19598],{"className":19577},[2185,2186],[2061,19579,19581,19595],{"className":19580},[2190],[2061,19582,19584],{"className":19583,"style":2370},[2194],[2061,19585,19586,19589],{"style":2302},[2061,19587],{"className":19588,"style":2203},[2202],[2061,19590,19592],{"className":19591},[2207,2208,2209,2210],[2061,19593,2123],{"className":19594},[2169,2210],[2061,19596,2218],{"className":19597},[2217],[2061,19599,19601],{"className":19600},[2190],[2061,19602,19604],{"className":19603,"style":2225},[2194],[2061,19605],{},[2061,19607,2127],{"className":19608},[2396],[2061,19610],{"className":19611,"style":2400},[2231],[2061,19613,19615,19618],{"className":19614},[2169],[2061,19616,1798],{"className":19617},[2169,2170],[2061,19619,19621],{"className":19620},[2181],[2061,19622,19624,19644],{"className":19623},[2185,2186],[2061,19625,19627,19641],{"className":19626},[2190],[2061,19628,19630],{"className":19629,"style":2370},[2194],[2061,19631,19632,19635],{"style":2302},[2061,19633],{"className":19634,"style":2203},[2202],[2061,19636,19638],{"className":19637},[2207,2208,2209,2210],[2061,19639,2134],{"className":19640},[2169,2210],[2061,19642,2218],{"className":19643},[2217],[2061,19645,19647],{"className":19646},[2190],[2061,19648,19650],{"className":19649,"style":2225},[2194],[2061,19651],{},[2061,19653,2127],{"className":19654},[2396],[2061,19656],{"className":19657,"style":2400},[2231],[2061,19659,7160],{"className":19660},[2169,2170],[2061,19662,2137],{"className":19663},[2444],[2061,19665],{"className":19666,"style":2232},[2231],[2061,19668,2099],{"className":19669},[2236],[2061,19671],{"className":19672,"style":2232},[2231],[2061,19674,19676,19680,19830,19833],{"className":19675},[2160],[2061,19677],{"className":19678,"style":19679},[2164],"height:2.604em;vertical-align:-0.95em;",[2061,19681,19683,19802],{"className":19682},[3967],[2061,19684,19686,19694,19796],{"className":19685},[3967],[2061,19687,19691],{"className":19688,"style":19690},[2253,19689],"delimcenter","top:0em;",[2061,19692,2114],{"className":19693},[3974,2209],[2061,19695,19697,19700,19793],{"className":19696},[2169],[2061,19698],{"className":19699},[2253,2254],[2061,19701,19703],{"className":19702},[2101],[2061,19704,19706,19785],{"className":19705},[2185,2186],[2061,19707,19709,19782],{"className":19708},[2190],[2061,19710,19712,19760,19768],{"className":19711,"style":16495},[2194],[2061,19713,19714,19717],{"style":2270},[2061,19715],{"className":19716,"style":2274},[2202],[2061,19718,19720],{"className":19719},[2169],[2061,19721,19723,19726],{"className":19722},[2169],[2061,19724,1798],{"className":19725},[2169,2170],[2061,19727,19729],{"className":19728},[2181],[2061,19730,19732,19752],{"className":19731},[2185,2186],[2061,19733,19735,19749],{"className":19734},[2190],[2061,19736,19738],{"className":19737,"style":2370},[2194],[2061,19739,19740,19743],{"style":2302},[2061,19741],{"className":19742,"style":2203},[2202],[2061,19744,19746],{"className":19745},[2207,2208,2209,2210],[2061,19747,2123],{"className":19748},[2169,2210],[2061,19750,2218],{"className":19751},[2217],[2061,19753,19755],{"className":19754},[2190],[2061,19756,19758],{"className":19757,"style":2225},[2194],[2061,19759],{},[2061,19761,19762,19765],{"style":2325},[2061,19763],{"className":19764,"style":2274},[2202],[2061,19766],{"className":19767,"style":2333},[2332],[2061,19769,19770,19773],{"style":2336},[2061,19771],{"className":19772,"style":2274},[2202],[2061,19774,19776,19779],{"className":19775},[2169],[2061,19777,14191],{"className":19778},[2169],[2061,19780,7160],{"className":19781},[2169,2170],[2061,19783,2218],{"className":19784},[2217],[2061,19786,19788],{"className":19787},[2190],[2061,19789,19791],{"className":19790,"style":8254},[2194],[2061,19792],{},[2061,19794],{"className":19795},[2444,2254],[2061,19797,19799],{"className":19798,"style":19690},[2444,19689],[2061,19800,2137],{"className":19801},[3974,2209],[2061,19803,19805],{"className":19804},[2181],[2061,19806,19808],{"className":19807},[2185],[2061,19809,19811],{"className":19810},[2190],[2061,19812,19815],{"className":19813,"style":19814},[2194],"height:1.654em;",[2061,19816,19818,19821],{"style":19817},"top:-3.9029em;margin-right:0.05em;",[2061,19819],{"className":19820,"style":2203},[2202],[2061,19822,19824],{"className":19823},[2207,2208,2209,2210],[2061,19825,19827],{"className":19826},[2169,2210],[2061,19828,14191],{"className":19829},[2169,2210],[2061,19831],{"className":19832,"style":2400},[2231],[2061,19834,19836,19953],{"className":19835},[3967],[2061,19837,19839,19845,19947],{"className":19838},[3967],[2061,19840,19842],{"className":19841,"style":19690},[2253,19689],[2061,19843,2114],{"className":19844},[3974,2209],[2061,19846,19848,19851,19944],{"className":19847},[2169],[2061,19849],{"className":19850},[2253,2254],[2061,19852,19854],{"className":19853},[2101],[2061,19855,19857,19936],{"className":19856},[2185,2186],[2061,19858,19860,19933],{"className":19859},[2190],[2061,19861,19863,19911,19919],{"className":19862,"style":16495},[2194],[2061,19864,19865,19868],{"style":2270},[2061,19866],{"className":19867,"style":2274},[2202],[2061,19869,19871],{"className":19870},[2169],[2061,19872,19874,19877],{"className":19873},[2169],[2061,19875,1798],{"className":19876},[2169,2170],[2061,19878,19880],{"className":19879},[2181],[2061,19881,19883,19903],{"className":19882},[2185,2186],[2061,19884,19886,19900],{"className":19885},[2190],[2061,19887,19889],{"className":19888,"style":2370},[2194],[2061,19890,19891,19894],{"style":2302},[2061,19892],{"className":19893,"style":2203},[2202],[2061,19895,19897],{"className":19896},[2207,2208,2209,2210],[2061,19898,2134],{"className":19899},[2169,2210],[2061,19901,2218],{"className":19902},[2217],[2061,19904,19906],{"className":19905},[2190],[2061,19907,19909],{"className":19908,"style":2225},[2194],[2061,19910],{},[2061,19912,19913,19916],{"style":2325},[2061,19914],{"className":19915,"style":2274},[2202],[2061,19917],{"className":19918,"style":2333},[2332],[2061,19920,19921,19924],{"style":2336},[2061,19922],{"className":19923,"style":2274},[2202],[2061,19925,19927,19930],{"className":19926},[2169],[2061,19928,14200],{"className":19929},[2169],[2061,19931,7160],{"className":19932},[2169,2170],[2061,19934,2218],{"className":19935},[2217],[2061,19937,19939],{"className":19938},[2190],[2061,19940,19942],{"className":19941,"style":8254},[2194],[2061,19943],{},[2061,19945],{"className":19946},[2444,2254],[2061,19948,19950],{"className":19949,"style":19690},[2444,19689],[2061,19951,2137],{"className":19952},[3974,2209],[2061,19954,19956],{"className":19955},[2181],[2061,19957,19959],{"className":19958},[2185],[2061,19960,19962],{"className":19961},[2190],[2061,19963,19965],{"className":19964,"style":19814},[2194],[2061,19966,19967,19970],{"style":19817},[2061,19968],{"className":19969,"style":2203},[2202],[2061,19971,19973],{"className":19972},[2207,2208,2209,2210],[2061,19974,19976],{"className":19975},[2169,2210],[2061,19977,14200],{"className":19978},[2169,2210],[1798,19980,19981],{},[1865,19982,19983],{},"(3) 希克斯需求函数",[1798,19985,19986,19987,20038],{},"对于柯布-道格拉斯函数，我们需要反解间接效用函数。从 ",[2061,19988,19990,20008],{"className":19989},[2068],[2061,19991,19993],{"className":19992},[2072],[2074,19994,19995],{"xmlns":2076},[2079,19996,19997,20005],{},[2082,19998,19999,20001,20003],{},[2085,20000,6887],{},[2097,20002,2099],{},[2085,20004,11462],{},[2149,20006,20007],{"encoding":2151},"v = u",[2061,20009,20011,20029],{"className":20010,"ariaHidden":2126},[2156],[2061,20012,20014,20017,20020,20023,20026],{"className":20013},[2160],[2061,20015],{"className":20016,"style":6568},[2164],[2061,20018,6887],{"className":20019,"style":6572},[2169,2170],[2061,20021],{"className":20022,"style":2232},[2231],[2061,20024,2099],{"className":20025},[2236],[2061,20027],{"className":20028,"style":2232},[2231],[2061,20030,20032,20035],{"className":20031},[2160],[2061,20033],{"className":20034,"style":6568},[2164],[2061,20036,11462],{"className":20037},[2169,2170]," 可以得到所需的最小支出：",[1798,20040,20041],{},"支出函数（可以通过求解EMP得到）：",[2061,20043,20045],{"className":20044},[2064],[2061,20046,20048,20129],{"className":20047},[2068],[2061,20049,20051],{"className":20050},[2072],[2074,20052,20053],{"xmlns":2076,"display":2077},[2079,20054,20055,20126],{},[2082,20056,20057,20059,20061,20067,20069,20075,20077,20079,20081,20083,20086,20088,20106,20124],{},[2085,20058,12585],{},[2097,20060,2114],{"stretchy":2113},[2089,20062,20063,20065],{},[2085,20064,1798],{},[2121,20066,2123],{},[2097,20068,2127],{"separator":2126},[2089,20070,20071,20073],{},[2085,20072,1798],{},[2121,20074,2134],{},[2097,20076,2127],{"separator":2126},[2085,20078,11462],{},[2097,20080,2137],{"stretchy":2113},[2097,20082,2099],{},[2085,20084,20085],{},"K",[2097,20087,16566],{},[2500,20089,20090,20092,20094],{},[2085,20091,1798],{},[2121,20093,2123],{},[2101,20095,20096,20098],{},[2085,20097,4596],{},[2082,20099,20100,20102,20104],{},[2085,20101,4596],{},[2097,20103,2762],{},[2085,20105,4605],{},[2500,20107,20108,20110,20112],{},[2085,20109,1798],{},[2121,20111,2134],{},[2101,20113,20114,20116],{},[2085,20115,4605],{},[2082,20117,20118,20120,20122],{},[2085,20119,4596],{},[2097,20121,2762],{},[2085,20123,4605],{},[2085,20125,11462],{},[2149,20127,20128],{"encoding":2151},"e(p_1, p_2, u) = K \\cdot p_1^{\\frac{\\alpha}{\\alpha+\\beta}} p_2^{\\frac{\\beta}{\\alpha+\\beta}} u",[2061,20130,20132,20251,20270],{"className":20131,"ariaHidden":2126},[2156],[2061,20133,20135,20138,20141,20144,20184,20187,20190,20230,20233,20236,20239,20242,20245,20248],{"className":20134},[2160],[2061,20136],{"className":20137,"style":4634},[2164],[2061,20139,12585],{"className":20140},[2169,2170],[2061,20142,2114],{"className":20143},[2253],[2061,20145,20147,20150],{"className":20146},[2169],[2061,20148,1798],{"className":20149},[2169,2170],[2061,20151,20153],{"className":20152},[2181],[2061,20154,20156,20176],{"className":20155},[2185,2186],[2061,20157,20159,20173],{"className":20158},[2190],[2061,20160,20162],{"className":20161,"style":2370},[2194],[2061,20163,20164,20167],{"style":2302},[2061,20165],{"className":20166,"style":2203},[2202],[2061,20168,20170],{"className":20169},[2207,2208,2209,2210],[2061,20171,2123],{"className":20172},[2169,2210],[2061,20174,2218],{"className":20175},[2217],[2061,20177,20179],{"className":20178},[2190],[2061,20180,20182],{"className":20181,"style":2225},[2194],[2061,20183],{},[2061,20185,2127],{"className":20186},[2396],[2061,20188],{"className":20189,"style":2400},[2231],[2061,20191,20193,20196],{"className":20192},[2169],[2061,20194,1798],{"className":20195},[2169,2170],[2061,20197,20199],{"className":20198},[2181],[2061,20200,20202,20222],{"className":20201},[2185,2186],[2061,20203,20205,20219],{"className":20204},[2190],[2061,20206,20208],{"className":20207,"style":2370},[2194],[2061,20209,20210,20213],{"style":2302},[2061,20211],{"className":20212,"style":2203},[2202],[2061,20214,20216],{"className":20215},[2207,2208,2209,2210],[2061,20217,2134],{"className":20218},[2169,2210],[2061,20220,2218],{"className":20221},[2217],[2061,20223,20225],{"className":20224},[2190],[2061,20226,20228],{"className":20227,"style":2225},[2194],[2061,20229],{},[2061,20231,2127],{"className":20232},[2396],[2061,20234],{"className":20235,"style":2400},[2231],[2061,20237,11462],{"className":20238},[2169,2170],[2061,20240,2137],{"className":20241},[2444],[2061,20243],{"className":20244,"style":2232},[2231],[2061,20246,2099],{"className":20247},[2236],[2061,20249],{"className":20250,"style":2232},[2231],[2061,20252,20254,20257,20261,20264,20267],{"className":20253},[2160],[2061,20255],{"className":20256,"style":8096},[2164],[2061,20258,20085],{"className":20259,"style":20260},[2169,2170],"margin-right:0.0715em;",[2061,20262],{"className":20263,"style":2980},[2231],[2061,20265,16566],{"className":20266},[2984],[2061,20268],{"className":20269,"style":2980},[2231],[2061,20271,20273,20277,20412,20540],{"className":20272},[2160],[2061,20274],{"className":20275,"style":20276},[2164],"height:1.62em;vertical-align:-0.2663em;",[2061,20278,20280,20283],{"className":20279},[2169],[2061,20281,1798],{"className":20282},[2169,2170],[2061,20284,20286],{"className":20285},[2181],[2061,20287,20289,20404],{"className":20288},[2185,2186],[2061,20290,20292,20401],{"className":20291},[2190],[2061,20293,20296,20308],{"className":20294,"style":20295},[2194],"height:1.1669em;",[2061,20297,20299,20302],{"style":20298},"top:-2.7337em;margin-left:0em;margin-right:0.05em;",[2061,20300],{"className":20301,"style":2274},[2202],[2061,20303,20305],{"className":20304},[2207,2208,2209,2210],[2061,20306,2123],{"className":20307},[2169,2210],[2061,20309,20311,20314],{"style":20310},"top:-3.6828em;margin-right:0.05em;",[2061,20312],{"className":20313,"style":2274},[2202],[2061,20315,20317],{"className":20316},[2207,2208,2209,2210],[2061,20318,20320],{"className":20319},[2169,2210],[2061,20321,20323,20327,20398],{"className":20322},[2169,2210],[2061,20324],{"className":20325},[2253,2254,2207,5333,20326],"size6",[2061,20328,20330],{"className":20329},[2101],[2061,20331,20333,20389],{"className":20332},[2185,2186],[2061,20334,20336,20386],{"className":20335},[2190],[2061,20337,20340,20361,20371],{"className":20338,"style":20339},[2194],"height:0.6915em;",[2061,20341,20343,20346],{"style":20342},"top:-2.656em;",[2061,20344],{"className":20345,"style":2274},[2202],[2061,20347,20349],{"className":20348},[2207,5333,5334,2210],[2061,20350,20352,20355,20358],{"className":20351},[2169,2210],[2061,20353,4596],{"className":20354,"style":4792},[2169,2170,2210],[2061,20356,2762],{"className":20357},[2984,2210],[2061,20359,4605],{"className":20360,"style":4851},[2169,2170,2210],[2061,20362,20364,20367],{"style":20363},"top:-3.2255em;",[2061,20365],{"className":20366,"style":2274},[2202],[2061,20368],{"className":20369,"style":20370},[2332,2210],"border-bottom-width:0.049em;",[2061,20372,20374,20377],{"style":20373},"top:-3.384em;",[2061,20375],{"className":20376,"style":2274},[2202],[2061,20378,20380],{"className":20379},[2207,5333,5334,2210],[2061,20381,20383],{"className":20382},[2169,2210],[2061,20384,4596],{"className":20385,"style":4792},[2169,2170,2210],[2061,20387,2218],{"className":20388},[2217],[2061,20390,20392],{"className":20391},[2190],[2061,20393,20396],{"className":20394,"style":20395},[2194],"height:0.4829em;",[2061,20397],{},[2061,20399],{"className":20400},[2444,2254,2207,5333,20326],[2061,20402,2218],{"className":20403},[2217],[2061,20405,20407],{"className":20406},[2190],[2061,20408,20410],{"className":20409,"style":4861},[2194],[2061,20411],{},[2061,20413,20415,20418],{"className":20414},[2169],[2061,20416,1798],{"className":20417},[2169,2170],[2061,20419,20421],{"className":20420},[2181],[2061,20422,20424,20532],{"className":20423},[2185,2186],[2061,20425,20427,20529],{"className":20426},[2190],[2061,20428,20431,20442],{"className":20429,"style":20430},[2194],"height:1.3537em;",[2061,20432,20433,20436],{"style":20298},[2061,20434],{"className":20435,"style":2274},[2202],[2061,20437,20439],{"className":20438},[2207,2208,2209,2210],[2061,20440,2134],{"className":20441},[2169,2210],[2061,20443,20444,20447],{"style":20310},[2061,20445],{"className":20446,"style":2274},[2202],[2061,20448,20450],{"className":20449},[2207,2208,2209,2210],[2061,20451,20453],{"className":20452},[2169,2210],[2061,20454,20456,20459,20526],{"className":20455},[2169,2210],[2061,20457],{"className":20458},[2253,2254,2207,5333,20326],[2061,20460,20462],{"className":20461},[2101],[2061,20463,20465,20518],{"className":20464},[2185,2186],[2061,20466,20468,20515],{"className":20467},[2190],[2061,20469,20472,20492,20500],{"className":20470,"style":20471},[2194],"height:0.9584em;",[2061,20473,20474,20477],{"style":20342},[2061,20475],{"className":20476,"style":2274},[2202],[2061,20478,20480],{"className":20479},[2207,5333,5334,2210],[2061,20481,20483,20486,20489],{"className":20482},[2169,2210],[2061,20484,4596],{"className":20485,"style":4792},[2169,2170,2210],[2061,20487,2762],{"className":20488},[2984,2210],[2061,20490,4605],{"className":20491,"style":4851},[2169,2170,2210],[2061,20493,20494,20497],{"style":20363},[2061,20495],{"className":20496,"style":2274},[2202],[2061,20498],{"className":20499,"style":20370},[2332,2210],[2061,20501,20503,20506],{"style":20502},"top:-3.4624em;",[2061,20504],{"className":20505,"style":2274},[2202],[2061,20507,20509],{"className":20508},[2207,5333,5334,2210],[2061,20510,20512],{"className":20511},[2169,2210],[2061,20513,4605],{"className":20514,"style":4851},[2169,2170,2210],[2061,20516,2218],{"className":20517},[2217],[2061,20519,20521],{"className":20520},[2190],[2061,20522,20524],{"className":20523,"style":20395},[2194],[2061,20525],{},[2061,20527],{"className":20528},[2444,2254,2207,5333,20326],[2061,20530,2218],{"className":20531},[2217],[2061,20533,20535],{"className":20534},[2190],[2061,20536,20538],{"className":20537,"style":4861},[2194],[2061,20539],{},[2061,20541,11462],{"className":20542},[2169,2170],[1798,20544,20545,20546,20574],{},"其中 ",[2061,20547,20549,20562],{"className":20548},[2068],[2061,20550,20552],{"className":20551},[2072],[2074,20553,20554],{"xmlns":2076},[2079,20555,20556,20560],{},[2082,20557,20558],{},[2085,20559,20085],{},[2149,20561,20085],{"encoding":2151},[2061,20563,20565],{"className":20564,"ariaHidden":2126},[2156],[2061,20566,20568,20571],{"className":20567},[2160],[2061,20569],{"className":20570,"style":8096},[2164],[2061,20572,20085],{"className":20573,"style":20260},[2169,2170]," 是与效用函数参数相关的常数。",[1798,20576,20577],{},"希克斯需求函数（由谢泼德引理）：",[2061,20579,20581],{"className":20580},[2064],[2061,20582,20584,20644],{"className":20583},[2068],[2061,20585,20587],{"className":20586},[2072],[2074,20588,20589],{"xmlns":2076,"display":2077},[2079,20590,20591,20641],{},[2082,20592,20593,20599,20601,20607,20609,20615,20617,20619,20621,20623],{},[2089,20594,20595,20597],{},[2085,20596,12029],{},[2121,20598,2123],{},[2097,20600,2114],{"stretchy":2113},[2089,20602,20603,20605],{},[2085,20604,1798],{},[2121,20606,2123],{},[2097,20608,2127],{"separator":2126},[2089,20610,20611,20613],{},[2085,20612,1798],{},[2121,20614,2134],{},[2097,20616,2127],{"separator":2126},[2085,20618,11462],{},[2097,20620,2137],{"stretchy":2113},[2097,20622,2099],{},[2101,20624,20625,20631],{},[2082,20626,20627,20629],{},[2085,20628,2108],{"mathvariant":2107},[2085,20630,12585],{},[2082,20632,20633,20635],{},[2085,20634,2108],{"mathvariant":2107},[2089,20636,20637,20639],{},[2085,20638,1798],{},[2121,20640,2123],{},[2149,20642,20643],{"encoding":2151},"h_1(p_1, p_2, u) = \\frac{\\partial e}{\\partial p_1}",[2061,20645,20647,20803],{"className":20646,"ariaHidden":2126},[2156],[2061,20648,20650,20653,20693,20696,20736,20739,20742,20782,20785,20788,20791,20794,20797,20800],{"className":20649},[2160],[2061,20651],{"className":20652,"style":4634},[2164],[2061,20654,20656,20659],{"className":20655},[2169],[2061,20657,12029],{"className":20658},[2169,2170],[2061,20660,20662],{"className":20661},[2181],[2061,20663,20665,20685],{"className":20664},[2185,2186],[2061,20666,20668,20682],{"className":20667},[2190],[2061,20669,20671],{"className":20670,"style":2370},[2194],[2061,20672,20673,20676],{"style":2302},[2061,20674],{"className":20675,"style":2203},[2202],[2061,20677,20679],{"className":20678},[2207,2208,2209,2210],[2061,20680,2123],{"className":20681},[2169,2210],[2061,20683,2218],{"className":20684},[2217],[2061,20686,20688],{"className":20687},[2190],[2061,20689,20691],{"className":20690,"style":2225},[2194],[2061,20692],{},[2061,20694,2114],{"className":20695},[2253],[2061,20697,20699,20702],{"className":20698},[2169],[2061,20700,1798],{"className":20701},[2169,2170],[2061,20703,20705],{"className":20704},[2181],[2061,20706,20708,20728],{"className":20707},[2185,2186],[2061,20709,20711,20725],{"className":20710},[2190],[2061,20712,20714],{"className":20713,"style":2370},[2194],[2061,20715,20716,20719],{"style":2302},[2061,20717],{"className":20718,"style":2203},[2202],[2061,20720,20722],{"className":20721},[2207,2208,2209,2210],[2061,20723,2123],{"className":20724},[2169,2210],[2061,20726,2218],{"className":20727},[2217],[2061,20729,20731],{"className":20730},[2190],[2061,20732,20734],{"className":20733,"style":2225},[2194],[2061,20735],{},[2061,20737,2127],{"className":20738},[2396],[2061,20740],{"className":20741,"style":2400},[2231],[2061,20743,20745,20748],{"className":20744},[2169],[2061,20746,1798],{"className":20747},[2169,2170],[2061,20749,20751],{"className":20750},[2181],[2061,20752,20754,20774],{"className":20753},[2185,2186],[2061,20755,20757,20771],{"className":20756},[2190],[2061,20758,20760],{"className":20759,"style":2370},[2194],[2061,20761,20762,20765],{"style":2302},[2061,20763],{"className":20764,"style":2203},[2202],[2061,20766,20768],{"className":20767},[2207,2208,2209,2210],[2061,20769,2134],{"className":20770},[2169,2210],[2061,20772,2218],{"className":20773},[2217],[2061,20775,20777],{"className":20776},[2190],[2061,20778,20780],{"className":20779,"style":2225},[2194],[2061,20781],{},[2061,20783,2127],{"className":20784},[2396],[2061,20786],{"className":20787,"style":2400},[2231],[2061,20789,11462],{"className":20790},[2169,2170],[2061,20792,2137],{"className":20793},[2444],[2061,20795],{"className":20796,"style":2232},[2231],[2061,20798,2099],{"className":20799},[2236],[2061,20801],{"className":20802,"style":2232},[2231],[2061,20804,20806,20810],{"className":20805},[2160],[2061,20807],{"className":20808,"style":20809},[2164],"height:2.2519em;vertical-align:-0.8804em;",[2061,20811,20813,20816,20912],{"className":20812},[2169],[2061,20814],{"className":20815},[2253,2254],[2061,20817,20819],{"className":20818},[2101],[2061,20820,20822,20904],{"className":20821},[2185,2186],[2061,20823,20825,20901],{"className":20824},[2190],[2061,20826,20828,20879,20887],{"className":20827,"style":2846},[2194],[2061,20829,20830,20833],{"style":2270},[2061,20831],{"className":20832,"style":2274},[2202],[2061,20834,20836,20839],{"className":20835},[2169],[2061,20837,2108],{"className":20838,"style":2281},[2169],[2061,20840,20842,20845],{"className":20841},[2169],[2061,20843,1798],{"className":20844},[2169,2170],[2061,20846,20848],{"className":20847},[2181],[2061,20849,20851,20871],{"className":20850},[2185,2186],[2061,20852,20854,20868],{"className":20853},[2190],[2061,20855,20857],{"className":20856,"style":2370},[2194],[2061,20858,20859,20862],{"style":2302},[2061,20860],{"className":20861,"style":2203},[2202],[2061,20863,20865],{"className":20864},[2207,2208,2209,2210],[2061,20866,2123],{"className":20867},[2169,2210],[2061,20869,2218],{"className":20870},[2217],[2061,20872,20874],{"className":20873},[2190],[2061,20875,20877],{"className":20876,"style":2225},[2194],[2061,20878],{},[2061,20880,20881,20884],{"style":2325},[2061,20882],{"className":20883,"style":2274},[2202],[2061,20885],{"className":20886,"style":2333},[2332],[2061,20888,20889,20892],{"style":2336},[2061,20890],{"className":20891,"style":2274},[2202],[2061,20893,20895,20898],{"className":20894},[2169],[2061,20896,2108],{"className":20897,"style":2281},[2169],[2061,20899,12585],{"className":20900},[2169,2170],[2061,20902,2218],{"className":20903},[2217],[2061,20905,20907],{"className":20906},[2190],[2061,20908,20910],{"className":20909,"style":8254},[2194],[2061,20911],{},[2061,20913],{"className":20914},[2444,2254],[1847,20916,20918],{"id":20917},"例题-2-完全互补品的情况","例题 2: 完全互补品的情况",[1798,20920,20921,20923,20924,20994,20995,21065,21066,21344,21345,14527,21437,21529,21530,21582],{},[1865,20922,14147],{},": 消费者消费咖啡(",[2061,20925,20927,20945],{"className":20926},[2068],[2061,20928,20930],{"className":20929},[2072],[2074,20931,20932],{"xmlns":2076},[2079,20933,20934,20942],{},[2082,20935,20936],{},[2089,20937,20938,20940],{},[2085,20939,2119],{},[2121,20941,2123],{},[2149,20943,20944],{"encoding":2151},"x_1",[2061,20946,20948],{"className":20947,"ariaHidden":2126},[2156],[2061,20949,20951,20954],{"className":20950},[2160],[2061,20952],{"className":20953,"style":7092},[2164],[2061,20955,20957,20960],{"className":20956},[2169],[2061,20958,2119],{"className":20959},[2169,2170],[2061,20961,20963],{"className":20962},[2181],[2061,20964,20966,20986],{"className":20965},[2185,2186],[2061,20967,20969,20983],{"className":20968},[2190],[2061,20970,20972],{"className":20971,"style":2370},[2194],[2061,20973,20974,20977],{"style":2302},[2061,20975],{"className":20976,"style":2203},[2202],[2061,20978,20980],{"className":20979},[2207,2208,2209,2210],[2061,20981,2123],{"className":20982},[2169,2210],[2061,20984,2218],{"className":20985},[2217],[2061,20987,20989],{"className":20988},[2190],[2061,20990,20992],{"className":20991,"style":2225},[2194],[2061,20993],{},")和糖(",[2061,20996,20998,21016],{"className":20997},[2068],[2061,20999,21001],{"className":21000},[2072],[2074,21002,21003],{"xmlns":2076},[2079,21004,21005,21013],{},[2082,21006,21007],{},[2089,21008,21009,21011],{},[2085,21010,2119],{},[2121,21012,2134],{},[2149,21014,21015],{"encoding":2151},"x_2",[2061,21017,21019],{"className":21018,"ariaHidden":2126},[2156],[2061,21020,21022,21025],{"className":21021},[2160],[2061,21023],{"className":21024,"style":7092},[2164],[2061,21026,21028,21031],{"className":21027},[2169],[2061,21029,2119],{"className":21030},[2169,2170],[2061,21032,21034],{"className":21033},[2181],[2061,21035,21037,21057],{"className":21036},[2185,2186],[2061,21038,21040,21054],{"className":21039},[2190],[2061,21041,21043],{"className":21042,"style":2370},[2194],[2061,21044,21045,21048],{"style":2302},[2061,21046],{"className":21047,"style":2203},[2202],[2061,21049,21051],{"className":21050},[2207,2208,2209,2210],[2061,21052,2134],{"className":21053},[2169,2210],[2061,21055,2218],{"className":21056},[2217],[2061,21058,21060],{"className":21059},[2190],[2061,21061,21063],{"className":21062,"style":2225},[2194],[2061,21064],{},")，效用函数为 ",[2061,21067,21069,21127],{"className":21068},[2068],[2061,21070,21072],{"className":21071},[2072],[2074,21073,21074],{"xmlns":2076},[2079,21075,21076,21124],{},[2082,21077,21078,21080,21082,21088,21090,21096,21098,21100,21102,21104,21106,21112,21114,21116,21122],{},[2085,21079,2005],{},[2097,21081,2114],{"stretchy":2113},[2089,21083,21084,21086],{},[2085,21085,2119],{},[2121,21087,2123],{},[2097,21089,2127],{"separator":2126},[2089,21091,21092,21094],{},[2085,21093,2119],{},[2121,21095,2134],{},[2097,21097,2137],{"stretchy":2113},[2097,21099,2099],{},[2085,21101,5777],{},[2097,21103,4951],{},[2097,21105,5782],{"stretchy":2113},[2089,21107,21108,21110],{},[2085,21109,2119],{},[2121,21111,2123],{},[2097,21113,2127],{"separator":2126},[2121,21115,2134],{},[2089,21117,21118,21120],{},[2085,21119,2119],{},[2121,21121,2134],{},[2097,21123,5803],{"stretchy":2113},[2149,21125,21126],{"encoding":2151},"U(x_1, x_2) = \\min\\{x_1, 2x_2\\}",[2061,21128,21130,21240],{"className":21129,"ariaHidden":2126},[2156],[2061,21131,21133,21136,21139,21142,21182,21185,21188,21228,21231,21234,21237],{"className":21132},[2160],[2061,21134],{"className":21135,"style":4634},[2164],[2061,21137,2005],{"className":21138,"style":2171},[2169,2170],[2061,21140,2114],{"className":21141},[2253],[2061,21143,21145,21148],{"className":21144},[2169],[2061,21146,2119],{"className":21147},[2169,2170],[2061,21149,21151],{"className":21150},[2181],[2061,21152,21154,21174],{"className":21153},[2185,2186],[2061,21155,21157,21171],{"className":21156},[2190],[2061,21158,21160],{"className":21159,"style":2370},[2194],[2061,21161,21162,21165],{"style":2302},[2061,21163],{"className":21164,"style":2203},[2202],[2061,21166,21168],{"className":21167},[2207,2208,2209,2210],[2061,21169,2123],{"className":21170},[2169,2210],[2061,21172,2218],{"className":21173},[2217],[2061,21175,21177],{"className":21176},[2190],[2061,21178,21180],{"className":21179,"style":2225},[2194],[2061,21181],{},[2061,21183,2127],{"className":21184},[2396],[2061,21186],{"className":21187,"style":2400},[2231],[2061,21189,21191,21194],{"className":21190},[2169],[2061,21192,2119],{"className":21193},[2169,2170],[2061,21195,21197],{"className":21196},[2181],[2061,21198,21200,21220],{"className":21199},[2185,2186],[2061,21201,21203,21217],{"className":21202},[2190],[2061,21204,21206],{"className":21205,"style":2370},[2194],[2061,21207,21208,21211],{"style":2302},[2061,21209],{"className":21210,"style":2203},[2202],[2061,21212,21214],{"className":21213},[2207,2208,2209,2210],[2061,21215,2134],{"className":21216},[2169,2210],[2061,21218,2218],{"className":21219},[2217],[2061,21221,21223],{"className":21222},[2190],[2061,21224,21226],{"className":21225,"style":2225},[2194],[2061,21227],{},[2061,21229,2137],{"className":21230},[2444],[2061,21232],{"className":21233,"style":2232},[2231],[2061,21235,2099],{"className":21236},[2236],[2061,21238],{"className":21239,"style":2232},[2231],[2061,21241,21243,21246,21249,21252,21292,21295,21298,21301,21341],{"className":21242},[2160],[2061,21244],{"className":21245,"style":4634},[2164],[2061,21247,5777],{"className":21248},[5104],[2061,21250,5782],{"className":21251},[2253],[2061,21253,21255,21258],{"className":21254},[2169],[2061,21256,2119],{"className":21257},[2169,2170],[2061,21259,21261],{"className":21260},[2181],[2061,21262,21264,21284],{"className":21263},[2185,2186],[2061,21265,21267,21281],{"className":21266},[2190],[2061,21268,21270],{"className":21269,"style":2370},[2194],[2061,21271,21272,21275],{"style":2302},[2061,21273],{"className":21274,"style":2203},[2202],[2061,21276,21278],{"className":21277},[2207,2208,2209,2210],[2061,21279,2123],{"className":21280},[2169,2210],[2061,21282,2218],{"className":21283},[2217],[2061,21285,21287],{"className":21286},[2190],[2061,21288,21290],{"className":21289,"style":2225},[2194],[2061,21291],{},[2061,21293,2127],{"className":21294},[2396],[2061,21296],{"className":21297,"style":2400},[2231],[2061,21299,2134],{"className":21300},[2169],[2061,21302,21304,21307],{"className":21303},[2169],[2061,21305,2119],{"className":21306},[2169,2170],[2061,21308,21310],{"className":21309},[2181],[2061,21311,21313,21333],{"className":21312},[2185,2186],[2061,21314,21316,21330],{"className":21315},[2190],[2061,21317,21319],{"className":21318,"style":2370},[2194],[2061,21320,21321,21324],{"style":2302},[2061,21322],{"className":21323,"style":2203},[2202],[2061,21325,21327],{"className":21326},[2207,2208,2209,2210],[2061,21328,2134],{"className":21329},[2169,2210],[2061,21331,2218],{"className":21332},[2217],[2061,21334,21336],{"className":21335},[2190],[2061,21337,21339],{"className":21338,"style":2225},[2194],[2061,21340],{},[2061,21342,5803],{"className":21343},[2444],"（一杯咖啡配两勺糖）。价格 ",[2061,21346,21348,21370],{"className":21347},[2068],[2061,21349,21351],{"className":21350},[2072],[2074,21352,21353],{"xmlns":2076},[2079,21354,21355,21367],{},[2082,21356,21357,21363,21365],{},[2089,21358,21359,21361],{},[2085,21360,1798],{},[2121,21362,2123],{},[2097,21364,2099],{},[2121,21366,19361],{},[2149,21368,21369],{"encoding":2151},"p_1 = 4",[2061,21371,21373,21428],{"className":21372,"ariaHidden":2126},[2156],[2061,21374,21376,21379,21419,21422,21425],{"className":21375},[2160],[2061,21377],{"className":21378,"style":6705},[2164],[2061,21380,21382,21385],{"className":21381},[2169],[2061,21383,1798],{"className":21384},[2169,2170],[2061,21386,21388],{"className":21387},[2181],[2061,21389,21391,21411],{"className":21390},[2185,2186],[2061,21392,21394,21408],{"className":21393},[2190],[2061,21395,21397],{"className":21396,"style":2370},[2194],[2061,21398,21399,21402],{"style":2302},[2061,21400],{"className":21401,"style":2203},[2202],[2061,21403,21405],{"className":21404},[2207,2208,2209,2210],[2061,21406,2123],{"className":21407},[2169,2210],[2061,21409,2218],{"className":21410},[2217],[2061,21412,21414],{"className":21413},[2190],[2061,21415,21417],{"className":21416,"style":2225},[2194],[2061,21418],{},[2061,21420],{"className":21421,"style":2232},[2231],[2061,21423,2099],{"className":21424},[2236],[2061,21426],{"className":21427,"style":2232},[2231],[2061,21429,21431,21434],{"className":21430},[2160],[2061,21432],{"className":21433,"style":2692},[2164],[2061,21435,19361],{"className":21436},[2169],[2061,21438,21440,21462],{"className":21439},[2068],[2061,21441,21443],{"className":21442},[2072],[2074,21444,21445],{"xmlns":2076},[2079,21446,21447,21459],{},[2082,21448,21449,21455,21457],{},[2089,21450,21451,21453],{},[2085,21452,1798],{},[2121,21454,2134],{},[2097,21456,2099],{},[2121,21458,2123],{},[2149,21460,21461],{"encoding":2151},"p_2 = 1",[2061,21463,21465,21520],{"className":21464,"ariaHidden":2126},[2156],[2061,21466,21468,21471,21511,21514,21517],{"className":21467},[2160],[2061,21469],{"className":21470,"style":6705},[2164],[2061,21472,21474,21477],{"className":21473},[2169],[2061,21475,1798],{"className":21476},[2169,2170],[2061,21478,21480],{"className":21479},[2181],[2061,21481,21483,21503],{"className":21482},[2185,2186],[2061,21484,21486,21500],{"className":21485},[2190],[2061,21487,21489],{"className":21488,"style":2370},[2194],[2061,21490,21491,21494],{"style":2302},[2061,21492],{"className":21493,"style":2203},[2202],[2061,21495,21497],{"className":21496},[2207,2208,2209,2210],[2061,21498,2134],{"className":21499},[2169,2210],[2061,21501,2218],{"className":21502},[2217],[2061,21504,21506],{"className":21505},[2190],[2061,21507,21509],{"className":21508,"style":2225},[2194],[2061,21510],{},[2061,21512],{"className":21513,"style":2232},[2231],[2061,21515,2099],{"className":21516},[2236],[2061,21518],{"className":21519,"style":2232},[2231],[2061,21521,21523,21526],{"className":21522},[2160],[2061,21524],{"className":21525,"style":2692},[2164],[2061,21527,2123],{"className":21528},[2169],"，收入 ",[2061,21531,21533,21552],{"className":21532},[2068],[2061,21534,21536],{"className":21535},[2072],[2074,21537,21538],{"xmlns":2076},[2079,21539,21540,21549],{},[2082,21541,21542,21544,21546],{},[2085,21543,7160],{},[2097,21545,2099],{},[2121,21547,21548],{},"100",[2149,21550,21551],{"encoding":2151},"m = 100",[2061,21553,21555,21573],{"className":21554,"ariaHidden":2126},[2156],[2061,21556,21558,21561,21564,21567,21570],{"className":21557},[2160],[2061,21559],{"className":21560,"style":6568},[2164],[2061,21562,7160],{"className":21563},[2169,2170],[2061,21565],{"className":21566,"style":2232},[2231],[2061,21568,2099],{"className":21569},[2236],[2061,21571],{"className":21572,"style":2232},[2231],[2061,21574,21576,21579],{"className":21575},[2160],[2061,21577],{"className":21578,"style":2692},[2164],[2061,21580,21548],{"className":21581},[2169],"。求最优消费束。",[1798,21584,21585,4550],{},[1865,21586,14690],{},[1798,21588,21589],{},"对于完全互补品，最优解总是在\"直角拐点\"处，即：",[2061,21591,21593],{"className":21592},[2064],[2061,21594,21596,21624],{"className":21595},[2068],[2061,21597,21599],{"className":21598},[2072],[2074,21600,21601],{"xmlns":2076,"display":2077},[2079,21602,21603,21621],{},[2082,21604,21605,21611,21613,21615],{},[2089,21606,21607,21609],{},[2085,21608,2119],{},[2121,21610,2123],{},[2097,21612,2099],{},[2121,21614,2134],{},[2089,21616,21617,21619],{},[2085,21618,2119],{},[2121,21620,2134],{},[2149,21622,21623],{"encoding":2151},"x_1 = 2x_2",[2061,21625,21627,21682],{"className":21626,"ariaHidden":2126},[2156],[2061,21628,21630,21633,21673,21676,21679],{"className":21629},[2160],[2061,21631],{"className":21632,"style":7092},[2164],[2061,21634,21636,21639],{"className":21635},[2169],[2061,21637,2119],{"className":21638},[2169,2170],[2061,21640,21642],{"className":21641},[2181],[2061,21643,21645,21665],{"className":21644},[2185,2186],[2061,21646,21648,21662],{"className":21647},[2190],[2061,21649,21651],{"className":21650,"style":2370},[2194],[2061,21652,21653,21656],{"style":2302},[2061,21654],{"className":21655,"style":2203},[2202],[2061,21657,21659],{"className":21658},[2207,2208,2209,2210],[2061,21660,2123],{"className":21661},[2169,2210],[2061,21663,2218],{"className":21664},[2217],[2061,21666,21668],{"className":21667},[2190],[2061,21669,21671],{"className":21670,"style":2225},[2194],[2061,21672],{},[2061,21674],{"className":21675,"style":2232},[2231],[2061,21677,2099],{"className":21678},[2236],[2061,21680],{"className":21681,"style":2232},[2231],[2061,21683,21685,21688,21691],{"className":21684},[2160],[2061,21686],{"className":21687,"style":14943},[2164],[2061,21689,2134],{"className":21690},[2169],[2061,21692,21694,21697],{"className":21693},[2169],[2061,21695,2119],{"className":21696},[2169,2170],[2061,21698,21700],{"className":21699},[2181],[2061,21701,21703,21723],{"className":21702},[2185,2186],[2061,21704,21706,21720],{"className":21705},[2190],[2061,21707,21709],{"className":21708,"style":2370},[2194],[2061,21710,21711,21714],{"style":2302},[2061,21712],{"className":21713,"style":2203},[2202],[2061,21715,21717],{"className":21716},[2207,2208,2209,2210],[2061,21718,2134],{"className":21719},[2169,2210],[2061,21721,2218],{"className":21722},[2217],[2061,21724,21726],{"className":21725},[2190],[2061,21727,21729],{"className":21728,"style":2225},[2194],[2061,21730],{},[1798,21732,17307],{},[2061,21734,21736],{"className":21735},[2064],[2061,21737,21739,21771],{"className":21738},[2068],[2061,21740,21742],{"className":21741},[2072],[2074,21743,21744],{"xmlns":2076,"display":2077},[2079,21745,21746,21768],{},[2082,21747,21748,21750,21756,21758,21764,21766],{},[2121,21749,19361],{},[2089,21751,21752,21754],{},[2085,21753,2119],{},[2121,21755,2123],{},[2097,21757,2762],{},[2089,21759,21760,21762],{},[2085,21761,2119],{},[2121,21763,2134],{},[2097,21765,2099],{},[2121,21767,21548],{},[2149,21769,21770],{"encoding":2151},"4x_1 + x_2 = 100",[2061,21772,21774,21832,21887],{"className":21773,"ariaHidden":2126},[2156],[2061,21775,21777,21780,21783,21823,21826,21829],{"className":21776},[2160],[2061,21778],{"className":21779,"style":14943},[2164],[2061,21781,19361],{"className":21782},[2169],[2061,21784,21786,21789],{"className":21785},[2169],[2061,21787,2119],{"className":21788},[2169,2170],[2061,21790,21792],{"className":21791},[2181],[2061,21793,21795,21815],{"className":21794},[2185,2186],[2061,21796,21798,21812],{"className":21797},[2190],[2061,21799,21801],{"className":21800,"style":2370},[2194],[2061,21802,21803,21806],{"style":2302},[2061,21804],{"className":21805,"style":2203},[2202],[2061,21807,21809],{"className":21808},[2207,2208,2209,2210],[2061,21810,2123],{"className":21811},[2169,2210],[2061,21813,2218],{"className":21814},[2217],[2061,21816,21818],{"className":21817},[2190],[2061,21819,21821],{"className":21820,"style":2225},[2194],[2061,21822],{},[2061,21824],{"className":21825,"style":2980},[2231],[2061,21827,2762],{"className":21828},[2984],[2061,21830],{"className":21831,"style":2980},[2231],[2061,21833,21835,21838,21878,21881,21884],{"className":21834},[2160],[2061,21836],{"className":21837,"style":7092},[2164],[2061,21839,21841,21844],{"className":21840},[2169],[2061,21842,2119],{"className":21843},[2169,2170],[2061,21845,21847],{"className":21846},[2181],[2061,21848,21850,21870],{"className":21849},[2185,2186],[2061,21851,21853,21867],{"className":21852},[2190],[2061,21854,21856],{"className":21855,"style":2370},[2194],[2061,21857,21858,21861],{"style":2302},[2061,21859],{"className":21860,"style":2203},[2202],[2061,21862,21864],{"className":21863},[2207,2208,2209,2210],[2061,21865,2134],{"className":21866},[2169,2210],[2061,21868,2218],{"className":21869},[2217],[2061,21871,21873],{"className":21872},[2190],[2061,21874,21876],{"className":21875,"style":2225},[2194],[2061,21877],{},[2061,21879],{"className":21880,"style":2232},[2231],[2061,21882,2099],{"className":21883},[2236],[2061,21885],{"className":21886,"style":2232},[2231],[2061,21888,21890,21893],{"className":21889},[2160],[2061,21891],{"className":21892,"style":2692},[2164],[2061,21894,21548],{"className":21895},[2169],[2061,21897,21899],{"className":21898},[2064],[2061,21900,21902,21940],{"className":21901},[2068],[2061,21903,21905],{"className":21904},[2072],[2074,21906,21907],{"xmlns":2076,"display":2077},[2079,21908,21909,21937],{},[2082,21910,21911,21913,21915,21917,21923,21925,21927,21933,21935],{},[2121,21912,19361],{},[2097,21914,2114],{"stretchy":2113},[2121,21916,2134],{},[2089,21918,21919,21921],{},[2085,21920,2119],{},[2121,21922,2134],{},[2097,21924,2137],{"stretchy":2113},[2097,21926,2762],{},[2089,21928,21929,21931],{},[2085,21930,2119],{},[2121,21932,2134],{},[2097,21934,2099],{},[2121,21936,21548],{},[2149,21938,21939],{"encoding":2151},"4(2x_2) + x_2 = 100",[2061,21941,21943,22010,22065],{"className":21942,"ariaHidden":2126},[2156],[2061,21944,21946,21949,21952,21955,21958,21998,22001,22004,22007],{"className":21945},[2160],[2061,21947],{"className":21948,"style":4634},[2164],[2061,21950,19361],{"className":21951},[2169],[2061,21953,2114],{"className":21954},[2253],[2061,21956,2134],{"className":21957},[2169],[2061,21959,21961,21964],{"className":21960},[2169],[2061,21962,2119],{"className":21963},[2169,2170],[2061,21965,21967],{"className":21966},[2181],[2061,21968,21970,21990],{"className":21969},[2185,2186],[2061,21971,21973,21987],{"className":21972},[2190],[2061,21974,21976],{"className":21975,"style":2370},[2194],[2061,21977,21978,21981],{"style":2302},[2061,21979],{"className":21980,"style":2203},[2202],[2061,21982,21984],{"className":21983},[2207,2208,2209,2210],[2061,21985,2134],{"className":21986},[2169,2210],[2061,21988,2218],{"className":21989},[2217],[2061,21991,21993],{"className":21992},[2190],[2061,21994,21996],{"className":21995,"style":2225},[2194],[2061,21997],{},[2061,21999,2137],{"className":22000},[2444],[2061,22002],{"className":22003,"style":2980},[2231],[2061,22005,2762],{"className":22006},[2984],[2061,22008],{"className":22009,"style":2980},[2231],[2061,22011,22013,22016,22056,22059,22062],{"className":22012},[2160],[2061,22014],{"className":22015,"style":7092},[2164],[2061,22017,22019,22022],{"className":22018},[2169],[2061,22020,2119],{"className":22021},[2169,2170],[2061,22023,22025],{"className":22024},[2181],[2061,22026,22028,22048],{"className":22027},[2185,2186],[2061,22029,22031,22045],{"className":22030},[2190],[2061,22032,22034],{"className":22033,"style":2370},[2194],[2061,22035,22036,22039],{"style":2302},[2061,22037],{"className":22038,"style":2203},[2202],[2061,22040,22042],{"className":22041},[2207,2208,2209,2210],[2061,22043,2134],{"className":22044},[2169,2210],[2061,22046,2218],{"className":22047},[2217],[2061,22049,22051],{"className":22050},[2190],[2061,22052,22054],{"className":22053,"style":2225},[2194],[2061,22055],{},[2061,22057],{"className":22058,"style":2232},[2231],[2061,22060,2099],{"className":22061},[2236],[2061,22063],{"className":22064,"style":2232},[2231],[2061,22066,22068,22071],{"className":22067},[2160],[2061,22069],{"className":22070,"style":2692},[2164],[2061,22072,21548],{"className":22073},[2169],[2061,22075,22077],{"className":22076},[2064],[2061,22078,22080,22105],{"className":22079},[2068],[2061,22081,22083],{"className":22082},[2072],[2074,22084,22085],{"xmlns":2076,"display":2077},[2079,22086,22087,22102],{},[2082,22088,22089,22092,22098,22100],{},[2121,22090,22091],{},"9",[2089,22093,22094,22096],{},[2085,22095,2119],{},[2121,22097,2134],{},[2097,22099,2099],{},[2121,22101,21548],{},[2149,22103,22104],{"encoding":2151},"9x_2 = 100",[2061,22106,22108,22166],{"className":22107,"ariaHidden":2126},[2156],[2061,22109,22111,22114,22117,22157,22160,22163],{"className":22110},[2160],[2061,22112],{"className":22113,"style":14943},[2164],[2061,22115,22091],{"className":22116},[2169],[2061,22118,22120,22123],{"className":22119},[2169],[2061,22121,2119],{"className":22122},[2169,2170],[2061,22124,22126],{"className":22125},[2181],[2061,22127,22129,22149],{"className":22128},[2185,2186],[2061,22130,22132,22146],{"className":22131},[2190],[2061,22133,22135],{"className":22134,"style":2370},[2194],[2061,22136,22137,22140],{"style":2302},[2061,22138],{"className":22139,"style":2203},[2202],[2061,22141,22143],{"className":22142},[2207,2208,2209,2210],[2061,22144,2134],{"className":22145},[2169,2210],[2061,22147,2218],{"className":22148},[2217],[2061,22150,22152],{"className":22151},[2190],[2061,22153,22155],{"className":22154,"style":2225},[2194],[2061,22156],{},[2061,22158],{"className":22159,"style":2232},[2231],[2061,22161,2099],{"className":22162},[2236],[2061,22164],{"className":22165,"style":2232},[2231],[2061,22167,22169,22172],{"className":22168},[2160],[2061,22170],{"className":22171,"style":2692},[2164],[2061,22173,21548],{"className":22174},[2169],[2061,22176,22178],{"className":22177},[2064],[2061,22179,22181,22241],{"className":22180},[2068],[2061,22182,22184],{"className":22183},[2072],[2074,22185,22186],{"xmlns":2076,"display":2077},[2079,22187,22188,22238],{},[2082,22189,22190,22198,22200,22206,22209,22212,22214,22216,22224,22226,22233,22235],{},[2500,22191,22192,22194,22196],{},[2085,22193,2119],{},[2121,22195,2134],{},[2097,22197,10359],{},[2097,22199,2099],{},[2101,22201,22202,22204],{},[2121,22203,21548],{},[2121,22205,22091],{},[2097,22207,22208],{},"≈",[2121,22210,22211],{},"11.11",[2097,22213,2127],{"separator":2126},[2231,22215],{"width":4610},[2500,22217,22218,22220,22222],{},[2085,22219,2119],{},[2121,22221,2123],{},[2097,22223,10359],{},[2097,22225,2099],{},[2101,22227,22228,22231],{},[2121,22229,22230],{},"200",[2121,22232,22091],{},[2097,22234,22208],{},[2121,22236,22237],{},"22.22",[2149,22239,22240],{"encoding":2151},"x_2^* = \\frac{100}{9} \\approx 11.11, \\quad x_1^* = \\frac{200}{9} \\approx 22.22",[2061,22242,22244,22310,22387,22465,22542],{"className":22243,"ariaHidden":2126},[2156],[2061,22245,22247,22250,22301,22304,22307],{"className":22246},[2160],[2061,22248],{"className":22249,"style":10402},[2164],[2061,22251,22253,22256],{"className":22252},[2169],[2061,22254,2119],{"className":22255},[2169,2170],[2061,22257,22259],{"className":22258},[2181],[2061,22260,22262,22293],{"className":22261},[2185,2186],[2061,22263,22265,22290],{"className":22264},[2190],[2061,22266,22268,22279],{"className":22267,"style":10421},[2194],[2061,22269,22270,22273],{"style":4767},[2061,22271],{"className":22272,"style":2203},[2202],[2061,22274,22276],{"className":22275},[2207,2208,2209,2210],[2061,22277,2134],{"className":22278},[2169,2210],[2061,22280,22281,22284],{"style":4779},[2061,22282],{"className":22283,"style":2203},[2202],[2061,22285,22287],{"className":22286},[2207,2208,2209,2210],[2061,22288,10359],{"className":22289},[2984,2210],[2061,22291,2218],{"className":22292},[2217],[2061,22294,22296],{"className":22295},[2190],[2061,22297,22299],{"className":22298,"style":4802},[2194],[2061,22300],{},[2061,22302],{"className":22303,"style":2232},[2231],[2061,22305,2099],{"className":22306},[2236],[2061,22308],{"className":22309,"style":2232},[2231],[2061,22311,22313,22316,22378,22381,22384],{"className":22312},[2160],[2061,22314],{"className":22315,"style":16476},[2164],[2061,22317,22319,22322,22375],{"className":22318},[2169],[2061,22320],{"className":22321},[2253,2254],[2061,22323,22325],{"className":22324},[2101],[2061,22326,22328,22367],{"className":22327},[2185,2186],[2061,22329,22331,22364],{"className":22330},[2190],[2061,22332,22334,22345,22353],{"className":22333,"style":16495},[2194],[2061,22335,22336,22339],{"style":2270},[2061,22337],{"className":22338,"style":2274},[2202],[2061,22340,22342],{"className":22341},[2169],[2061,22343,22091],{"className":22344},[2169],[2061,22346,22347,22350],{"style":2325},[2061,22348],{"className":22349,"style":2274},[2202],[2061,22351],{"className":22352,"style":2333},[2332],[2061,22354,22355,22358],{"style":2336},[2061,22356],{"className":22357,"style":2274},[2202],[2061,22359,22361],{"className":22360},[2169],[2061,22362,21548],{"className":22363},[2169],[2061,22365,2218],{"className":22366},[2217],[2061,22368,22370],{"className":22369},[2190],[2061,22371,22373],{"className":22372,"style":9692},[2194],[2061,22374],{},[2061,22376],{"className":22377},[2444,2254],[2061,22379],{"className":22380,"style":2232},[2231],[2061,22382,22208],{"className":22383},[2236],[2061,22385],{"className":22386,"style":2232},[2231],[2061,22388,22390,22393,22396,22399,22402,22405,22456,22459,22462],{"className":22389},[2160],[2061,22391],{"className":22392,"style":10402},[2164],[2061,22394,22211],{"className":22395},[2169],[2061,22397,2127],{"className":22398},[2396],[2061,22400],{"className":22401,"style":4870},[2231],[2061,22403],{"className":22404,"style":2400},[2231],[2061,22406,22408,22411],{"className":22407},[2169],[2061,22409,2119],{"className":22410},[2169,2170],[2061,22412,22414],{"className":22413},[2181],[2061,22415,22417,22448],{"className":22416},[2185,2186],[2061,22418,22420,22445],{"className":22419},[2190],[2061,22421,22423,22434],{"className":22422,"style":10421},[2194],[2061,22424,22425,22428],{"style":4767},[2061,22426],{"className":22427,"style":2203},[2202],[2061,22429,22431],{"className":22430},[2207,2208,2209,2210],[2061,22432,2123],{"className":22433},[2169,2210],[2061,22435,22436,22439],{"style":4779},[2061,22437],{"className":22438,"style":2203},[2202],[2061,22440,22442],{"className":22441},[2207,2208,2209,2210],[2061,22443,10359],{"className":22444},[2984,2210],[2061,22446,2218],{"className":22447},[2217],[2061,22449,22451],{"className":22450},[2190],[2061,22452,22454],{"className":22453,"style":4802},[2194],[2061,22455],{},[2061,22457],{"className":22458,"style":2232},[2231],[2061,22460,2099],{"className":22461},[2236],[2061,22463],{"className":22464,"style":2232},[2231],[2061,22466,22468,22471,22533,22536,22539],{"className":22467},[2160],[2061,22469],{"className":22470,"style":16476},[2164],[2061,22472,22474,22477,22530],{"className":22473},[2169],[2061,22475],{"className":22476},[2253,2254],[2061,22478,22480],{"className":22479},[2101],[2061,22481,22483,22522],{"className":22482},[2185,2186],[2061,22484,22486,22519],{"className":22485},[2190],[2061,22487,22489,22500,22508],{"className":22488,"style":16495},[2194],[2061,22490,22491,22494],{"style":2270},[2061,22492],{"className":22493,"style":2274},[2202],[2061,22495,22497],{"className":22496},[2169],[2061,22498,22091],{"className":22499},[2169],[2061,22501,22502,22505],{"style":2325},[2061,22503],{"className":22504,"style":2274},[2202],[2061,22506],{"className":22507,"style":2333},[2332],[2061,22509,22510,22513],{"style":2336},[2061,22511],{"className":22512,"style":2274},[2202],[2061,22514,22516],{"className":22515},[2169],[2061,22517,22230],{"className":22518},[2169],[2061,22520,2218],{"className":22521},[2217],[2061,22523,22525],{"className":22524},[2190],[2061,22526,22528],{"className":22527,"style":9692},[2194],[2061,22529],{},[2061,22531],{"className":22532},[2444,2254],[2061,22534],{"className":22535,"style":2232},[2231],[2061,22537,22208],{"className":22538},[2236],[2061,22540],{"className":22541,"style":2232},[2231],[2061,22543,22545,22548],{"className":22544},[2160],[2061,22546],{"className":22547,"style":2692},[2164],[2061,22549,22237],{"className":22550},[2169],[1798,22552,22553,22556,22557,22730,22731,1989],{},[1865,22554,22555],{},"一般规律",": 对于 ",[2061,22558,22560,22602],{"className":22559},[2068],[2061,22561,22563],{"className":22562},[2072],[2074,22564,22565],{"xmlns":2076},[2079,22566,22567,22599],{},[2082,22568,22569,22571,22573,22575,22577,22579,22581,22587,22589,22591,22597],{},[2085,22570,2005],{},[2097,22572,2099],{},[2085,22574,5777],{},[2097,22576,4951],{},[2097,22578,5782],{"stretchy":2113},[2085,22580,1827],{},[2089,22582,22583,22585],{},[2085,22584,2119],{},[2121,22586,2123],{},[2097,22588,2127],{"separator":2126},[2085,22590,5488],{},[2089,22592,22593,22595],{},[2085,22594,2119],{},[2121,22596,2134],{},[2097,22598,5803],{"stretchy":2113},[2149,22600,22601],{"encoding":2151},"U = \\min\\{ax_1, bx_2\\}",[2061,22603,22605,22623],{"className":22604,"ariaHidden":2126},[2156],[2061,22606,22608,22611,22614,22617,22620],{"className":22607},[2160],[2061,22609],{"className":22610,"style":8096},[2164],[2061,22612,2005],{"className":22613,"style":2171},[2169,2170],[2061,22615],{"className":22616,"style":2232},[2231],[2061,22618,2099],{"className":22619},[2236],[2061,22621],{"className":22622,"style":2232},[2231],[2061,22624,22626,22629,22632,22635,22638,22678,22681,22684,22687,22727],{"className":22625},[2160],[2061,22627],{"className":22628,"style":4634},[2164],[2061,22630,5777],{"className":22631},[5104],[2061,22633,5782],{"className":22634},[2253],[2061,22636,1827],{"className":22637},[2169,2170],[2061,22639,22641,22644],{"className":22640},[2169],[2061,22642,2119],{"className":22643},[2169,2170],[2061,22645,22647],{"className":22646},[2181],[2061,22648,22650,22670],{"className":22649},[2185,2186],[2061,22651,22653,22667],{"className":22652},[2190],[2061,22654,22656],{"className":22655,"style":2370},[2194],[2061,22657,22658,22661],{"style":2302},[2061,22659],{"className":22660,"style":2203},[2202],[2061,22662,22664],{"className":22663},[2207,2208,2209,2210],[2061,22665,2123],{"className":22666},[2169,2210],[2061,22668,2218],{"className":22669},[2217],[2061,22671,22673],{"className":22672},[2190],[2061,22674,22676],{"className":22675,"style":2225},[2194],[2061,22677],{},[2061,22679,2127],{"className":22680},[2396],[2061,22682],{"className":22683,"style":2400},[2231],[2061,22685,5488],{"className":22686},[2169,2170],[2061,22688,22690,22693],{"className":22689},[2169],[2061,22691,2119],{"className":22692},[2169,2170],[2061,22694,22696],{"className":22695},[2181],[2061,22697,22699,22719],{"className":22698},[2185,2186],[2061,22700,22702,22716],{"className":22701},[2190],[2061,22703,22705],{"className":22704,"style":2370},[2194],[2061,22706,22707,22710],{"style":2302},[2061,22708],{"className":22709,"style":2203},[2202],[2061,22711,22713],{"className":22712},[2207,2208,2209,2210],[2061,22714,2134],{"className":22715},[2169,2210],[2061,22717,2218],{"className":22718},[2217],[2061,22720,22722],{"className":22721},[2190],[2061,22723,22725],{"className":22724,"style":2225},[2194],[2061,22726],{},[2061,22728,5803],{"className":22729},[2444],"，最优解满足 ",[2061,22732,22734,22764],{"className":22733},[2068],[2061,22735,22737],{"className":22736},[2072],[2074,22738,22739],{"xmlns":2076},[2079,22740,22741,22761],{},[2082,22742,22743,22745,22751,22753,22755],{},[2085,22744,1827],{},[2089,22746,22747,22749],{},[2085,22748,2119],{},[2121,22750,2123],{},[2097,22752,2099],{},[2085,22754,5488],{},[2089,22756,22757,22759],{},[2085,22758,2119],{},[2121,22760,2134],{},[2149,22762,22763],{"encoding":2151},"ax_1 = bx_2",[2061,22765,22767,22825],{"className":22766,"ariaHidden":2126},[2156],[2061,22768,22770,22773,22776,22816,22819,22822],{"className":22769},[2160],[2061,22771],{"className":22772,"style":7092},[2164],[2061,22774,1827],{"className":22775},[2169,2170],[2061,22777,22779,22782],{"className":22778},[2169],[2061,22780,2119],{"className":22781},[2169,2170],[2061,22783,22785],{"className":22784},[2181],[2061,22786,22788,22808],{"className":22787},[2185,2186],[2061,22789,22791,22805],{"className":22790},[2190],[2061,22792,22794],{"className":22793,"style":2370},[2194],[2061,22795,22796,22799],{"style":2302},[2061,22797],{"className":22798,"style":2203},[2202],[2061,22800,22802],{"className":22801},[2207,2208,2209,2210],[2061,22803,2123],{"className":22804},[2169,2210],[2061,22806,2218],{"className":22807},[2217],[2061,22809,22811],{"className":22810},[2190],[2061,22812,22814],{"className":22813,"style":2225},[2194],[2061,22815],{},[2061,22817],{"className":22818,"style":2232},[2231],[2061,22820,2099],{"className":22821},[2236],[2061,22823],{"className":22824,"style":2232},[2231],[2061,22826,22828,22831,22834],{"className":22827},[2160],[2061,22829],{"className":22830,"style":5094},[2164],[2061,22832,5488],{"className":22833},[2169,2170],[2061,22835,22837,22840],{"className":22836},[2169],[2061,22838,2119],{"className":22839},[2169,2170],[2061,22841,22843],{"className":22842},[2181],[2061,22844,22846,22866],{"className":22845},[2185,2186],[2061,22847,22849,22863],{"className":22848},[2190],[2061,22850,22852],{"className":22851,"style":2370},[2194],[2061,22853,22854,22857],{"style":2302},[2061,22855],{"className":22856,"style":2203},[2202],[2061,22858,22860],{"className":22859},[2207,2208,2209,2210],[2061,22861,2134],{"className":22862},[2169,2210],[2061,22864,2218],{"className":22865},[2217],[2061,22867,22869],{"className":22868},[2190],[2061,22870,22872],{"className":22871,"style":2225},[2194],[2061,22873],{},[1840,22875],{},[1794,22877,22879],{"id":22878},"_5-需求函数的性质","5. 需求函数的性质",[1847,22881,22883],{"id":22882},"_51-齐次性-homogeneity","5.1 齐次性 (Homogeneity)",[1798,22885,22886,22887,22890],{},"马歇尔需求函数对价格和收入是",[1865,22888,22889],{},"零次齐次","的：",[2061,22892,22894],{"className":22893},[2064],[2061,22895,22897,22986],{"className":22896},[2068],[2061,22898,22900],{"className":22899},[2072],[2074,22901,22902],{"xmlns":2076,"display":2077},[2079,22903,22904,22983],{},[2082,22905,22906,22912,22914,22916,22922,22924,22926,22932,22934,22936,22938,22940,22942,22948,22950,22956,22958,22964,22966,22968,22970,22972,22974,22977,22979,22981],{},[2089,22907,22908,22910],{},[2085,22909,2119],{},[2085,22911,2095],{},[2097,22913,2114],{"stretchy":2113},[2085,22915,8630],{},[2089,22917,22918,22920],{},[2085,22919,1798],{},[2121,22921,2123],{},[2097,22923,2127],{"separator":2126},[2085,22925,8630],{},[2089,22927,22928,22930],{},[2085,22929,1798],{},[2121,22931,2134],{},[2097,22933,2127],{"separator":2126},[2085,22935,8630],{},[2085,22937,7160],{},[2097,22939,2137],{"stretchy":2113},[2097,22941,2099],{},[2089,22943,22944,22946],{},[2085,22945,2119],{},[2085,22947,2095],{},[2097,22949,2114],{"stretchy":2113},[2089,22951,22952,22954],{},[2085,22953,1798],{},[2121,22955,2123],{},[2097,22957,2127],{"separator":2126},[2089,22959,22960,22962],{},[2085,22961,1798],{},[2121,22963,2134],{},[2097,22965,2127],{"separator":2126},[2085,22967,7160],{},[2097,22969,2137],{"stretchy":2113},[2097,22971,2127],{"separator":2126},[2231,22973],{"width":4610},[2085,22975,22976],{"mathvariant":2107},"∀",[2085,22978,8630],{},[2097,22980,4619],{},[2121,22982,2513],{},[2149,22984,22985],{"encoding":2151},"x_i(\\lambda p_1, \\lambda p_2, \\lambda m) = x_i(p_1, p_2, m), \\quad \\forall \\lambda > 0",[2061,22987,22989,23152,23323],{"className":22988,"ariaHidden":2126},[2156],[2061,22990,22992,22995,23035,23038,23041,23081,23084,23087,23090,23130,23133,23136,23140,23143,23146,23149],{"className":22991},[2160],[2061,22993],{"className":22994,"style":4634},[2164],[2061,22996,22998,23001],{"className":22997},[2169],[2061,22999,2119],{"className":23000},[2169,2170],[2061,23002,23004],{"className":23003},[2181],[2061,23005,23007,23027],{"className":23006},[2185,2186],[2061,23008,23010,23024],{"className":23009},[2190],[2061,23011,23013],{"className":23012,"style":2195},[2194],[2061,23014,23015,23018],{"style":2302},[2061,23016],{"className":23017,"style":2203},[2202],[2061,23019,23021],{"className":23020},[2207,2208,2209,2210],[2061,23022,2095],{"className":23023},[2169,2170,2210],[2061,23025,2218],{"className":23026},[2217],[2061,23028,23030],{"className":23029},[2190],[2061,23031,23033],{"className":23032,"style":2225},[2194],[2061,23034],{},[2061,23036,2114],{"className":23037},[2253],[2061,23039,8630],{"className":23040},[2169,2170],[2061,23042,23044,23047],{"className":23043},[2169],[2061,23045,1798],{"className":23046},[2169,2170],[2061,23048,23050],{"className":23049},[2181],[2061,23051,23053,23073],{"className":23052},[2185,2186],[2061,23054,23056,23070],{"className":23055},[2190],[2061,23057,23059],{"className":23058,"style":2370},[2194],[2061,23060,23061,23064],{"style":2302},[2061,23062],{"className":23063,"style":2203},[2202],[2061,23065,23067],{"className":23066},[2207,2208,2209,2210],[2061,23068,2123],{"className":23069},[2169,2210],[2061,23071,2218],{"className":23072},[2217],[2061,23074,23076],{"className":23075},[2190],[2061,23077,23079],{"className":23078,"style":2225},[2194],[2061,23080],{},[2061,23082,2127],{"className":23083},[2396],[2061,23085],{"className":23086,"style":2400},[2231],[2061,23088,8630],{"className":23089},[2169,2170],[2061,23091,23093,23096],{"className":23092},[2169],[2061,23094,1798],{"className":23095},[2169,2170],[2061,23097,23099],{"className":23098},[2181],[2061,23100,23102,23122],{"className":23101},[2185,2186],[2061,23103,23105,23119],{"className":23104},[2190],[2061,23106,23108],{"className":23107,"style":2370},[2194],[2061,23109,23110,23113],{"style":2302},[2061,23111],{"className":23112,"style":2203},[2202],[2061,23114,23116],{"className":23115},[2207,2208,2209,2210],[2061,23117,2134],{"className":23118},[2169,2210],[2061,23120,2218],{"className":23121},[2217],[2061,23123,23125],{"className":23124},[2190],[2061,23126,23128],{"className":23127,"style":2225},[2194],[2061,23129],{},[2061,23131,2127],{"className":23132},[2396],[2061,23134],{"className":23135,"style":2400},[2231],[2061,23137,23139],{"className":23138},[2169,2170],"λm",[2061,23141,2137],{"className":23142},[2444],[2061,23144],{"className":23145,"style":2232},[2231],[2061,23147,2099],{"className":23148},[2236],[2061,23150],{"className":23151,"style":2232},[2231],[2061,23153,23155,23158,23198,23201,23241,23244,23247,23287,23290,23293,23296,23299,23302,23305,23308,23311,23314,23317,23320],{"className":23154},[2160],[2061,23156],{"className":23157,"style":4634},[2164],[2061,23159,23161,23164],{"className":23160},[2169],[2061,23162,2119],{"className":23163},[2169,2170],[2061,23165,23167],{"className":23166},[2181],[2061,23168,23170,23190],{"className":23169},[2185,2186],[2061,23171,23173,23187],{"className":23172},[2190],[2061,23174,23176],{"className":23175,"style":2195},[2194],[2061,23177,23178,23181],{"style":2302},[2061,23179],{"className":23180,"style":2203},[2202],[2061,23182,23184],{"className":23183},[2207,2208,2209,2210],[2061,23185,2095],{"className":23186},[2169,2170,2210],[2061,23188,2218],{"className":23189},[2217],[2061,23191,23193],{"className":23192},[2190],[2061,23194,23196],{"className":23195,"style":2225},[2194],[2061,23197],{},[2061,23199,2114],{"className":23200},[2253],[2061,23202,23204,23207],{"className":23203},[2169],[2061,23205,1798],{"className":23206},[2169,2170],[2061,23208,23210],{"className":23209},[2181],[2061,23211,23213,23233],{"className":23212},[2185,2186],[2061,23214,23216,23230],{"className":23215},[2190],[2061,23217,23219],{"className":23218,"style":2370},[2194],[2061,23220,23221,23224],{"style":2302},[2061,23222],{"className":23223,"style":2203},[2202],[2061,23225,23227],{"className":23226},[2207,2208,2209,2210],[2061,23228,2123],{"className":23229},[2169,2210],[2061,23231,2218],{"className":23232},[2217],[2061,23234,23236],{"className":23235},[2190],[2061,23237,23239],{"className":23238,"style":2225},[2194],[2061,23240],{},[2061,23242,2127],{"className":23243},[2396],[2061,23245],{"className":23246,"style":2400},[2231],[2061,23248,23250,23253],{"className":23249},[2169],[2061,23251,1798],{"className":23252},[2169,2170],[2061,23254,23256],{"className":23255},[2181],[2061,23257,23259,23279],{"className":23258},[2185,2186],[2061,23260,23262,23276],{"className":23261},[2190],[2061,23263,23265],{"className":23264,"style":2370},[2194],[2061,23266,23267,23270],{"style":2302},[2061,23268],{"className":23269,"style":2203},[2202],[2061,23271,23273],{"className":23272},[2207,2208,2209,2210],[2061,23274,2134],{"className":23275},[2169,2210],[2061,23277,2218],{"className":23278},[2217],[2061,23280,23282],{"className":23281},[2190],[2061,23283,23285],{"className":23284,"style":2225},[2194],[2061,23286],{},[2061,23288,2127],{"className":23289},[2396],[2061,23291],{"className":23292,"style":2400},[2231],[2061,23294,7160],{"className":23295},[2169,2170],[2061,23297,2137],{"className":23298},[2444],[2061,23300,2127],{"className":23301},[2396],[2061,23303],{"className":23304,"style":4870},[2231],[2061,23306],{"className":23307,"style":2400},[2231],[2061,23309,22976],{"className":23310},[2169],[2061,23312,8630],{"className":23313},[2169,2170],[2061,23315],{"className":23316,"style":2232},[2231],[2061,23318,4619],{"className":23319},[2236],[2061,23321],{"className":23322,"style":2232},[2231],[2061,23324,23326,23329],{"className":23325},[2160],[2061,23327],{"className":23328,"style":2692},[2164],[2061,23330,2513],{"className":23331},[2169],[1798,23333,23334,23337,23338,1989],{},[1865,23335,23336],{},"经济学含义",": 如果所有价格和收入同比例变化（如货币贬值一半），实际购买力不变，需求也不变。这被称为",[1865,23339,23340],{},"无货币幻觉",[1798,23342,23343,23344,22890],{},"间接效用函数对价格和收入是",[1865,23345,23346],{},"一次齐次",[2061,23348,23350],{"className":23349},[2064],[2061,23351,23353,23421],{"className":23352},[2068],[2061,23354,23356],{"className":23355},[2072],[2074,23357,23358],{"xmlns":2076,"display":2077},[2079,23359,23360,23418],{},[2082,23361,23362,23364,23366,23368,23374,23376,23378,23384,23386,23388,23390,23392,23394,23396,23398,23404,23406,23412,23414,23416],{},[2085,23363,6887],{},[2097,23365,2114],{"stretchy":2113},[2085,23367,8630],{},[2089,23369,23370,23372],{},[2085,23371,1798],{},[2121,23373,2123],{},[2097,23375,2127],{"separator":2126},[2085,23377,8630],{},[2089,23379,23380,23382],{},[2085,23381,1798],{},[2121,23383,2134],{},[2097,23385,2127],{"separator":2126},[2085,23387,8630],{},[2085,23389,7160],{},[2097,23391,2137],{"stretchy":2113},[2097,23393,2099],{},[2085,23395,6887],{},[2097,23397,2114],{"stretchy":2113},[2089,23399,23400,23402],{},[2085,23401,1798],{},[2121,23403,2123],{},[2097,23405,2127],{"separator":2126},[2089,23407,23408,23410],{},[2085,23409,1798],{},[2121,23411,2134],{},[2097,23413,2127],{"separator":2126},[2085,23415,7160],{},[2097,23417,2137],{"stretchy":2113},[2149,23419,23420],{"encoding":2151},"v(\\lambda p_1, \\lambda p_2, \\lambda m) = v(p_1, p_2, m)",[2061,23422,23424,23549],{"className":23423,"ariaHidden":2126},[2156],[2061,23425,23427,23430,23433,23436,23439,23479,23482,23485,23488,23528,23531,23534,23537,23540,23543,23546],{"className":23426},[2160],[2061,23428],{"className":23429,"style":4634},[2164],[2061,23431,6887],{"className":23432,"style":6572},[2169,2170],[2061,23434,2114],{"className":23435},[2253],[2061,23437,8630],{"className":23438},[2169,2170],[2061,23440,23442,23445],{"className":23441},[2169],[2061,23443,1798],{"className":23444},[2169,2170],[2061,23446,23448],{"className":23447},[2181],[2061,23449,23451,23471],{"className":23450},[2185,2186],[2061,23452,23454,23468],{"className":23453},[2190],[2061,23455,23457],{"className":23456,"style":2370},[2194],[2061,23458,23459,23462],{"style":2302},[2061,23460],{"className":23461,"style":2203},[2202],[2061,23463,23465],{"className":23464},[2207,2208,2209,2210],[2061,23466,2123],{"className":23467},[2169,2210],[2061,23469,2218],{"className":23470},[2217],[2061,23472,23474],{"className":23473},[2190],[2061,23475,23477],{"className":23476,"style":2225},[2194],[2061,23478],{},[2061,23480,2127],{"className":23481},[2396],[2061,23483],{"className":23484,"style":2400},[2231],[2061,23486,8630],{"className":23487},[2169,2170],[2061,23489,23491,23494],{"className":23490},[2169],[2061,23492,1798],{"className":23493},[2169,2170],[2061,23495,23497],{"className":23496},[2181],[2061,23498,23500,23520],{"className":23499},[2185,2186],[2061,23501,23503,23517],{"className":23502},[2190],[2061,23504,23506],{"className":23505,"style":2370},[2194],[2061,23507,23508,23511],{"style":2302},[2061,23509],{"className":23510,"style":2203},[2202],[2061,23512,23514],{"className":23513},[2207,2208,2209,2210],[2061,23515,2134],{"className":23516},[2169,2210],[2061,23518,2218],{"className":23519},[2217],[2061,23521,23523],{"className":23522},[2190],[2061,23524,23526],{"className":23525,"style":2225},[2194],[2061,23527],{},[2061,23529,2127],{"className":23530},[2396],[2061,23532],{"className":23533,"style":2400},[2231],[2061,23535,23139],{"className":23536},[2169,2170],[2061,23538,2137],{"className":23539},[2444],[2061,23541],{"className":23542,"style":2232},[2231],[2061,23544,2099],{"className":23545},[2236],[2061,23547],{"className":23548,"style":2232},[2231],[2061,23550,23552,23555,23558,23561,23601,23604,23607,23647,23650,23653,23656],{"className":23551},[2160],[2061,23553],{"className":23554,"style":4634},[2164],[2061,23556,6887],{"className":23557,"style":6572},[2169,2170],[2061,23559,2114],{"className":23560},[2253],[2061,23562,23564,23567],{"className":23563},[2169],[2061,23565,1798],{"className":23566},[2169,2170],[2061,23568,23570],{"className":23569},[2181],[2061,23571,23573,23593],{"className":23572},[2185,2186],[2061,23574,23576,23590],{"className":23575},[2190],[2061,23577,23579],{"className":23578,"style":2370},[2194],[2061,23580,23581,23584],{"style":2302},[2061,23582],{"className":23583,"style":2203},[2202],[2061,23585,23587],{"className":23586},[2207,2208,2209,2210],[2061,23588,2123],{"className":23589},[2169,2210],[2061,23591,2218],{"className":23592},[2217],[2061,23594,23596],{"className":23595},[2190],[2061,23597,23599],{"className":23598,"style":2225},[2194],[2061,23600],{},[2061,23602,2127],{"className":23603},[2396],[2061,23605],{"className":23606,"style":2400},[2231],[2061,23608,23610,23613],{"className":23609},[2169],[2061,23611,1798],{"className":23612},[2169,2170],[2061,23614,23616],{"className":23615},[2181],[2061,23617,23619,23639],{"className":23618},[2185,2186],[2061,23620,23622,23636],{"className":23621},[2190],[2061,23623,23625],{"className":23624,"style":2370},[2194],[2061,23626,23627,23630],{"style":2302},[2061,23628],{"className":23629,"style":2203},[2202],[2061,23631,23633],{"className":23632},[2207,2208,2209,2210],[2061,23634,2134],{"className":23635},[2169,2210],[2061,23637,2218],{"className":23638},[2217],[2061,23640,23642],{"className":23641},[2190],[2061,23643,23645],{"className":23644,"style":2225},[2194],[2061,23646],{},[2061,23648,2127],{"className":23649},[2396],[2061,23651],{"className":23652,"style":2400},[2231],[2061,23654,7160],{"className":23655},[2169,2170],[2061,23657,2137],{"className":23658},[2444],[1847,23660,23662],{"id":23661},"_52-瓦尔拉斯法则-walras-law","5.2 瓦尔拉斯法则 (Walras' Law)",[1798,23664,23665],{},"在最优解下，预算约束必然是紧约束（消费者花光所有收入）：",[2061,23667,23669],{"className":23668},[2064],[2061,23670,23672,23758],{"className":23671},[2068],[2061,23673,23675],{"className":23674},[2072],[2074,23676,23677],{"xmlns":2076,"display":2077},[2079,23678,23679,23755],{},[2082,23680,23681,23687,23693,23695,23701,23703,23709,23711,23713,23715,23717,23723,23729,23731,23737,23739,23745,23747,23749,23751,23753],{},[2089,23682,23683,23685],{},[2085,23684,1798],{},[2121,23686,2123],{},[2089,23688,23689,23691],{},[2085,23690,2119],{},[2121,23692,2123],{},[2097,23694,2114],{"stretchy":2113},[2089,23696,23697,23699],{},[2085,23698,1798],{},[2121,23700,2123],{},[2097,23702,2127],{"separator":2126},[2089,23704,23705,23707],{},[2085,23706,1798],{},[2121,23708,2134],{},[2097,23710,2127],{"separator":2126},[2085,23712,7160],{},[2097,23714,2137],{"stretchy":2113},[2097,23716,2762],{},[2089,23718,23719,23721],{},[2085,23720,1798],{},[2121,23722,2134],{},[2089,23724,23725,23727],{},[2085,23726,2119],{},[2121,23728,2134],{},[2097,23730,2114],{"stretchy":2113},[2089,23732,23733,23735],{},[2085,23734,1798],{},[2121,23736,2123],{},[2097,23738,2127],{"separator":2126},[2089,23740,23741,23743],{},[2085,23742,1798],{},[2121,23744,2134],{},[2097,23746,2127],{"separator":2126},[2085,23748,7160],{},[2097,23750,2137],{"stretchy":2113},[2097,23752,2099],{},[2085,23754,7160],{},[2149,23756,23757],{"encoding":2151},"p_1 x_1(p_1, p_2, m) + p_2 x_2(p_1, p_2, m) = m",[2061,23759,23761,23957,24153],{"className":23760,"ariaHidden":2126},[2156],[2061,23762,23764,23767,23807,23847,23850,23890,23893,23896,23936,23939,23942,23945,23948,23951,23954],{"className":23763},[2160],[2061,23765],{"className":23766,"style":4634},[2164],[2061,23768,23770,23773],{"className":23769},[2169],[2061,23771,1798],{"className":23772},[2169,2170],[2061,23774,23776],{"className":23775},[2181],[2061,23777,23779,23799],{"className":23778},[2185,2186],[2061,23780,23782,23796],{"className":23781},[2190],[2061,23783,23785],{"className":23784,"style":2370},[2194],[2061,23786,23787,23790],{"style":2302},[2061,23788],{"className":23789,"style":2203},[2202],[2061,23791,23793],{"className":23792},[2207,2208,2209,2210],[2061,23794,2123],{"className":23795},[2169,2210],[2061,23797,2218],{"className":23798},[2217],[2061,23800,23802],{"className":23801},[2190],[2061,23803,23805],{"className":23804,"style":2225},[2194],[2061,23806],{},[2061,23808,23810,23813],{"className":23809},[2169],[2061,23811,2119],{"className":23812},[2169,2170],[2061,23814,23816],{"className":23815},[2181],[2061,23817,23819,23839],{"className":23818},[2185,2186],[2061,23820,23822,23836],{"className":23821},[2190],[2061,23823,23825],{"className":23824,"style":2370},[2194],[2061,23826,23827,23830],{"style":2302},[2061,23828],{"className":23829,"style":2203},[2202],[2061,23831,23833],{"className":23832},[2207,2208,2209,2210],[2061,23834,2123],{"className":23835},[2169,2210],[2061,23837,2218],{"className":23838},[2217],[2061,23840,23842],{"className":23841},[2190],[2061,23843,23845],{"className":23844,"style":2225},[2194],[2061,23846],{},[2061,23848,2114],{"className":23849},[2253],[2061,23851,23853,23856],{"className":23852},[2169],[2061,23854,1798],{"className":23855},[2169,2170],[2061,23857,23859],{"className":23858},[2181],[2061,23860,23862,23882],{"className":23861},[2185,2186],[2061,23863,23865,23879],{"className":23864},[2190],[2061,23866,23868],{"className":23867,"style":2370},[2194],[2061,23869,23870,23873],{"style":2302},[2061,23871],{"className":23872,"style":2203},[2202],[2061,23874,23876],{"className":23875},[2207,2208,2209,2210],[2061,23877,2123],{"className":23878},[2169,2210],[2061,23880,2218],{"className":23881},[2217],[2061,23883,23885],{"className":23884},[2190],[2061,23886,23888],{"className":23887,"style":2225},[2194],[2061,23889],{},[2061,23891,2127],{"className":23892},[2396],[2061,23894],{"className":23895,"style":2400},[2231],[2061,23897,23899,23902],{"className":23898},[2169],[2061,23900,1798],{"className":23901},[2169,2170],[2061,23903,23905],{"className":23904},[2181],[2061,23906,23908,23928],{"className":23907},[2185,2186],[2061,23909,23911,23925],{"className":23910},[2190],[2061,23912,23914],{"className":23913,"style":2370},[2194],[2061,23915,23916,23919],{"style":2302},[2061,23917],{"className":23918,"style":2203},[2202],[2061,23920,23922],{"className":23921},[2207,2208,2209,2210],[2061,23923,2134],{"className":23924},[2169,2210],[2061,23926,2218],{"className":23927},[2217],[2061,23929,23931],{"className":23930},[2190],[2061,23932,23934],{"className":23933,"style":2225},[2194],[2061,23935],{},[2061,23937,2127],{"className":23938},[2396],[2061,23940],{"className":23941,"style":2400},[2231],[2061,23943,7160],{"className":23944},[2169,2170],[2061,23946,2137],{"className":23947},[2444],[2061,23949],{"className":23950,"style":2980},[2231],[2061,23952,2762],{"className":23953},[2984],[2061,23955],{"className":23956,"style":2980},[2231],[2061,23958,23960,23963,24003,24043,24046,24086,24089,24092,24132,24135,24138,24141,24144,24147,24150],{"className":23959},[2160],[2061,23961],{"className":23962,"style":4634},[2164],[2061,23964,23966,23969],{"className":23965},[2169],[2061,23967,1798],{"className":23968},[2169,2170],[2061,23970,23972],{"className":23971},[2181],[2061,23973,23975,23995],{"className":23974},[2185,2186],[2061,23976,23978,23992],{"className":23977},[2190],[2061,23979,23981],{"className":23980,"style":2370},[2194],[2061,23982,23983,23986],{"style":2302},[2061,23984],{"className":23985,"style":2203},[2202],[2061,23987,23989],{"className":23988},[2207,2208,2209,2210],[2061,23990,2134],{"className":23991},[2169,2210],[2061,23993,2218],{"className":23994},[2217],[2061,23996,23998],{"className":23997},[2190],[2061,23999,24001],{"className":24000,"style":2225},[2194],[2061,24002],{},[2061,24004,24006,24009],{"className":24005},[2169],[2061,24007,2119],{"className":24008},[2169,2170],[2061,24010,24012],{"className":24011},[2181],[2061,24013,24015,24035],{"className":24014},[2185,2186],[2061,24016,24018,24032],{"className":24017},[2190],[2061,24019,24021],{"className":24020,"style":2370},[2194],[2061,24022,24023,24026],{"style":2302},[2061,24024],{"className":24025,"style":2203},[2202],[2061,24027,24029],{"className":24028},[2207,2208,2209,2210],[2061,24030,2134],{"className":24031},[2169,2210],[2061,24033,2218],{"className":24034},[2217],[2061,24036,24038],{"className":24037},[2190],[2061,24039,24041],{"className":24040,"style":2225},[2194],[2061,24042],{},[2061,24044,2114],{"className":24045},[2253],[2061,24047,24049,24052],{"className":24048},[2169],[2061,24050,1798],{"className":24051},[2169,2170],[2061,24053,24055],{"className":24054},[2181],[2061,24056,24058,24078],{"className":24057},[2185,2186],[2061,24059,24061,24075],{"className":24060},[2190],[2061,24062,24064],{"className":24063,"style":2370},[2194],[2061,24065,24066,24069],{"style":2302},[2061,24067],{"className":24068,"style":2203},[2202],[2061,24070,24072],{"className":24071},[2207,2208,2209,2210],[2061,24073,2123],{"className":24074},[2169,2210],[2061,24076,2218],{"className":24077},[2217],[2061,24079,24081],{"className":24080},[2190],[2061,24082,24084],{"className":24083,"style":2225},[2194],[2061,24085],{},[2061,24087,2127],{"className":24088},[2396],[2061,24090],{"className":24091,"style":2400},[2231],[2061,24093,24095,24098],{"className":24094},[2169],[2061,24096,1798],{"className":24097},[2169,2170],[2061,24099,24101],{"className":24100},[2181],[2061,24102,24104,24124],{"className":24103},[2185,2186],[2061,24105,24107,24121],{"className":24106},[2190],[2061,24108,24110],{"className":24109,"style":2370},[2194],[2061,24111,24112,24115],{"style":2302},[2061,24113],{"className":24114,"style":2203},[2202],[2061,24116,24118],{"className":24117},[2207,2208,2209,2210],[2061,24119,2134],{"className":24120},[2169,2210],[2061,24122,2218],{"className":24123},[2217],[2061,24125,24127],{"className":24126},[2190],[2061,24128,24130],{"className":24129,"style":2225},[2194],[2061,24131],{},[2061,24133,2127],{"className":24134},[2396],[2061,24136],{"className":24137,"style":2400},[2231],[2061,24139,7160],{"className":24140},[2169,2170],[2061,24142,2137],{"className":24143},[2444],[2061,24145],{"className":24146,"style":2232},[2231],[2061,24148,2099],{"className":24149},[2236],[2061,24151],{"className":24152,"style":2232},[2231],[2061,24154,24156,24159],{"className":24155},[2160],[2061,24157],{"className":24158,"style":6568},[2164],[2061,24160,7160],{"className":24161},[2169,2170],[1798,24163,24164],{},"这在任何价格和收入水平下都成立。",[1847,24166,24168],{"id":24167},"_53-恩格尔聚集-engel-aggregation","5.3 恩格尔聚集 (Engel Aggregation)",[1798,24170,24171],{},"对需求函数关于收入求偏导：",[2061,24173,24175],{"className":24174},[2064],[2061,24176,24178,24235],{"className":24177},[2068],[2061,24179,24181],{"className":24180},[2072],[2074,24182,24183],{"xmlns":2076,"display":2077},[2079,24184,24185,24232],{},[2082,24186,24187,24204,24210,24228,24230],{},[24188,24189,24190,24193,24201],"munderover",{},[2097,24191,24192],{},"∑",[2082,24194,24195,24197,24199],{},[2085,24196,2095],{},[2097,24198,2099],{},[2121,24200,2123],{},[2085,24202,24203],{},"n",[2089,24205,24206,24208],{},[2085,24207,1798],{},[2085,24209,2095],{},[2101,24211,24212,24222],{},[2082,24213,24214,24216],{},[2085,24215,2108],{"mathvariant":2107},[2089,24217,24218,24220],{},[2085,24219,2119],{},[2085,24221,2095],{},[2082,24223,24224,24226],{},[2085,24225,2108],{"mathvariant":2107},[2085,24227,7160],{},[2097,24229,2099],{},[2121,24231,2123],{},[2149,24233,24234],{"encoding":2151},"\\sum_{i=1}^{n} p_i \\frac{\\partial x_i}{\\partial m} = 1",[2061,24236,24238,24477],{"className":24237,"ariaHidden":2126},[2156],[2061,24239,24241,24245,24320,24323,24363,24468,24471,24474],{"className":24240},[2160],[2061,24242],{"className":24243,"style":24244},[2164],"height:2.9291em;vertical-align:-1.2777em;",[2061,24246,24248],{"className":24247},[5104,7552],[2061,24249,24251,24311],{"className":24250},[2185,2186],[2061,24252,24254,24308],{"className":24253},[2190],[2061,24255,24258,24280,24293],{"className":24256,"style":24257},[2194],"height:1.6514em;",[2061,24259,24261,24265],{"style":24260},"top:-1.8723em;margin-left:0em;",[2061,24262],{"className":24263,"style":24264},[2202],"height:3.05em;",[2061,24266,24268],{"className":24267},[2207,2208,2209,2210],[2061,24269,24271,24274,24277],{"className":24270},[2169,2210],[2061,24272,2095],{"className":24273},[2169,2170,2210],[2061,24275,2099],{"className":24276},[2236,2210],[2061,24278,2123],{"className":24279},[2169,2210],[2061,24281,24283,24286],{"style":24282},"top:-3.05em;",[2061,24284],{"className":24285,"style":24264},[2202],[2061,24287,24288],{},[2061,24289,24192],{"className":24290},[5104,24291,24292],"op-symbol","large-op",[2061,24294,24296,24299],{"style":24295},"top:-4.3em;margin-left:0em;",[2061,24297],{"className":24298,"style":24264},[2202],[2061,24300,24302],{"className":24301},[2207,2208,2209,2210],[2061,24303,24305],{"className":24304},[2169,2210],[2061,24306,24203],{"className":24307},[2169,2170,2210],[2061,24309,2218],{"className":24310},[2217],[2061,24312,24314],{"className":24313},[2190],[2061,24315,24318],{"className":24316,"style":24317},[2194],"height:1.2777em;",[2061,24319],{},[2061,24321],{"className":24322,"style":2400},[2231],[2061,24324,24326,24329],{"className":24325},[2169],[2061,24327,1798],{"className":24328},[2169,2170],[2061,24330,24332],{"className":24331},[2181],[2061,24333,24335,24355],{"className":24334},[2185,2186],[2061,24336,24338,24352],{"className":24337},[2190],[2061,24339,24341],{"className":24340,"style":2195},[2194],[2061,24342,24343,24346],{"style":2302},[2061,24344],{"className":24345,"style":2203},[2202],[2061,24347,24349],{"className":24348},[2207,2208,2209,2210],[2061,24350,2095],{"className":24351},[2169,2170,2210],[2061,24353,2218],{"className":24354},[2217],[2061,24356,24358],{"className":24357},[2190],[2061,24359,24361],{"className":24360,"style":2225},[2194],[2061,24362],{},[2061,24364,24366,24369,24465],{"className":24365},[2169],[2061,24367],{"className":24368},[2253,2254],[2061,24370,24372],{"className":24371},[2101],[2061,24373,24375,24457],{"className":24374},[2185,2186],[2061,24376,24378,24454],{"className":24377},[2190],[2061,24379,24381,24395,24403],{"className":24380,"style":2846},[2194],[2061,24382,24383,24386],{"style":2270},[2061,24384],{"className":24385,"style":2274},[2202],[2061,24387,24389,24392],{"className":24388},[2169],[2061,24390,2108],{"className":24391,"style":2281},[2169],[2061,24393,7160],{"className":24394},[2169,2170],[2061,24396,24397,24400],{"style":2325},[2061,24398],{"className":24399,"style":2274},[2202],[2061,24401],{"className":24402,"style":2333},[2332],[2061,24404,24405,24408],{"style":2336},[2061,24406],{"className":24407,"style":2274},[2202],[2061,24409,24411,24414],{"className":24410},[2169],[2061,24412,2108],{"className":24413,"style":2281},[2169],[2061,24415,24417,24420],{"className":24416},[2169],[2061,24418,2119],{"className":24419},[2169,2170],[2061,24421,24423],{"className":24422},[2181],[2061,24424,24426,24446],{"className":24425},[2185,2186],[2061,24427,24429,24443],{"className":24428},[2190],[2061,24430,24432],{"className":24431,"style":2195},[2194],[2061,24433,24434,24437],{"style":2302},[2061,24435],{"className":24436,"style":2203},[2202],[2061,24438,24440],{"className":24439},[2207,2208,2209,2210],[2061,24441,2095],{"className":24442},[2169,2170,2210],[2061,24444,2218],{"className":24445},[2217],[2061,24447,24449],{"className":24448},[2190],[2061,24450,24452],{"className":24451,"style":2225},[2194],[2061,24453],{},[2061,24455,2218],{"className":24456},[2217],[2061,24458,24460],{"className":24459},[2190],[2061,24461,24463],{"className":24462,"style":9692},[2194],[2061,24464],{},[2061,24466],{"className":24467},[2444,2254],[2061,24469],{"className":24470,"style":2232},[2231],[2061,24472,2099],{"className":24473},[2236],[2061,24475],{"className":24476,"style":2232},[2231],[2061,24478,24480,24483],{"className":24479},[2160],[2061,24481],{"className":24482,"style":2692},[2164],[2061,24484,2123],{"className":24485},[2169],[1798,24487,24488,24491],{},[1865,24489,24490],{},"解释",": 额外一单位收入的增加，必然全部被分配到各种商品的消费上。",[1847,24493,24495],{"id":24494},"_54-库尔诺聚集-cournot-aggregation","5.4 库尔诺聚集 (Cournot Aggregation)",[2061,24497,24499],{"className":24498},[2064],[2061,24500,24502,24569],{"className":24501},[2068],[2061,24503,24505],{"className":24504},[2072],[2074,24506,24507],{"xmlns":2076,"display":2077},[2079,24508,24509,24566],{},[2082,24510,24511,24526,24532,24554,24556,24562,24564],{},[24188,24512,24513,24515,24524],{},[2097,24514,24192],{},[2082,24516,24517,24520,24522],{},[2085,24518,24519],{},"j",[2097,24521,2099],{},[2121,24523,2123],{},[2085,24525,24203],{},[2089,24527,24528,24530],{},[2085,24529,1798],{},[2085,24531,24519],{},[2101,24533,24534,24544],{},[2082,24535,24536,24538],{},[2085,24537,2108],{"mathvariant":2107},[2089,24539,24540,24542],{},[2085,24541,2119],{},[2085,24543,2095],{},[2082,24545,24546,24548],{},[2085,24547,2108],{"mathvariant":2107},[2089,24549,24550,24552],{},[2085,24551,1798],{},[2085,24553,24519],{},[2097,24555,2762],{},[2089,24557,24558,24560],{},[2085,24559,2119],{},[2085,24561,2095],{},[2097,24563,2099],{},[2121,24565,2513],{},[2149,24567,24568],{"encoding":2151},"\\sum_{j=1}^{n} p_j \\frac{\\partial x_i}{\\partial p_j} + x_i = 0",[2061,24570,24572,24844,24899],{"className":24571,"ariaHidden":2126},[2156],[2061,24573,24575,24579,24648,24651,24692,24835,24838,24841],{"className":24574},[2160],[2061,24576],{"className":24577,"style":24578},[2164],"height:3.0652em;vertical-align:-1.4138em;",[2061,24580,24582],{"className":24581},[5104,7552],[2061,24583,24585,24639],{"className":24584},[2185,2186],[2061,24586,24588,24636],{"className":24587},[2190],[2061,24589,24591,24612,24622],{"className":24590,"style":24257},[2194],[2061,24592,24593,24596],{"style":24260},[2061,24594],{"className":24595,"style":24264},[2202],[2061,24597,24599],{"className":24598},[2207,2208,2209,2210],[2061,24600,24602,24606,24609],{"className":24601},[2169,2210],[2061,24603,24519],{"className":24604,"style":24605},[2169,2170,2210],"margin-right:0.0572em;",[2061,24607,2099],{"className":24608},[2236,2210],[2061,24610,2123],{"className":24611},[2169,2210],[2061,24613,24614,24617],{"style":24282},[2061,24615],{"className":24616,"style":24264},[2202],[2061,24618,24619],{},[2061,24620,24192],{"className":24621},[5104,24291,24292],[2061,24623,24624,24627],{"style":24295},[2061,24625],{"className":24626,"style":24264},[2202],[2061,24628,24630],{"className":24629},[2207,2208,2209,2210],[2061,24631,24633],{"className":24632},[2169,2210],[2061,24634,24203],{"className":24635},[2169,2170,2210],[2061,24637,2218],{"className":24638},[2217],[2061,24640,24642],{"className":24641},[2190],[2061,24643,24646],{"className":24644,"style":24645},[2194],"height:1.4138em;",[2061,24647],{},[2061,24649],{"className":24650,"style":2400},[2231],[2061,24652,24654,24657],{"className":24653},[2169],[2061,24655,1798],{"className":24656},[2169,2170],[2061,24658,24660],{"className":24659},[2181],[2061,24661,24663,24683],{"className":24662},[2185,2186],[2061,24664,24666,24680],{"className":24665},[2190],[2061,24667,24669],{"className":24668,"style":2195},[2194],[2061,24670,24671,24674],{"style":2302},[2061,24672],{"className":24673,"style":2203},[2202],[2061,24675,24677],{"className":24676},[2207,2208,2209,2210],[2061,24678,24519],{"className":24679,"style":24605},[2169,2170,2210],[2061,24681,2218],{"className":24682},[2217],[2061,24684,24686],{"className":24685},[2190],[2061,24687,24690],{"className":24688,"style":24689},[2194],"height:0.2861em;",[2061,24691],{},[2061,24693,24695,24698,24832],{"className":24694},[2169],[2061,24696],{"className":24697},[2253,2254],[2061,24699,24701],{"className":24700},[2101],[2061,24702,24704,24823],{"className":24703},[2185,2186],[2061,24705,24707,24820],{"className":24706},[2190],[2061,24708,24710,24761,24769],{"className":24709,"style":2846},[2194],[2061,24711,24712,24715],{"style":2270},[2061,24713],{"className":24714,"style":2274},[2202],[2061,24716,24718,24721],{"className":24717},[2169],[2061,24719,2108],{"className":24720,"style":2281},[2169],[2061,24722,24724,24727],{"className":24723},[2169],[2061,24725,1798],{"className":24726},[2169,2170],[2061,24728,24730],{"className":24729},[2181],[2061,24731,24733,24753],{"className":24732},[2185,2186],[2061,24734,24736,24750],{"className":24735},[2190],[2061,24737,24739],{"className":24738,"style":2195},[2194],[2061,24740,24741,24744],{"style":2302},[2061,24742],{"className":24743,"style":2203},[2202],[2061,24745,24747],{"className":24746},[2207,2208,2209,2210],[2061,24748,24519],{"className":24749,"style":24605},[2169,2170,2210],[2061,24751,2218],{"className":24752},[2217],[2061,24754,24756],{"className":24755},[2190],[2061,24757,24759],{"className":24758,"style":24689},[2194],[2061,24760],{},[2061,24762,24763,24766],{"style":2325},[2061,24764],{"className":24765,"style":2274},[2202],[2061,24767],{"className":24768,"style":2333},[2332],[2061,24770,24771,24774],{"style":2336},[2061,24772],{"className":24773,"style":2274},[2202],[2061,24775,24777,24780],{"className":24776},[2169],[2061,24778,2108],{"className":24779,"style":2281},[2169],[2061,24781,24783,24786],{"className":24782},[2169],[2061,24784,2119],{"className":24785},[2169,2170],[2061,24787,24789],{"className":24788},[2181],[2061,24790,24792,24812],{"className":24791},[2185,2186],[2061,24793,24795,24809],{"className":24794},[2190],[2061,24796,24798],{"className":24797,"style":2195},[2194],[2061,24799,24800,24803],{"style":2302},[2061,24801],{"className":24802,"style":2203},[2202],[2061,24804,24806],{"className":24805},[2207,2208,2209,2210],[2061,24807,2095],{"className":24808},[2169,2170,2210],[2061,24810,2218],{"className":24811},[2217],[2061,24813,24815],{"className":24814},[2190],[2061,24816,24818],{"className":24817,"style":2225},[2194],[2061,24819],{},[2061,24821,2218],{"className":24822},[2217],[2061,24824,24826],{"className":24825},[2190],[2061,24827,24830],{"className":24828,"style":24829},[2194],"height:0.9721em;",[2061,24831],{},[2061,24833],{"className":24834},[2444,2254],[2061,24836],{"className":24837,"style":2980},[2231],[2061,24839,2762],{"className":24840},[2984],[2061,24842],{"className":24843,"style":2980},[2231],[2061,24845,24847,24850,24890,24893,24896],{"className":24846},[2160],[2061,24848],{"className":24849,"style":7092},[2164],[2061,24851,24853,24856],{"className":24852},[2169],[2061,24854,2119],{"className":24855},[2169,2170],[2061,24857,24859],{"className":24858},[2181],[2061,24860,24862,24882],{"className":24861},[2185,2186],[2061,24863,24865,24879],{"className":24864},[2190],[2061,24866,24868],{"className":24867,"style":2195},[2194],[2061,24869,24870,24873],{"style":2302},[2061,24871],{"className":24872,"style":2203},[2202],[2061,24874,24876],{"className":24875},[2207,2208,2209,2210],[2061,24877,2095],{"className":24878},[2169,2170,2210],[2061,24880,2218],{"className":24881},[2217],[2061,24883,24885],{"className":24884},[2190],[2061,24886,24888],{"className":24887,"style":2225},[2194],[2061,24889],{},[2061,24891],{"className":24892,"style":2232},[2231],[2061,24894,2099],{"className":24895},[2236],[2061,24897],{"className":24898,"style":2232},[2231],[2061,24900,24902,24905],{"className":24901},[2160],[2061,24903],{"className":24904,"style":2692},[2164],[2061,24906,2513],{"className":24907},[2169],[1840,24909],{},[1794,24911,24913],{"id":24912},"_6-对偶理论的深入理解","6. 对偶理论的深入理解",[1847,24915,24917],{"id":24916},"_61-为什么要研究对偶问题","6.1 为什么要研究对偶问题？",[1860,24919,24920,24926,24932,24938],{},[1808,24921,24922,24925],{},[1865,24923,24924],{},"理论优雅性",": UMP和EMP提供了同一经济现象的两种对称视角",[1808,24927,24928,24931],{},[1865,24929,24930],{},"计算便利性",": 有时EMP比UMP更容易求解",[1808,24933,24934,24937],{},[1865,24935,24936],{},"福利分析",": 支出函数是精确衡量福利变化的基础（CV、EV）",[1808,24939,24940,24943],{},[1865,24941,24942],{},"比较静态分析",": 希克斯需求隔离了纯粹的替代效应",[1847,24945,24947],{"id":24946},"_62-对偶性的数学表达","6.2 对偶性的数学表达",[1798,24949,24950,24953],{},[1865,24951,24952],{},"命题",": 以下两个优化问题互为对偶：",[1798,24955,24956,4550],{},[1865,24957,24958],{},"原问题 (UMP)",[2061,24960,24962],{"className":24961},[2064],[2061,24963,24965,25025],{"className":24964},[2068],[2061,24966,24968],{"className":24967},[2072],[2074,24969,24970],{"xmlns":2076,"display":2077},[2079,24971,24972,25022],{},[2082,24973,24974,24976,24978,24980,24982,24984,24986,24988,24998,25000,25002,25004,25006,25008,25010,25012,25014,25016,25018,25020],{},[2085,24975,6887],{},[2097,24977,2114],{"stretchy":2113},[2085,24979,1798],{},[2097,24981,2127],{"separator":2126},[2085,24983,7160],{},[2097,24985,2137],{"stretchy":2113},[2097,24987,2099],{},[7453,24989,24990,24996],{},[2082,24991,24992,24994],{},[2085,24993,7459],{},[2097,24995,4951],{},[2085,24997,2119],{},[2097,24999,5782],{"stretchy":2113},[2085,25001,2005],{},[2097,25003,2114],{"stretchy":2113},[2085,25005,2119],{},[2097,25007,2137],{"stretchy":2113},[2097,25009,4550],{},[2085,25011,1798],{},[2097,25013,16566],{},[2085,25015,2119],{},[2097,25017,6122],{},[2085,25019,7160],{},[2097,25021,5803],{"stretchy":2113},[2149,25023,25024],{"encoding":2151},"v(p, m) = \\max_{x} \\{U(x) : p \\cdot x \\le m\\}",[2061,25026,25028,25064,25143,25162,25181],{"className":25027,"ariaHidden":2126},[2156],[2061,25029,25031,25034,25037,25040,25043,25046,25049,25052,25055,25058,25061],{"className":25030},[2160],[2061,25032],{"className":25033,"style":4634},[2164],[2061,25035,6887],{"className":25036,"style":6572},[2169,2170],[2061,25038,2114],{"className":25039},[2253],[2061,25041,1798],{"className":25042},[2169,2170],[2061,25044,2127],{"className":25045},[2396],[2061,25047],{"className":25048,"style":2400},[2231],[2061,25050,7160],{"className":25051},[2169,2170],[2061,25053,2137],{"className":25054},[2444],[2061,25056],{"className":25057,"style":2232},[2231],[2061,25059,2099],{"className":25060},[2236],[2061,25062],{"className":25063,"style":2232},[2231],[2061,25065,25067,25071,25119,25122,25125,25128,25131,25134,25137,25140],{"className":25066},[2160],[2061,25068],{"className":25069,"style":25070},[2164],"height:1.45em;vertical-align:-0.7em;",[2061,25072,25074],{"className":25073},[5104,7552],[2061,25075,25077,25110],{"className":25076},[2185,2186],[2061,25078,25080,25107],{"className":25079},[2190],[2061,25081,25083,25097],{"className":25082,"style":6568},[2194],[2061,25084,25085,25088],{"style":7564},[2061,25086],{"className":25087,"style":2274},[2202],[2061,25089,25091],{"className":25090},[2207,2208,2209,2210],[2061,25092,25094],{"className":25093},[2169,2210],[2061,25095,2119],{"className":25096},[2169,2170,2210],[2061,25098,25099,25102],{"style":7659},[2061,25100],{"className":25101,"style":2274},[2202],[2061,25103,25104],{},[2061,25105,7459],{"className":25106},[5104],[2061,25108,2218],{"className":25109},[2217],[2061,25111,25113],{"className":25112},[2190],[2061,25114,25117],{"className":25115,"style":25116},[2194],"height:0.7em;",[2061,25118],{},[2061,25120,5782],{"className":25121},[2253],[2061,25123,2005],{"className":25124,"style":2171},[2169,2170],[2061,25126,2114],{"className":25127},[2253],[2061,25129,2119],{"className":25130},[2169,2170],[2061,25132,2137],{"className":25133},[2444],[2061,25135],{"className":25136,"style":2232},[2231],[2061,25138,4550],{"className":25139},[2236],[2061,25141],{"className":25142,"style":2232},[2231],[2061,25144,25146,25150,25153,25156,25159],{"className":25145},[2160],[2061,25147],{"className":25148,"style":25149},[2164],"height:0.6389em;vertical-align:-0.1944em;",[2061,25151,1798],{"className":25152},[2169,2170],[2061,25154],{"className":25155,"style":2980},[2231],[2061,25157,16566],{"className":25158},[2984],[2061,25160],{"className":25161,"style":2980},[2231],[2061,25163,25165,25169,25172,25175,25178],{"className":25164},[2160],[2061,25166],{"className":25167,"style":25168},[2164],"height:0.7719em;vertical-align:-0.136em;",[2061,25170,2119],{"className":25171},[2169,2170],[2061,25173],{"className":25174,"style":2232},[2231],[2061,25176,6122],{"className":25177},[2236],[2061,25179],{"className":25180,"style":2232},[2231],[2061,25182,25184,25187,25190],{"className":25183},[2160],[2061,25185],{"className":25186,"style":4634},[2164],[2061,25188,7160],{"className":25189},[2169,2170],[2061,25191,5803],{"className":25192},[2444],[1798,25194,25195,4550],{},[1865,25196,25197],{},"对偶问题 (EMP)",[2061,25199,25201],{"className":25200},[2064],[2061,25202,25204,25264],{"className":25203},[2068],[2061,25205,25207],{"className":25206},[2072],[2074,25208,25209],{"xmlns":2076,"display":2077},[2079,25210,25211,25261],{},[2082,25212,25213,25215,25217,25219,25221,25223,25225,25227,25237,25239,25241,25243,25245,25247,25249,25251,25253,25255,25257,25259],{},[2085,25214,12585],{},[2097,25216,2114],{"stretchy":2113},[2085,25218,1798],{},[2097,25220,2127],{"separator":2126},[2085,25222,11462],{},[2097,25224,2137],{"stretchy":2113},[2097,25226,2099],{},[7453,25228,25229,25235],{},[2082,25230,25231,25233],{},[2085,25232,5777],{},[2097,25234,4951],{},[2085,25236,2119],{},[2097,25238,5782],{"stretchy":2113},[2085,25240,1798],{},[2097,25242,16566],{},[2085,25244,2119],{},[2097,25246,4550],{},[2085,25248,2005],{},[2097,25250,2114],{"stretchy":2113},[2085,25252,2119],{},[2097,25254,2137],{"stretchy":2113},[2097,25256,11557],{},[2085,25258,11462],{},[2097,25260,5803],{"stretchy":2113},[2149,25262,25263],{"encoding":2151},"e(p, u) = \\min_{x} \\{p \\cdot x : U(x) \\ge u\\}",[2061,25265,25267,25303,25371,25389,25416],{"className":25266,"ariaHidden":2126},[2156],[2061,25268,25270,25273,25276,25279,25282,25285,25288,25291,25294,25297,25300],{"className":25269},[2160],[2061,25271],{"className":25272,"style":4634},[2164],[2061,25274,12585],{"className":25275},[2169,2170],[2061,25277,2114],{"className":25278},[2253],[2061,25280,1798],{"className":25281},[2169,2170],[2061,25283,2127],{"className":25284},[2396],[2061,25286],{"className":25287,"style":2400},[2231],[2061,25289,11462],{"className":25290},[2169,2170],[2061,25292,2137],{"className":25293},[2444],[2061,25295],{"className":25296,"style":2232},[2231],[2061,25298,2099],{"className":25299},[2236],[2061,25301],{"className":25302,"style":2232},[2231],[2061,25304,25306,25309,25356,25359,25362,25365,25368],{"className":25305},[2160],[2061,25307],{"className":25308,"style":25070},[2164],[2061,25310,25312],{"className":25311},[5104,7552],[2061,25313,25315,25348],{"className":25314},[2185,2186],[2061,25316,25318,25345],{"className":25317},[2190],[2061,25319,25321,25335],{"className":25320,"style":11585},[2194],[2061,25322,25323,25326],{"style":7564},[2061,25324],{"className":25325,"style":2274},[2202],[2061,25327,25329],{"className":25328},[2207,2208,2209,2210],[2061,25330,25332],{"className":25331},[2169,2210],[2061,25333,2119],{"className":25334},[2169,2170,2210],[2061,25336,25337,25340],{"style":7659},[2061,25338],{"className":25339,"style":2274},[2202],[2061,25341,25342],{},[2061,25343,5777],{"className":25344},[5104],[2061,25346,2218],{"className":25347},[2217],[2061,25349,25351],{"className":25350},[2190],[2061,25352,25354],{"className":25353,"style":25116},[2194],[2061,25355],{},[2061,25357,5782],{"className":25358},[2253],[2061,25360,1798],{"className":25361},[2169,2170],[2061,25363],{"className":25364,"style":2980},[2231],[2061,25366,16566],{"className":25367},[2984],[2061,25369],{"className":25370,"style":2980},[2231],[2061,25372,25374,25377,25380,25383,25386],{"className":25373},[2160],[2061,25375],{"className":25376,"style":6568},[2164],[2061,25378,2119],{"className":25379},[2169,2170],[2061,25381],{"className":25382,"style":2232},[2231],[2061,25384,4550],{"className":25385},[2236],[2061,25387],{"className":25388,"style":2232},[2231],[2061,25390,25392,25395,25398,25401,25404,25407,25410,25413],{"className":25391},[2160],[2061,25393],{"className":25394,"style":4634},[2164],[2061,25396,2005],{"className":25397,"style":2171},[2169,2170],[2061,25399,2114],{"className":25400},[2253],[2061,25402,2119],{"className":25403},[2169,2170],[2061,25405,2137],{"className":25406},[2444],[2061,25408],{"className":25409,"style":2232},[2231],[2061,25411,11557],{"className":25412},[2236],[2061,25414],{"className":25415,"style":2232},[2231],[2061,25417,25419,25422,25425],{"className":25418},[2160],[2061,25420],{"className":25421,"style":4634},[2164],[2061,25423,11462],{"className":25424},[2169,2170],[2061,25426,5803],{"className":25427},[2444],[1798,25429,25430,4550],{},[1865,25431,25432],{},"对偶关系",[1860,25434,25435,25541,25647,25813],{},[1808,25436,25437],{},[2061,25438,25440,25478],{"className":25439},[2068],[2061,25441,25443],{"className":25442},[2072],[2074,25444,25445],{"xmlns":2076},[2079,25446,25447,25475],{},[2082,25448,25449,25451,25453,25455,25457,25459,25461,25463,25465,25467,25469,25471,25473],{},[2085,25450,12585],{},[2097,25452,2114],{"stretchy":2113},[2085,25454,1798],{},[2097,25456,2127],{"separator":2126},[2085,25458,6887],{},[2097,25460,2114],{"stretchy":2113},[2085,25462,1798],{},[2097,25464,2127],{"separator":2126},[2085,25466,7160],{},[2097,25468,2137],{"stretchy":2113},[2097,25470,2137],{"stretchy":2113},[2097,25472,2099],{},[2085,25474,7160],{},[2149,25476,25477],{"encoding":2151},"e(p, v(p, m)) = m",[2061,25479,25481,25532],{"className":25480,"ariaHidden":2126},[2156],[2061,25482,25484,25487,25490,25493,25496,25499,25502,25505,25508,25511,25514,25517,25520,25523,25526,25529],{"className":25483},[2160],[2061,25485],{"className":25486,"style":4634},[2164],[2061,25488,12585],{"className":25489},[2169,2170],[2061,25491,2114],{"className":25492},[2253],[2061,25494,1798],{"className":25495},[2169,2170],[2061,25497,2127],{"className":25498},[2396],[2061,25500],{"className":25501,"style":2400},[2231],[2061,25503,6887],{"className":25504,"style":6572},[2169,2170],[2061,25506,2114],{"className":25507},[2253],[2061,25509,1798],{"className":25510},[2169,2170],[2061,25512,2127],{"className":25513},[2396],[2061,25515],{"className":25516,"style":2400},[2231],[2061,25518,7160],{"className":25519},[2169,2170],[2061,25521,11446],{"className":25522},[2444],[2061,25524],{"className":25525,"style":2232},[2231],[2061,25527,2099],{"className":25528},[2236],[2061,25530],{"className":25531,"style":2232},[2231],[2061,25533,25535,25538],{"className":25534},[2160],[2061,25536],{"className":25537,"style":6568},[2164],[2061,25539,7160],{"className":25540},[2169,2170],[1808,25542,25543],{},[2061,25544,25546,25584],{"className":25545},[2068],[2061,25547,25549],{"className":25548},[2072],[2074,25550,25551],{"xmlns":2076},[2079,25552,25553,25581],{},[2082,25554,25555,25557,25559,25561,25563,25565,25567,25569,25571,25573,25575,25577,25579],{},[2085,25556,6887],{},[2097,25558,2114],{"stretchy":2113},[2085,25560,1798],{},[2097,25562,2127],{"separator":2126},[2085,25564,12585],{},[2097,25566,2114],{"stretchy":2113},[2085,25568,1798],{},[2097,25570,2127],{"separator":2126},[2085,25572,11462],{},[2097,25574,2137],{"stretchy":2113},[2097,25576,2137],{"stretchy":2113},[2097,25578,2099],{},[2085,25580,11462],{},[2149,25582,25583],{"encoding":2151},"v(p, e(p, u)) = u",[2061,25585,25587,25638],{"className":25586,"ariaHidden":2126},[2156],[2061,25588,25590,25593,25596,25599,25602,25605,25608,25611,25614,25617,25620,25623,25626,25629,25632,25635],{"className":25589},[2160],[2061,25591],{"className":25592,"style":4634},[2164],[2061,25594,6887],{"className":25595,"style":6572},[2169,2170],[2061,25597,2114],{"className":25598},[2253],[2061,25600,1798],{"className":25601},[2169,2170],[2061,25603,2127],{"className":25604},[2396],[2061,25606],{"className":25607,"style":2400},[2231],[2061,25609,12585],{"className":25610},[2169,2170],[2061,25612,2114],{"className":25613},[2253],[2061,25615,1798],{"className":25616},[2169,2170],[2061,25618,2127],{"className":25619},[2396],[2061,25621],{"className":25622,"style":2400},[2231],[2061,25624,11462],{"className":25625},[2169,2170],[2061,25627,11446],{"className":25628},[2444],[2061,25630],{"className":25631,"style":2232},[2231],[2061,25633,2099],{"className":25634},[2236],[2061,25636],{"className":25637,"style":2232},[2231],[2061,25639,25641,25644],{"className":25640},[2160],[2061,25642],{"className":25643,"style":6568},[2164],[2061,25645,11462],{"className":25646},[2169,2170],[1808,25648,25649,25812],{},[2061,25650,25652,25704],{"className":25651},[2068],[2061,25653,25655],{"className":25654},[2072],[2074,25656,25657],{"xmlns":2076},[2079,25658,25659,25701],{},[2082,25660,25661,25667,25669,25671,25673,25675,25677,25679,25681,25683,25685,25687,25689,25691,25693,25695,25697,25699],{},[2487,25662,25663,25665],{},[2085,25664,2119],{},[2097,25666,10359],{},[2097,25668,2114],{"stretchy":2113},[2085,25670,1798],{},[2097,25672,2127],{"separator":2126},[2085,25674,7160],{},[2097,25676,2137],{"stretchy":2113},[2097,25678,2099],{},[2085,25680,12029],{},[2097,25682,2114],{"stretchy":2113},[2085,25684,1798],{},[2097,25686,2127],{"separator":2126},[2085,25688,6887],{},[2097,25690,2114],{"stretchy":2113},[2085,25692,1798],{},[2097,25694,2127],{"separator":2126},[2085,25696,7160],{},[2097,25698,2137],{"stretchy":2113},[2097,25700,2137],{"stretchy":2113},[2149,25702,25703],{"encoding":2151},"x^*(p, m) = h(p, v(p, m))",[2061,25705,25707,25770],{"className":25706,"ariaHidden":2126},[2156],[2061,25708,25710,25713,25743,25746,25749,25752,25755,25758,25761,25764,25767],{"className":25709},[2160],[2061,25711],{"className":25712,"style":4634},[2164],[2061,25714,25716,25719],{"className":25715},[2169],[2061,25717,2119],{"className":25718},[2169,2170],[2061,25720,25722],{"className":25721},[2181],[2061,25723,25725],{"className":25724},[2185],[2061,25726,25728],{"className":25727},[2190],[2061,25729,25732],{"className":25730,"style":25731},[2194],"height:0.6887em;",[2061,25733,25734,25737],{"style":2649},[2061,25735],{"className":25736,"style":2203},[2202],[2061,25738,25740],{"className":25739},[2207,2208,2209,2210],[2061,25741,10359],{"className":25742},[2984,2210],[2061,25744,2114],{"className":25745},[2253],[2061,25747,1798],{"className":25748},[2169,2170],[2061,25750,2127],{"className":25751},[2396],[2061,25753],{"className":25754,"style":2400},[2231],[2061,25756,7160],{"className":25757},[2169,2170],[2061,25759,2137],{"className":25760},[2444],[2061,25762],{"className":25763,"style":2232},[2231],[2061,25765,2099],{"className":25766},[2236],[2061,25768],{"className":25769,"style":2232},[2231],[2061,25771,25773,25776,25779,25782,25785,25788,25791,25794,25797,25800,25803,25806,25809],{"className":25772},[2160],[2061,25774],{"className":25775,"style":4634},[2164],[2061,25777,12029],{"className":25778},[2169,2170],[2061,25780,2114],{"className":25781},[2253],[2061,25783,1798],{"className":25784},[2169,2170],[2061,25786,2127],{"className":25787},[2396],[2061,25789],{"className":25790,"style":2400},[2231],[2061,25792,6887],{"className":25793,"style":6572},[2169,2170],[2061,25795,2114],{"className":25796},[2253],[2061,25798,1798],{"className":25799},[2169,2170],[2061,25801,2127],{"className":25802},[2396],[2061,25804],{"className":25805,"style":2400},[2231],[2061,25807,7160],{"className":25808},[2169,2170],[2061,25810,11446],{"className":25811},[2444]," （在最优解处，马歇尔需求等于希克斯需求）",[1808,25814,25815],{},[2061,25816,25818,25870],{"className":25817},[2068],[2061,25819,25821],{"className":25820},[2072],[2074,25822,25823],{"xmlns":2076},[2079,25824,25825,25867],{},[2082,25826,25827,25829,25831,25833,25835,25837,25839,25841,25847,25849,25851,25853,25855,25857,25859,25861,25863,25865],{},[2085,25828,12029],{},[2097,25830,2114],{"stretchy":2113},[2085,25832,1798],{},[2097,25834,2127],{"separator":2126},[2085,25836,11462],{},[2097,25838,2137],{"stretchy":2113},[2097,25840,2099],{},[2487,25842,25843,25845],{},[2085,25844,2119],{},[2097,25846,10359],{},[2097,25848,2114],{"stretchy":2113},[2085,25850,1798],{},[2097,25852,2127],{"separator":2126},[2085,25854,12585],{},[2097,25856,2114],{"stretchy":2113},[2085,25858,1798],{},[2097,25860,2127],{"separator":2126},[2085,25862,11462],{},[2097,25864,2137],{"stretchy":2113},[2097,25866,2137],{"stretchy":2113},[2149,25868,25869],{"encoding":2151},"h(p, u) = x^*(p, e(p, u))",[2061,25871,25873,25909],{"className":25872,"ariaHidden":2126},[2156],[2061,25874,25876,25879,25882,25885,25888,25891,25894,25897,25900,25903,25906],{"className":25875},[2160],[2061,25877],{"className":25878,"style":4634},[2164],[2061,25880,12029],{"className":25881},[2169,2170],[2061,25883,2114],{"className":25884},[2253],[2061,25886,1798],{"className":25887},[2169,2170],[2061,25889,2127],{"className":25890},[2396],[2061,25892],{"className":25893,"style":2400},[2231],[2061,25895,11462],{"className":25896},[2169,2170],[2061,25898,2137],{"className":25899},[2444],[2061,25901],{"className":25902,"style":2232},[2231],[2061,25904,2099],{"className":25905},[2236],[2061,25907],{"className":25908,"style":2232},[2231],[2061,25910,25912,25915,25944,25947,25950,25953,25956,25959,25962,25965,25968,25971,25974],{"className":25911},[2160],[2061,25913],{"className":25914,"style":4634},[2164],[2061,25916,25918,25921],{"className":25917},[2169],[2061,25919,2119],{"className":25920},[2169,2170],[2061,25922,25924],{"className":25923},[2181],[2061,25925,25927],{"className":25926},[2185],[2061,25928,25930],{"className":25929},[2190],[2061,25931,25933],{"className":25932,"style":25731},[2194],[2061,25934,25935,25938],{"style":2649},[2061,25936],{"className":25937,"style":2203},[2202],[2061,25939,25941],{"className":25940},[2207,2208,2209,2210],[2061,25942,10359],{"className":25943},[2984,2210],[2061,25945,2114],{"className":25946},[2253],[2061,25948,1798],{"className":25949},[2169,2170],[2061,25951,2127],{"className":25952},[2396],[2061,25954],{"className":25955,"style":2400},[2231],[2061,25957,12585],{"className":25958},[2169,2170],[2061,25960,2114],{"className":25961},[2253],[2061,25963,1798],{"className":25964},[2169,2170],[2061,25966,2127],{"className":25967},[2396],[2061,25969],{"className":25970,"style":2400},[2231],[2061,25972,11462],{"className":25973},[2169,2170],[2061,25975,11446],{"className":25976},[2444],[1847,25978,25980],{"id":25979},"_63-包络定理的应用","6.3 包络定理的应用",[1798,25982,25983,25986],{},[1865,25984,25985],{},"包络定理 (Envelope Theorem)",": 在最优化问题中，价值函数对参数的导数等于拉格朗日函数对该参数的偏导数（在最优解处）。",[1798,25988,25989,4550],{},[1865,25990,25991],{},"应用于UMP",[2061,25993,25995],{"className":25994},[2064],[2061,25996,25998,26032],{"className":25997},[2068],[2061,25999,26001],{"className":26000},[2072],[2074,26002,26003],{"xmlns":2076,"display":2077},[2079,26004,26005,26029],{},[2082,26006,26007,26021,26023],{},[2101,26008,26009,26015],{},[2082,26010,26011,26013],{},[2085,26012,2108],{"mathvariant":2107},[2085,26014,6887],{},[2082,26016,26017,26019],{},[2085,26018,2108],{"mathvariant":2107},[2085,26020,7160],{},[2097,26022,2099],{},[2487,26024,26025,26027],{},[2085,26026,8630],{},[2097,26028,10359],{},[2149,26030,26031],{"encoding":2151},"\\frac{\\partial v}{\\partial m} = \\lambda^*",[2061,26033,26035,26119],{"className":26034,"ariaHidden":2126},[2156],[2061,26036,26038,26042,26110,26113,26116],{"className":26037},[2160],[2061,26039],{"className":26040,"style":26041},[2164],"height:2.0574em;vertical-align:-0.686em;",[2061,26043,26045,26048,26107],{"className":26044},[2169],[2061,26046],{"className":26047},[2253,2254],[2061,26049,26051],{"className":26050},[2101],[2061,26052,26054,26099],{"className":26053},[2185,2186],[2061,26055,26057,26096],{"className":26056},[2190],[2061,26058,26060,26074,26082],{"className":26059,"style":2846},[2194],[2061,26061,26062,26065],{"style":2270},[2061,26063],{"className":26064,"style":2274},[2202],[2061,26066,26068,26071],{"className":26067},[2169],[2061,26069,2108],{"className":26070,"style":2281},[2169],[2061,26072,7160],{"className":26073},[2169,2170],[2061,26075,26076,26079],{"style":2325},[2061,26077],{"className":26078,"style":2274},[2202],[2061,26080],{"className":26081,"style":2333},[2332],[2061,26083,26084,26087],{"style":2336},[2061,26085],{"className":26086,"style":2274},[2202],[2061,26088,26090,26093],{"className":26089},[2169],[2061,26091,2108],{"className":26092,"style":2281},[2169],[2061,26094,6887],{"className":26095,"style":6572},[2169,2170],[2061,26097,2218],{"className":26098},[2217],[2061,26100,26102],{"className":26101},[2190],[2061,26103,26105],{"className":26104,"style":9692},[2194],[2061,26106],{},[2061,26108],{"className":26109},[2444,2254],[2061,26111],{"className":26112,"style":2232},[2231],[2061,26114,2099],{"className":26115},[2236],[2061,26117],{"className":26118,"style":2232},[2231],[2061,26120,26122,26125],{"className":26121},[2160],[2061,26123],{"className":26124,"style":10421},[2164],[2061,26126,26128,26131],{"className":26127},[2169],[2061,26129,8630],{"className":26130},[2169,2170],[2061,26132,26134],{"className":26133},[2181],[2061,26135,26137],{"className":26136},[2185],[2061,26138,26140],{"className":26139},[2190],[2061,26141,26143],{"className":26142,"style":10421},[2194],[2061,26144,26145,26148],{"style":4779},[2061,26146],{"className":26147,"style":2203},[2202],[2061,26149,26151],{"className":26150},[2207,2208,2209,2210],[2061,26152,10359],{"className":26153},[2984,2210],[1798,26155,26156,26157,26216,26217,1989],{},"这里 ",[2061,26158,26160,26178],{"className":26159},[2068],[2061,26161,26163],{"className":26162},[2072],[2074,26164,26165],{"xmlns":2076},[2079,26166,26167,26175],{},[2082,26168,26169],{},[2487,26170,26171,26173],{},[2085,26172,8630],{},[2097,26174,10359],{},[2149,26176,26177],{"encoding":2151},"\\lambda^*",[2061,26179,26181],{"className":26180,"ariaHidden":2126},[2156],[2061,26182,26184,26187],{"className":26183},[2160],[2061,26185],{"className":26186,"style":2805},[2164],[2061,26188,26190,26193],{"className":26189},[2169],[2061,26191,8630],{"className":26192},[2169,2170],[2061,26194,26196],{"className":26195},[2181],[2061,26197,26199],{"className":26198},[2185],[2061,26200,26202],{"className":26201},[2190],[2061,26203,26205],{"className":26204,"style":25731},[2194],[2061,26206,26207,26210],{"style":2649},[2061,26208],{"className":26209,"style":2203},[2202],[2061,26211,26213],{"className":26212},[2207,2208,2209,2210],[2061,26214,10359],{"className":26215},[2984,2210]," 是最优拉格朗日乘数，经济学上称为",[1865,26218,26219],{},"货币的边际效用",[1798,26221,26222,4550],{},[1865,26223,26224],{},"应用于EMP",[2061,26226,26228],{"className":26227},[2064],[2061,26229,26231,26284],{"className":26230},[2068],[2061,26232,26234],{"className":26233},[2072],[2074,26235,26236],{"xmlns":2076,"display":2077},[2079,26237,26238,26281],{},[2082,26239,26240,26258,26260,26266,26268,26270,26272,26274,26276,26278],{},[2101,26241,26242,26248],{},[2082,26243,26244,26246],{},[2085,26245,2108],{"mathvariant":2107},[2085,26247,12585],{},[2082,26249,26250,26252],{},[2085,26251,2108],{"mathvariant":2107},[2089,26253,26254,26256],{},[2085,26255,1798],{},[2085,26257,2095],{},[2097,26259,2099],{},[2089,26261,26262,26264],{},[2085,26263,12029],{},[2085,26265,2095],{},[2097,26267,2114],{"stretchy":2113},[2085,26269,1798],{},[2097,26271,2127],{"separator":2126},[2085,26273,11462],{},[2097,26275,2137],{"stretchy":2113},[2231,26277],{"width":4610},[7501,26279,26280],{},"(谢泼德引理)",[2149,26282,26283],{"encoding":2151},"\\frac{\\partial e}{\\partial p_i} = h_i(p, u) \\quad \\text{(谢泼德引理)}",[2061,26285,26287,26407],{"className":26286,"ariaHidden":2126},[2156],[2061,26288,26290,26293,26398,26401,26404],{"className":26289},[2160],[2061,26291],{"className":26292,"style":20809},[2164],[2061,26294,26296,26299,26395],{"className":26295},[2169],[2061,26297],{"className":26298},[2253,2254],[2061,26300,26302],{"className":26301},[2101],[2061,26303,26305,26387],{"className":26304},[2185,2186],[2061,26306,26308,26384],{"className":26307},[2190],[2061,26309,26311,26362,26370],{"className":26310,"style":2846},[2194],[2061,26312,26313,26316],{"style":2270},[2061,26314],{"className":26315,"style":2274},[2202],[2061,26317,26319,26322],{"className":26318},[2169],[2061,26320,2108],{"className":26321,"style":2281},[2169],[2061,26323,26325,26328],{"className":26324},[2169],[2061,26326,1798],{"className":26327},[2169,2170],[2061,26329,26331],{"className":26330},[2181],[2061,26332,26334,26354],{"className":26333},[2185,2186],[2061,26335,26337,26351],{"className":26336},[2190],[2061,26338,26340],{"className":26339,"style":2195},[2194],[2061,26341,26342,26345],{"style":2302},[2061,26343],{"className":26344,"style":2203},[2202],[2061,26346,26348],{"className":26347},[2207,2208,2209,2210],[2061,26349,2095],{"className":26350},[2169,2170,2210],[2061,26352,2218],{"className":26353},[2217],[2061,26355,26357],{"className":26356},[2190],[2061,26358,26360],{"className":26359,"style":2225},[2194],[2061,26361],{},[2061,26363,26364,26367],{"style":2325},[2061,26365],{"className":26366,"style":2274},[2202],[2061,26368],{"className":26369,"style":2333},[2332],[2061,26371,26372,26375],{"style":2336},[2061,26373],{"className":26374,"style":2274},[2202],[2061,26376,26378,26381],{"className":26377},[2169],[2061,26379,2108],{"className":26380,"style":2281},[2169],[2061,26382,12585],{"className":26383},[2169,2170],[2061,26385,2218],{"className":26386},[2217],[2061,26388,26390],{"className":26389},[2190],[2061,26391,26393],{"className":26392,"style":8254},[2194],[2061,26394],{},[2061,26396],{"className":26397},[2444,2254],[2061,26399],{"className":26400,"style":2232},[2231],[2061,26402,2099],{"className":26403},[2236],[2061,26405],{"className":26406,"style":2232},[2231],[2061,26408,26410,26413,26453,26456,26459,26462,26465,26468,26471,26474],{"className":26409},[2160],[2061,26411],{"className":26412,"style":4634},[2164],[2061,26414,26416,26419],{"className":26415},[2169],[2061,26417,12029],{"className":26418},[2169,2170],[2061,26420,26422],{"className":26421},[2181],[2061,26423,26425,26445],{"className":26424},[2185,2186],[2061,26426,26428,26442],{"className":26427},[2190],[2061,26429,26431],{"className":26430,"style":2195},[2194],[2061,26432,26433,26436],{"style":2302},[2061,26434],{"className":26435,"style":2203},[2202],[2061,26437,26439],{"className":26438},[2207,2208,2209,2210],[2061,26440,2095],{"className":26441},[2169,2170,2210],[2061,26443,2218],{"className":26444},[2217],[2061,26446,26448],{"className":26447},[2190],[2061,26449,26451],{"className":26450,"style":2225},[2194],[2061,26452],{},[2061,26454,2114],{"className":26455},[2253],[2061,26457,1798],{"className":26458},[2169,2170],[2061,26460,2127],{"className":26461},[2396],[2061,26463],{"className":26464,"style":2400},[2231],[2061,26466,11462],{"className":26467},[2169,2170],[2061,26469,2137],{"className":26470},[2444],[2061,26472],{"className":26473,"style":4870},[2231],[2061,26475,26477,26480,26485],{"className":26476},[2169,7784],[2061,26478,2114],{"className":26479},[2169],[2061,26481,26484],{"className":26482},[2169,26483],"cjk_fallback","谢泼德引理",[2061,26486,2137],{"className":26487},[2169],[1840,26489],{},[1794,26491,26493],{"id":26492},"_7-拓展话题","7. 拓展话题",[1847,26495,26497],{"id":26496},"_71-显示偏好理论-revealed-preference","7.1 显示偏好理论 (Revealed Preference)",[1798,26499,26500],{},"萨缪尔森提出的显示偏好理论允许我们在不直接观察效用函数的情况下，从消费者的选择行为中推断其偏好。",[1798,26502,26503,26506,26507,26567,26568,26627,26628,26687,26688,26747,26748,26567,26807,26866,26867,26925,26926,26984],{},[1865,26504,26505],{},"弱公理 (WARP)",": 如果在价格 ",[2061,26508,26510,26528],{"className":26509},[2068],[2061,26511,26513],{"className":26512},[2072],[2074,26514,26515],{"xmlns":2076},[2079,26516,26517,26525],{},[2082,26518,26519],{},[2487,26520,26521,26523],{},[2085,26522,1798],{},[2121,26524,2123],{},[2149,26526,26527],{"encoding":2151},"p^1",[2061,26529,26531],{"className":26530,"ariaHidden":2126},[2156],[2061,26532,26534,26538],{"className":26533},[2160],[2061,26535],{"className":26536,"style":26537},[2164],"height:1.0085em;vertical-align:-0.1944em;",[2061,26539,26541,26544],{"className":26540},[2169],[2061,26542,1798],{"className":26543},[2169,2170],[2061,26545,26547],{"className":26546},[2181],[2061,26548,26550],{"className":26549},[2185],[2061,26551,26553],{"className":26552},[2190],[2061,26554,26556],{"className":26555,"style":2646},[2194],[2061,26557,26558,26561],{"style":2649},[2061,26559],{"className":26560,"style":2203},[2202],[2061,26562,26564],{"className":26563},[2207,2208,2209,2210],[2061,26565,2123],{"className":26566},[2169,2210],"、收入 ",[2061,26569,26571,26589],{"className":26570},[2068],[2061,26572,26574],{"className":26573},[2072],[2074,26575,26576],{"xmlns":2076},[2079,26577,26578,26586],{},[2082,26579,26580],{},[2487,26581,26582,26584],{},[2085,26583,7160],{},[2121,26585,2123],{},[2149,26587,26588],{"encoding":2151},"m^1",[2061,26590,26592],{"className":26591,"ariaHidden":2126},[2156],[2061,26593,26595,26598],{"className":26594},[2160],[2061,26596],{"className":26597,"style":2646},[2164],[2061,26599,26601,26604],{"className":26600},[2169],[2061,26602,7160],{"className":26603},[2169,2170],[2061,26605,26607],{"className":26606},[2181],[2061,26608,26610],{"className":26609},[2185],[2061,26611,26613],{"className":26612},[2190],[2061,26614,26616],{"className":26615,"style":2646},[2194],[2061,26617,26618,26621],{"style":2649},[2061,26619],{"className":26620,"style":2203},[2202],[2061,26622,26624],{"className":26623},[2207,2208,2209,2210],[2061,26625,2123],{"className":26626},[2169,2210]," 下选择了 ",[2061,26629,26631,26649],{"className":26630},[2068],[2061,26632,26634],{"className":26633},[2072],[2074,26635,26636],{"xmlns":2076},[2079,26637,26638,26646],{},[2082,26639,26640],{},[2487,26641,26642,26644],{},[2085,26643,2119],{},[2121,26645,2123],{},[2149,26647,26648],{"encoding":2151},"x^1",[2061,26650,26652],{"className":26651,"ariaHidden":2126},[2156],[2061,26653,26655,26658],{"className":26654},[2160],[2061,26656],{"className":26657,"style":2646},[2164],[2061,26659,26661,26664],{"className":26660},[2169],[2061,26662,2119],{"className":26663},[2169,2170],[2061,26665,26667],{"className":26666},[2181],[2061,26668,26670],{"className":26669},[2185],[2061,26671,26673],{"className":26672},[2190],[2061,26674,26676],{"className":26675,"style":2646},[2194],[2061,26677,26678,26681],{"style":2649},[2061,26679],{"className":26680,"style":2203},[2202],[2061,26682,26684],{"className":26683},[2207,2208,2209,2210],[2061,26685,2123],{"className":26686},[2169,2210],"，而 ",[2061,26689,26691,26709],{"className":26690},[2068],[2061,26692,26694],{"className":26693},[2072],[2074,26695,26696],{"xmlns":2076},[2079,26697,26698,26706],{},[2082,26699,26700],{},[2487,26701,26702,26704],{},[2085,26703,2119],{},[2121,26705,2134],{},[2149,26707,26708],{"encoding":2151},"x^2",[2061,26710,26712],{"className":26711,"ariaHidden":2126},[2156],[2061,26713,26715,26718],{"className":26714},[2160],[2061,26716],{"className":26717,"style":2646},[2164],[2061,26719,26721,26724],{"className":26720},[2169],[2061,26722,2119],{"className":26723},[2169,2170],[2061,26725,26727],{"className":26726},[2181],[2061,26728,26730],{"className":26729},[2185],[2061,26731,26733],{"className":26732},[2190],[2061,26734,26736],{"className":26735,"style":2646},[2194],[2061,26737,26738,26741],{"style":2649},[2061,26739],{"className":26740,"style":2203},[2202],[2061,26742,26744],{"className":26743},[2207,2208,2209,2210],[2061,26745,2134],{"className":26746},[2169,2210]," 也在预算集内，那么在价格 ",[2061,26749,26751,26769],{"className":26750},[2068],[2061,26752,26754],{"className":26753},[2072],[2074,26755,26756],{"xmlns":2076},[2079,26757,26758,26766],{},[2082,26759,26760],{},[2487,26761,26762,26764],{},[2085,26763,1798],{},[2121,26765,2134],{},[2149,26767,26768],{"encoding":2151},"p^2",[2061,26770,26772],{"className":26771,"ariaHidden":2126},[2156],[2061,26773,26775,26778],{"className":26774},[2160],[2061,26776],{"className":26777,"style":26537},[2164],[2061,26779,26781,26784],{"className":26780},[2169],[2061,26782,1798],{"className":26783},[2169,2170],[2061,26785,26787],{"className":26786},[2181],[2061,26788,26790],{"className":26789},[2185],[2061,26791,26793],{"className":26792},[2190],[2061,26794,26796],{"className":26795,"style":2646},[2194],[2061,26797,26798,26801],{"style":2649},[2061,26799],{"className":26800,"style":2203},[2202],[2061,26802,26804],{"className":26803},[2207,2208,2209,2210],[2061,26805,2134],{"className":26806},[2169,2210],[2061,26808,26810,26828],{"className":26809},[2068],[2061,26811,26813],{"className":26812},[2072],[2074,26814,26815],{"xmlns":2076},[2079,26816,26817,26825],{},[2082,26818,26819],{},[2487,26820,26821,26823],{},[2085,26822,7160],{},[2121,26824,2134],{},[2149,26826,26827],{"encoding":2151},"m^2",[2061,26829,26831],{"className":26830,"ariaHidden":2126},[2156],[2061,26832,26834,26837],{"className":26833},[2160],[2061,26835],{"className":26836,"style":2646},[2164],[2061,26838,26840,26843],{"className":26839},[2169],[2061,26841,7160],{"className":26842},[2169,2170],[2061,26844,26846],{"className":26845},[2181],[2061,26847,26849],{"className":26848},[2185],[2061,26850,26852],{"className":26851},[2190],[2061,26853,26855],{"className":26854,"style":2646},[2194],[2061,26856,26857,26860],{"style":2649},[2061,26858],{"className":26859,"style":2203},[2202],[2061,26861,26863],{"className":26862},[2207,2208,2209,2210],[2061,26864,2134],{"className":26865},[2169,2210]," 下若选择 ",[2061,26868,26870,26887],{"className":26869},[2068],[2061,26871,26873],{"className":26872},[2072],[2074,26874,26875],{"xmlns":2076},[2079,26876,26877,26885],{},[2082,26878,26879],{},[2487,26880,26881,26883],{},[2085,26882,2119],{},[2121,26884,2134],{},[2149,26886,26708],{"encoding":2151},[2061,26888,26890],{"className":26889,"ariaHidden":2126},[2156],[2061,26891,26893,26896],{"className":26892},[2160],[2061,26894],{"className":26895,"style":2646},[2164],[2061,26897,26899,26902],{"className":26898},[2169],[2061,26900,2119],{"className":26901},[2169,2170],[2061,26903,26905],{"className":26904},[2181],[2061,26906,26908],{"className":26907},[2185],[2061,26909,26911],{"className":26910},[2190],[2061,26912,26914],{"className":26913,"style":2646},[2194],[2061,26915,26916,26919],{"style":2649},[2061,26917],{"className":26918,"style":2203},[2202],[2061,26920,26922],{"className":26921},[2207,2208,2209,2210],[2061,26923,2134],{"className":26924},[2169,2210],"，则 ",[2061,26927,26929,26946],{"className":26928},[2068],[2061,26930,26932],{"className":26931},[2072],[2074,26933,26934],{"xmlns":2076},[2079,26935,26936,26944],{},[2082,26937,26938],{},[2487,26939,26940,26942],{},[2085,26941,2119],{},[2121,26943,2123],{},[2149,26945,26648],{"encoding":2151},[2061,26947,26949],{"className":26948,"ariaHidden":2126},[2156],[2061,26950,26952,26955],{"className":26951},[2160],[2061,26953],{"className":26954,"style":2646},[2164],[2061,26956,26958,26961],{"className":26957},[2169],[2061,26959,2119],{"className":26960},[2169,2170],[2061,26962,26964],{"className":26963},[2181],[2061,26965,26967],{"className":26966},[2185],[2061,26968,26970],{"className":26969},[2190],[2061,26971,26973],{"className":26972,"style":2646},[2194],[2061,26974,26975,26978],{"style":2649},[2061,26976],{"className":26977,"style":2203},[2202],[2061,26979,26981],{"className":26980},[2207,2208,2209,2210],[2061,26982,2123],{"className":26983},[2169,2210]," 必然不在新预算集内（或恰好在边界上）。",[1798,26986,26987],{},"这确保了选择的一致性，是理性行为的可检验含义。",[1847,26989,26991],{"id":26990},"_72-多商品情况的推广","7.2 多商品情况的推广",[1798,26993,26994,26995,27023],{},"上述所有理论都可以推广到 ",[2061,26996,26998,27011],{"className":26997},[2068],[2061,26999,27001],{"className":27000},[2072],[2074,27002,27003],{"xmlns":2076},[2079,27004,27005,27009],{},[2082,27006,27007],{},[2085,27008,24203],{},[2149,27010,24203],{"encoding":2151},[2061,27012,27014],{"className":27013,"ariaHidden":2126},[2156],[2061,27015,27017,27020],{"className":27016},[2160],[2061,27018],{"className":27019,"style":6568},[2164],[2061,27021,24203],{"className":27022},[2169,2170]," 种商品的情况：",[1805,27025,27026,27240,27468],{},[1808,27027,27028,27029],{},"效用函数: ",[2061,27030,27032,27077],{"className":27031},[2068],[2061,27033,27035],{"className":27034},[2072],[2074,27036,27037],{"xmlns":2076},[2079,27038,27039,27074],{},[2082,27040,27041,27043,27045,27051,27053,27059,27061,27064,27066,27072],{},[2085,27042,2005],{},[2097,27044,2114],{"stretchy":2113},[2089,27046,27047,27049],{},[2085,27048,2119],{},[2121,27050,2123],{},[2097,27052,2127],{"separator":2126},[2089,27054,27055,27057],{},[2085,27056,2119],{},[2121,27058,2134],{},[2097,27060,2127],{"separator":2126},[2097,27062,27063],{},"…",[2097,27065,2127],{"separator":2126},[2089,27067,27068,27070],{},[2085,27069,2119],{},[2085,27071,24203],{},[2097,27073,2137],{"stretchy":2113},[2149,27075,27076],{"encoding":2151},"U(x_1, x_2, \\ldots, x_n)",[2061,27078,27080],{"className":27079,"ariaHidden":2126},[2156],[2061,27081,27083,27086,27089,27092,27132,27135,27138,27178,27181,27184,27187,27190,27193,27196,27237],{"className":27082},[2160],[2061,27084],{"className":27085,"style":4634},[2164],[2061,27087,2005],{"className":27088,"style":2171},[2169,2170],[2061,27090,2114],{"className":27091},[2253],[2061,27093,27095,27098],{"className":27094},[2169],[2061,27096,2119],{"className":27097},[2169,2170],[2061,27099,27101],{"className":27100},[2181],[2061,27102,27104,27124],{"className":27103},[2185,2186],[2061,27105,27107,27121],{"className":27106},[2190],[2061,27108,27110],{"className":27109,"style":2370},[2194],[2061,27111,27112,27115],{"style":2302},[2061,27113],{"className":27114,"style":2203},[2202],[2061,27116,27118],{"className":27117},[2207,2208,2209,2210],[2061,27119,2123],{"className":27120},[2169,2210],[2061,27122,2218],{"className":27123},[2217],[2061,27125,27127],{"className":27126},[2190],[2061,27128,27130],{"className":27129,"style":2225},[2194],[2061,27131],{},[2061,27133,2127],{"className":27134},[2396],[2061,27136],{"className":27137,"style":2400},[2231],[2061,27139,27141,27144],{"className":27140},[2169],[2061,27142,2119],{"className":27143},[2169,2170],[2061,27145,27147],{"className":27146},[2181],[2061,27148,27150,27170],{"className":27149},[2185,2186],[2061,27151,27153,27167],{"className":27152},[2190],[2061,27154,27156],{"className":27155,"style":2370},[2194],[2061,27157,27158,27161],{"style":2302},[2061,27159],{"className":27160,"style":2203},[2202],[2061,27162,27164],{"className":27163},[2207,2208,2209,2210],[2061,27165,2134],{"className":27166},[2169,2210],[2061,27168,2218],{"className":27169},[2217],[2061,27171,27173],{"className":27172},[2190],[2061,27174,27176],{"className":27175,"style":2225},[2194],[2061,27177],{},[2061,27179,2127],{"className":27180},[2396],[2061,27182],{"className":27183,"style":2400},[2231],[2061,27185,27063],{"className":27186},[3967],[2061,27188],{"className":27189,"style":2400},[2231],[2061,27191,2127],{"className":27192},[2396],[2061,27194],{"className":27195,"style":2400},[2231],[2061,27197,27199,27202],{"className":27198},[2169],[2061,27200,2119],{"className":27201},[2169,2170],[2061,27203,27205],{"className":27204},[2181],[2061,27206,27208,27229],{"className":27207},[2185,2186],[2061,27209,27211,27226],{"className":27210},[2190],[2061,27212,27215],{"className":27213,"style":27214},[2194],"height:0.1514em;",[2061,27216,27217,27220],{"style":2302},[2061,27218],{"className":27219,"style":2203},[2202],[2061,27221,27223],{"className":27222},[2207,2208,2209,2210],[2061,27224,24203],{"className":27225},[2169,2170,2210],[2061,27227,2218],{"className":27228},[2217],[2061,27230,27232],{"className":27231},[2190],[2061,27233,27235],{"className":27234,"style":2225},[2194],[2061,27236],{},[2061,27238,2137],{"className":27239},[2444],[1808,27241,27242,27243],{},"预算约束: ",[2061,27244,27246,27288],{"className":27245},[2068],[2061,27247,27249],{"className":27248},[2072],[2074,27250,27251],{"xmlns":2076},[2079,27252,27253,27285],{},[2082,27254,27255,27269,27275,27281,27283],{},[2500,27256,27257,27259,27267],{},[2097,27258,24192],{},[2082,27260,27261,27263,27265],{},[2085,27262,2095],{},[2097,27264,2099],{},[2121,27266,2123],{},[2085,27268,24203],{},[2089,27270,27271,27273],{},[2085,27272,1798],{},[2085,27274,2095],{},[2089,27276,27277,27279],{},[2085,27278,2119],{},[2085,27280,2095],{},[2097,27282,6122],{},[2085,27284,7160],{},[2149,27286,27287],{"encoding":2151},"\\sum_{i=1}^{n} p_i x_i \\le m",[2061,27289,27291,27459],{"className":27290,"ariaHidden":2126},[2156],[2061,27292,27294,27298,27367,27370,27410,27450,27453,27456],{"className":27293},[2160],[2061,27295],{"className":27296,"style":27297},[2164],"height:1.104em;vertical-align:-0.2997em;",[2061,27299,27301,27306],{"className":27300},[5104],[2061,27302,24192],{"className":27303,"style":27305},[5104,24291,27304],"small-op","position:relative;top:0em;",[2061,27307,27309],{"className":27308},[2181],[2061,27310,27312,27358],{"className":27311},[2185,2186],[2061,27313,27315,27355],{"className":27314},[2190],[2061,27316,27319,27340],{"className":27317,"style":27318},[2194],"height:0.8043em;",[2061,27320,27322,27325],{"style":27321},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[2061,27323],{"className":27324,"style":2203},[2202],[2061,27326,27328],{"className":27327},[2207,2208,2209,2210],[2061,27329,27331,27334,27337],{"className":27330},[2169,2210],[2061,27332,2095],{"className":27333},[2169,2170,2210],[2061,27335,2099],{"className":27336},[2236,2210],[2061,27338,2123],{"className":27339},[2169,2210],[2061,27341,27343,27346],{"style":27342},"top:-3.2029em;margin-right:0.05em;",[2061,27344],{"className":27345,"style":2203},[2202],[2061,27347,27349],{"className":27348},[2207,2208,2209,2210],[2061,27350,27352],{"className":27351},[2169,2210],[2061,27353,24203],{"className":27354},[2169,2170,2210],[2061,27356,2218],{"className":27357},[2217],[2061,27359,27361],{"className":27360},[2190],[2061,27362,27365],{"className":27363,"style":27364},[2194],"height:0.2997em;",[2061,27366],{},[2061,27368],{"className":27369,"style":2400},[2231],[2061,27371,27373,27376],{"className":27372},[2169],[2061,27374,1798],{"className":27375},[2169,2170],[2061,27377,27379],{"className":27378},[2181],[2061,27380,27382,27402],{"className":27381},[2185,2186],[2061,27383,27385,27399],{"className":27384},[2190],[2061,27386,27388],{"className":27387,"style":2195},[2194],[2061,27389,27390,27393],{"style":2302},[2061,27391],{"className":27392,"style":2203},[2202],[2061,27394,27396],{"className":27395},[2207,2208,2209,2210],[2061,27397,2095],{"className":27398},[2169,2170,2210],[2061,27400,2218],{"className":27401},[2217],[2061,27403,27405],{"className":27404},[2190],[2061,27406,27408],{"className":27407,"style":2225},[2194],[2061,27409],{},[2061,27411,27413,27416],{"className":27412},[2169],[2061,27414,2119],{"className":27415},[2169,2170],[2061,27417,27419],{"className":27418},[2181],[2061,27420,27422,27442],{"className":27421},[2185,2186],[2061,27423,27425,27439],{"className":27424},[2190],[2061,27426,27428],{"className":27427,"style":2195},[2194],[2061,27429,27430,27433],{"style":2302},[2061,27431],{"className":27432,"style":2203},[2202],[2061,27434,27436],{"className":27435},[2207,2208,2209,2210],[2061,27437,2095],{"className":27438},[2169,2170,2210],[2061,27440,2218],{"className":27441},[2217],[2061,27443,27445],{"className":27444},[2190],[2061,27446,27448],{"className":27447,"style":2225},[2194],[2061,27449],{},[2061,27451],{"className":27452,"style":2232},[2231],[2061,27454,6122],{"className":27455},[2236],[2061,27457],{"className":27458,"style":2232},[2231],[2061,27460,27462,27465],{"className":27461},[2160],[2061,27463],{"className":27464,"style":6568},[2164],[2061,27466,7160],{"className":27467},[2169,2170],[1808,27469,27470,27471,27522],{},"一阶条件变为 ",[2061,27472,27474,27492],{"className":27473},[2068],[2061,27475,27477],{"className":27476},[2072],[2074,27478,27479],{"xmlns":2076},[2079,27480,27481,27489],{},[2082,27482,27483,27485,27487],{},[2085,27484,24203],{},[2097,27486,2762],{},[2121,27488,2123],{},[2149,27490,27491],{"encoding":2151},"n+1",[2061,27493,27495,27513],{"className":27494,"ariaHidden":2126},[2156],[2061,27496,27498,27501,27504,27507,27510],{"className":27497},[2160],[2061,27499],{"className":27500,"style":6835},[2164],[2061,27502,24203],{"className":27503},[2169,2170],[2061,27505],{"className":27506,"style":2980},[2231],[2061,27508,2762],{"className":27509},[2984],[2061,27511],{"className":27512,"style":2980},[2231],[2061,27514,27516,27519],{"className":27515},[2160],[2061,27517],{"className":27518,"style":2692},[2164],[2061,27520,2123],{"className":27521},[2169]," 个方程的系统",[1847,27524,27526],{"id":27525},"_73-角点解-corner-solutions","7.3 角点解 (Corner Solutions)",[1798,27528,27529],{},"并非所有最优解都是内部解。如果某种商品的MRS始终大于（或小于）价格比，消费者会选择只消费一种商品（角点解）。",[1798,27531,27532,27535],{},[1865,27533,27534],{},"库恩-塔克条件 (Kuhn-Tucker Conditions)"," 是处理不等式约束和角点解的一般化工具：",[2061,27537,27539],{"className":27538},[2064],[2061,27540,27542,27676],{"className":27541},[2068],[2061,27543,27545],{"className":27544},[2072],[2074,27546,27547],{"xmlns":2076,"display":2077},[2079,27548,27549,27673],{},[9154,27550,27551,27613],{"rowspacing":9156,"columnalign":9157,"columnspacing":9158},[9160,27552,27553,27587],{},[9163,27554,27555],{},[9166,27556,27557],{"scriptlevel":2513,"displaystyle":2126},[2082,27558,27559,27577,27579,27581],{},[2101,27560,27561,27567],{},[2082,27562,27563,27565],{},[2085,27564,2108],{"mathvariant":2107},[2085,27566,2005],{},[2082,27568,27569,27571],{},[2085,27570,2108],{"mathvariant":2107},[2089,27572,27573,27575],{},[2085,27574,2119],{},[2085,27576,2095],{},[2097,27578,3204],{},[2085,27580,8630],{},[2089,27582,27583,27585],{},[2085,27584,1798],{},[2085,27586,2095],{},[9163,27588,27589],{},[9166,27590,27591],{"scriptlevel":2513,"displaystyle":2126},[2082,27592,27593,27595,27597,27599,27601,27603,27609,27611],{},[2082,27594],{},[2097,27596,6122],{},[2121,27598,2513],{},[2097,27600,2127],{"separator":2126},[2231,27602],{"width":4610},[2089,27604,27605,27607],{},[2085,27606,2119],{},[2085,27608,2095],{},[2097,27610,11557],{},[2121,27612,2513],{},[9160,27614,27615,27661],{},[9163,27616,27617],{},[9166,27618,27619],{"scriptlevel":2513,"displaystyle":2126},[2082,27620,27621,27627],{},[2089,27622,27623,27625],{},[2085,27624,2119],{},[2085,27626,2095],{},[2082,27628,27629,27631,27649,27651,27653,27659],{},[2097,27630,2114],{"fence":2126},[2101,27632,27633,27639],{},[2082,27634,27635,27637],{},[2085,27636,2108],{"mathvariant":2107},[2085,27638,2005],{},[2082,27640,27641,27643],{},[2085,27642,2108],{"mathvariant":2107},[2089,27644,27645,27647],{},[2085,27646,2119],{},[2085,27648,2095],{},[2097,27650,3204],{},[2085,27652,8630],{},[2089,27654,27655,27657],{},[2085,27656,1798],{},[2085,27658,2095],{},[2097,27660,2137],{"fence":2126},[9163,27662,27663],{},[9166,27664,27665],{"scriptlevel":2513,"displaystyle":2126},[2082,27666,27667,27669,27671],{},[2082,27668],{},[2097,27670,2099],{},[2121,27672,2513],{},[2149,27674,27675],{"encoding":2151},"\\begin{align*}\n\\frac{\\partial U}{\\partial x_i} - \\lambda p_i &\\le 0, \\quad x_i \\ge 0 \\\\\nx_i \\left(\\frac{\\partial U}{\\partial x_i} - \\lambda p_i\\right) &= 0\n\\end{align*}",[2061,27677,27679],{"className":27678,"ariaHidden":2126},[2156],[2061,27680,27682,27686],{"className":27681},[2160],[2061,27683],{"className":27684,"style":27685},[2164],"height:4.9075em;vertical-align:-2.2037em;",[2061,27687,27689],{"className":27688},[2169],[2061,27690,27692,28108],{"className":27691},[9154],[2061,27693,27695],{"className":27694},[9380],[2061,27696,27698,28099],{"className":27697},[2185,2186],[2061,27699,27701,28096],{"className":27700},[2190],[2061,27702,27705,27872],{"className":27703,"style":27704},[2194],"height:2.7037em;",[2061,27706,27708,27712],{"style":27707},"top:-4.7823em;",[2061,27709],{"className":27710,"style":27711},[2202],"height:3.45em;",[2061,27713,27715,27820,27823,27826,27829,27832],{"className":27714},[2169],[2061,27716,27718,27721,27817],{"className":27717},[2169],[2061,27719],{"className":27720},[2253,2254],[2061,27722,27724],{"className":27723},[2101],[2061,27725,27727,27809],{"className":27726},[2185,2186],[2061,27728,27730,27806],{"className":27729},[2190],[2061,27731,27733,27784,27792],{"className":27732,"style":2846},[2194],[2061,27734,27735,27738],{"style":2270},[2061,27736],{"className":27737,"style":2274},[2202],[2061,27739,27741,27744],{"className":27740},[2169],[2061,27742,2108],{"className":27743,"style":2281},[2169],[2061,27745,27747,27750],{"className":27746},[2169],[2061,27748,2119],{"className":27749},[2169,2170],[2061,27751,27753],{"className":27752},[2181],[2061,27754,27756,27776],{"className":27755},[2185,2186],[2061,27757,27759,27773],{"className":27758},[2190],[2061,27760,27762],{"className":27761,"style":2195},[2194],[2061,27763,27764,27767],{"style":2302},[2061,27765],{"className":27766,"style":2203},[2202],[2061,27768,27770],{"className":27769},[2207,2208,2209,2210],[2061,27771,2095],{"className":27772},[2169,2170,2210],[2061,27774,2218],{"className":27775},[2217],[2061,27777,27779],{"className":27778},[2190],[2061,27780,27782],{"className":27781,"style":2225},[2194],[2061,27783],{},[2061,27785,27786,27789],{"style":2325},[2061,27787],{"className":27788,"style":2274},[2202],[2061,27790],{"className":27791,"style":2333},[2332],[2061,27793,27794,27797],{"style":2336},[2061,27795],{"className":27796,"style":2274},[2202],[2061,27798,27800,27803],{"className":27799},[2169],[2061,27801,2108],{"className":27802,"style":2281},[2169],[2061,27804,2005],{"className":27805,"style":2171},[2169,2170],[2061,27807,2218],{"className":27808},[2217],[2061,27810,27812],{"className":27811},[2190],[2061,27813,27815],{"className":27814,"style":2454},[2194],[2061,27816],{},[2061,27818],{"className":27819},[2444,2254],[2061,27821],{"className":27822,"style":2980},[2231],[2061,27824,3204],{"className":27825},[2984],[2061,27827],{"className":27828,"style":2980},[2231],[2061,27830,8630],{"className":27831},[2169,2170],[2061,27833,27835,27838],{"className":27834},[2169],[2061,27836,1798],{"className":27837},[2169,2170],[2061,27839,27841],{"className":27840},[2181],[2061,27842,27844,27864],{"className":27843},[2185,2186],[2061,27845,27847,27861],{"className":27846},[2190],[2061,27848,27850],{"className":27849,"style":2195},[2194],[2061,27851,27852,27855],{"style":2302},[2061,27853],{"className":27854,"style":2203},[2202],[2061,27856,27858],{"className":27857},[2207,2208,2209,2210],[2061,27859,2095],{"className":27860},[2169,2170,2210],[2061,27862,2218],{"className":27863},[2217],[2061,27865,27867],{"className":27866},[2190],[2061,27868,27870],{"className":27869,"style":2225},[2194],[2061,27871],{},[2061,27873,27875,27878],{"style":27874},"top:-2.1963em;",[2061,27876],{"className":27877,"style":27711},[2202],[2061,27879,27881,27921,27924],{"className":27880},[2169],[2061,27882,27884,27887],{"className":27883},[2169],[2061,27885,2119],{"className":27886},[2169,2170],[2061,27888,27890],{"className":27889},[2181],[2061,27891,27893,27913],{"className":27892},[2185,2186],[2061,27894,27896,27910],{"className":27895},[2190],[2061,27897,27899],{"className":27898,"style":2195},[2194],[2061,27900,27901,27904],{"style":2302},[2061,27902],{"className":27903,"style":2203},[2202],[2061,27905,27907],{"className":27906},[2207,2208,2209,2210],[2061,27908,2095],{"className":27909},[2169,2170,2210],[2061,27911,2218],{"className":27912},[2217],[2061,27914,27916],{"className":27915},[2190],[2061,27917,27919],{"className":27918,"style":2225},[2194],[2061,27920],{},[2061,27922],{"className":27923,"style":2400},[2231],[2061,27925,27927,27933,28038,28041,28044,28047,28050,28090],{"className":27926},[3967],[2061,27928,27930],{"className":27929,"style":19690},[2253,19689],[2061,27931,2114],{"className":27932},[3974,2209],[2061,27934,27936,27939,28035],{"className":27935},[2169],[2061,27937],{"className":27938},[2253,2254],[2061,27940,27942],{"className":27941},[2101],[2061,27943,27945,28027],{"className":27944},[2185,2186],[2061,27946,27948,28024],{"className":27947},[2190],[2061,27949,27951,28002,28010],{"className":27950,"style":2846},[2194],[2061,27952,27953,27956],{"style":2270},[2061,27954],{"className":27955,"style":2274},[2202],[2061,27957,27959,27962],{"className":27958},[2169],[2061,27960,2108],{"className":27961,"style":2281},[2169],[2061,27963,27965,27968],{"className":27964},[2169],[2061,27966,2119],{"className":27967},[2169,2170],[2061,27969,27971],{"className":27970},[2181],[2061,27972,27974,27994],{"className":27973},[2185,2186],[2061,27975,27977,27991],{"className":27976},[2190],[2061,27978,27980],{"className":27979,"style":2195},[2194],[2061,27981,27982,27985],{"style":2302},[2061,27983],{"className":27984,"style":2203},[2202],[2061,27986,27988],{"className":27987},[2207,2208,2209,2210],[2061,27989,2095],{"className":27990},[2169,2170,2210],[2061,27992,2218],{"className":27993},[2217],[2061,27995,27997],{"className":27996},[2190],[2061,27998,28000],{"className":27999,"style":2225},[2194],[2061,28001],{},[2061,28003,28004,28007],{"style":2325},[2061,28005],{"className":28006,"style":2274},[2202],[2061,28008],{"className":28009,"style":2333},[2332],[2061,28011,28012,28015],{"style":2336},[2061,28013],{"className":28014,"style":2274},[2202],[2061,28016,28018,28021],{"className":28017},[2169],[2061,28019,2108],{"className":28020,"style":2281},[2169],[2061,28022,2005],{"className":28023,"style":2171},[2169,2170],[2061,28025,2218],{"className":28026},[2217],[2061,28028,28030],{"className":28029},[2190],[2061,28031,28033],{"className":28032,"style":2454},[2194],[2061,28034],{},[2061,28036],{"className":28037},[2444,2254],[2061,28039],{"className":28040,"style":2980},[2231],[2061,28042,3204],{"className":28043},[2984],[2061,28045],{"className":28046,"style":2980},[2231],[2061,28048,8630],{"className":28049},[2169,2170],[2061,28051,28053,28056],{"className":28052},[2169],[2061,28054,1798],{"className":28055},[2169,2170],[2061,28057,28059],{"className":28058},[2181],[2061,28060,28062,28082],{"className":28061},[2185,2186],[2061,28063,28065,28079],{"className":28064},[2190],[2061,28066,28068],{"className":28067,"style":2195},[2194],[2061,28069,28070,28073],{"style":2302},[2061,28071],{"className":28072,"style":2203},[2202],[2061,28074,28076],{"className":28075},[2207,2208,2209,2210],[2061,28077,2095],{"className":28078},[2169,2170,2210],[2061,28080,2218],{"className":28081},[2217],[2061,28083,28085],{"className":28084},[2190],[2061,28086,28088],{"className":28087,"style":2225},[2194],[2061,28089],{},[2061,28091,28093],{"className":28092,"style":19690},[2444,19689],[2061,28094,2137],{"className":28095},[3974,2209],[2061,28097,2218],{"className":28098},[2217],[2061,28100,28102],{"className":28101},[2190],[2061,28103,28106],{"className":28104,"style":28105},[2194],"height:2.2037em;",[2061,28107],{},[2061,28109,28111],{"className":28110},[9713],[2061,28112,28114,28230],{"className":28113},[2185,2186],[2061,28115,28117,28227],{"className":28116},[2190],[2061,28118,28120,28204],{"className":28119,"style":27704},[2194],[2061,28121,28122,28125],{"style":27707},[2061,28123],{"className":28124,"style":27711},[2202],[2061,28126,28128,28131,28134,28137,28140,28143,28146,28149,28152,28192,28195,28198,28201],{"className":28127},[2169],[2061,28129],{"className":28130},[2169],[2061,28132],{"className":28133,"style":2232},[2231],[2061,28135,6122],{"className":28136},[2236],[2061,28138],{"className":28139,"style":2232},[2231],[2061,28141,2513],{"className":28142},[2169],[2061,28144,2127],{"className":28145},[2396],[2061,28147],{"className":28148,"style":4870},[2231],[2061,28150],{"className":28151,"style":2400},[2231],[2061,28153,28155,28158],{"className":28154},[2169],[2061,28156,2119],{"className":28157},[2169,2170],[2061,28159,28161],{"className":28160},[2181],[2061,28162,28164,28184],{"className":28163},[2185,2186],[2061,28165,28167,28181],{"className":28166},[2190],[2061,28168,28170],{"className":28169,"style":2195},[2194],[2061,28171,28172,28175],{"style":2302},[2061,28173],{"className":28174,"style":2203},[2202],[2061,28176,28178],{"className":28177},[2207,2208,2209,2210],[2061,28179,2095],{"className":28180},[2169,2170,2210],[2061,28182,2218],{"className":28183},[2217],[2061,28185,28187],{"className":28186},[2190],[2061,28188,28190],{"className":28189,"style":2225},[2194],[2061,28191],{},[2061,28193],{"className":28194,"style":2232},[2231],[2061,28196,11557],{"className":28197},[2236],[2061,28199],{"className":28200,"style":2232},[2231],[2061,28202,2513],{"className":28203},[2169],[2061,28205,28206,28209],{"style":27874},[2061,28207],{"className":28208,"style":27711},[2202],[2061,28210,28212,28215,28218,28221,28224],{"className":28211},[2169],[2061,28213],{"className":28214},[2169],[2061,28216],{"className":28217,"style":2232},[2231],[2061,28219,2099],{"className":28220},[2236],[2061,28222],{"className":28223,"style":2232},[2231],[2061,28225,2513],{"className":28226},[2169],[2061,28228,2218],{"className":28229},[2217],[2061,28231,28233],{"className":28232},[2190],[2061,28234,28236],{"className":28235,"style":28105},[2194],[2061,28237],{},[1798,28239,28240,28241,28244,28245,28337],{},"第二个条件称为",[1865,28242,28243],{},"互补松弛条件","：要么 ",[2061,28246,28248,28270],{"className":28247},[2068],[2061,28249,28251],{"className":28250},[2072],[2074,28252,28253],{"xmlns":2076},[2079,28254,28255,28267],{},[2082,28256,28257,28263,28265],{},[2089,28258,28259,28261],{},[2085,28260,2119],{},[2085,28262,2095],{},[2097,28264,2099],{},[2121,28266,2513],{},[2149,28268,28269],{"encoding":2151},"x_i = 0",[2061,28271,28273,28328],{"className":28272,"ariaHidden":2126},[2156],[2061,28274,28276,28279,28319,28322,28325],{"className":28275},[2160],[2061,28277],{"className":28278,"style":7092},[2164],[2061,28280,28282,28285],{"className":28281},[2169],[2061,28283,2119],{"className":28284},[2169,2170],[2061,28286,28288],{"className":28287},[2181],[2061,28289,28291,28311],{"className":28290},[2185,2186],[2061,28292,28294,28308],{"className":28293},[2190],[2061,28295,28297],{"className":28296,"style":2195},[2194],[2061,28298,28299,28302],{"style":2302},[2061,28300],{"className":28301,"style":2203},[2202],[2061,28303,28305],{"className":28304},[2207,2208,2209,2210],[2061,28306,2095],{"className":28307},[2169,2170,2210],[2061,28309,2218],{"className":28310},[2217],[2061,28312,28314],{"className":28313},[2190],[2061,28315,28317],{"className":28316,"style":2225},[2194],[2061,28318],{},[2061,28320],{"className":28321,"style":2232},[2231],[2061,28323,2099],{"className":28324},[2236],[2061,28326],{"className":28327,"style":2232},[2231],[2061,28329,28331,28334],{"className":28330},[2160],[2061,28332],{"className":28333,"style":2692},[2164],[2061,28335,2513],{"className":28336},[2169],"（不消费），要么边际效用等于价格（内部解）。",[1840,28339],{},[1794,28341,28343],{"id":28342},"_8-历史背景与文献","8. 历史背景与文献",[1798,28345,28346],{},"消费者理论的现代形式主要建立于20世纪初至中期：",[1805,28348,28349,28355,28361,28367],{},[1808,28350,28351,28354],{},[1865,28352,28353],{},"帕累托 (Vilfredo Pareto, 1906)",": 提出序数效用和无差异曲线分析",[1808,28356,28357,28360],{},[1865,28358,28359],{},"希克斯和艾伦 (John Hicks & Roy Allen, 1934)",": 系统发展了序数效用理论",[1808,28362,28363,28366],{},[1865,28364,28365],{},"萨缪尔森 (Paul Samuelson, 1947)",": 在《经济分析基础》中建立了对偶理论和显示偏好理论",[1808,28368,28369,2006,28372,28375],{},[1865,28370,28371],{},"麦肯齐 (Lionel McKenzie)",[1865,28373,28374],{},"阿罗-德布鲁 (Arrow-Debreu)",": 推广到一般均衡框架",[1798,28377,28378,4550],{},[1865,28379,28380],{},"推荐阅读",[1860,28382,28383,28386,28389],{},[1808,28384,28385],{},"Mas-Colell, Whinston & Green (1995), Chapter 2-3",[1808,28387,28388],{},"Varian (1992), Chapters 7-10",[1808,28390,28391],{},"Jehle & Reny (2011), Chapters 1-2",[1840,28393],{},[1794,28395,28397],{"id":28396},"_9-小结","9. 小结",[1798,28399,28400],{},"本章建立了微观经济学的核心分析工具：",[1798,28402,28403,28404,28407,28408,28410,28411,28414,28415,28418,28419,28410,28421,28424,28425,28428,28410,28430,28424,28432,28435,28410,28437,28440,28441],{},"✅ ",[1865,28405,28406],{},"偏好公理"," → 效用函数",[2461,28409],{},"\n✅ ",[1865,28412,28413],{},"效用最大化"," (UMP) ↔ ",[1865,28416,28417],{},"支出最小化"," (EMP)",[2461,28420],{},[1865,28422,28423],{},"马歇尔需求"," ↔ ",[1865,28426,28427],{},"希克斯需求",[2461,28429],{},[1865,28431,14682],{},[1865,28433,28434],{},"支出函数",[2461,28436],{},[1865,28438,28439],{},"罗伊恒等式"," & ",[1865,28442,26484],{},[1794,28444,28445],{"id":28445},"自学检查",[1798,28447,28448,28451],{},[1865,28449,28450],{},"核心直觉回看","：消费者理论的中心不是“人一定会买多少”，而是“在给定偏好、价格和收入时，什么选择与理性最优化相一致”。无差异曲线给出主观权衡，预算线给出客观权衡，内部解处两者相等。",[1798,28453,28454,28457,28458,28515,28516,28573],{},[1865,28455,28456],{},"关键模型提醒","：效用最大化问题给出马歇尔需求 ",[2061,28459,28461,28485],{"className":28460},[2068],[2061,28462,28464],{"className":28463},[2072],[2074,28465,28466],{"xmlns":2076},[2079,28467,28468,28482],{},[2082,28469,28470,28472,28474,28476,28478,28480],{},[2085,28471,2119],{},[2097,28473,2114],{"stretchy":2113},[2085,28475,1798],{},[2097,28477,2127],{"separator":2126},[2085,28479,7160],{},[2097,28481,2137],{"stretchy":2113},[2149,28483,28484],{"encoding":2151},"x(p,m)",[2061,28486,28488],{"className":28487,"ariaHidden":2126},[2156],[2061,28489,28491,28494,28497,28500,28503,28506,28509,28512],{"className":28490},[2160],[2061,28492],{"className":28493,"style":4634},[2164],[2061,28495,2119],{"className":28496},[2169,2170],[2061,28498,2114],{"className":28499},[2253],[2061,28501,1798],{"className":28502},[2169,2170],[2061,28504,2127],{"className":28505},[2396],[2061,28507],{"className":28508,"style":2400},[2231],[2061,28510,7160],{"className":28511},[2169,2170],[2061,28513,2137],{"className":28514},[2444],"，支出最小化问题给出希克斯需求 ",[2061,28517,28519,28543],{"className":28518},[2068],[2061,28520,28522],{"className":28521},[2072],[2074,28523,28524],{"xmlns":2076},[2079,28525,28526,28540],{},[2082,28527,28528,28530,28532,28534,28536,28538],{},[2085,28529,12029],{},[2097,28531,2114],{"stretchy":2113},[2085,28533,1798],{},[2097,28535,2127],{"separator":2126},[2085,28537,11462],{},[2097,28539,2137],{"stretchy":2113},[2149,28541,28542],{"encoding":2151},"h(p,u)",[2061,28544,28546],{"className":28545,"ariaHidden":2126},[2156],[2061,28547,28549,28552,28555,28558,28561,28564,28567,28570],{"className":28548},[2160],[2061,28550],{"className":28551,"style":4634},[2164],[2061,28553,12029],{"className":28554},[2169,2170],[2061,28556,2114],{"className":28557},[2253],[2061,28559,1798],{"className":28560},[2169,2170],[2061,28562,2127],{"className":28563},[2396],[2061,28565],{"className":28566,"style":2400},[2231],[2061,28568,11462],{"className":28569},[2169,2170],[2061,28571,2137],{"className":28572},[2444],"。罗伊恒等式和谢泼德引理的作用，是让你可以从价值函数反推出需求。",[1847,28575,28576],{"id":28576},"常见误区",[1805,28578,28579,28736,28739,28742],{},[1808,28580,28581,28582,28735],{},"看到两个商品就直接写 ",[2061,28583,28585,28619],{"className":28584},[2068],[2061,28586,28588],{"className":28587},[2072],[2074,28589,28590],{"xmlns":2076},[2079,28591,28592,28616],{},[2082,28593,28594,28596,28598,28600,28602,28608,28610],{},[2085,28595,2087],{},[2085,28597,3784],{},[2085,28599,3789],{},[2097,28601,2099],{},[2089,28603,28604,28606],{},[2085,28605,1798],{},[2121,28607,2123],{},[2085,28609,3215],{"mathvariant":2107},[2089,28611,28612,28614],{},[2085,28613,1798],{},[2121,28615,2134],{},[2149,28617,28618],{"encoding":2151},"MRS=p_1\u002Fp_2",[2061,28620,28622,28646],{"className":28621,"ariaHidden":2126},[2156],[2061,28623,28625,28628,28631,28634,28637,28640,28643],{"className":28624},[2160],[2061,28626],{"className":28627,"style":8096},[2164],[2061,28629,2087],{"className":28630,"style":2171},[2169,2170],[2061,28632,3784],{"className":28633,"style":3902},[2169,2170],[2061,28635,3789],{"className":28636,"style":3909},[2169,2170],[2061,28638],{"className":28639,"style":2232},[2231],[2061,28641,2099],{"className":28642},[2236],[2061,28644],{"className":28645,"style":2232},[2231],[2061,28647,28649,28652,28692,28695],{"className":28648},[2160],[2061,28650],{"className":28651,"style":4634},[2164],[2061,28653,28655,28658],{"className":28654},[2169],[2061,28656,1798],{"className":28657},[2169,2170],[2061,28659,28661],{"className":28660},[2181],[2061,28662,28664,28684],{"className":28663},[2185,2186],[2061,28665,28667,28681],{"className":28666},[2190],[2061,28668,28670],{"className":28669,"style":2370},[2194],[2061,28671,28672,28675],{"style":2302},[2061,28673],{"className":28674,"style":2203},[2202],[2061,28676,28678],{"className":28677},[2207,2208,2209,2210],[2061,28679,2123],{"className":28680},[2169,2210],[2061,28682,2218],{"className":28683},[2217],[2061,28685,28687],{"className":28686},[2190],[2061,28688,28690],{"className":28689,"style":2225},[2194],[2061,28691],{},[2061,28693,3215],{"className":28694},[2169],[2061,28696,28698,28701],{"className":28697},[2169],[2061,28699,1798],{"className":28700},[2169,2170],[2061,28702,28704],{"className":28703},[2181],[2061,28705,28707,28727],{"className":28706},[2185,2186],[2061,28708,28710,28724],{"className":28709},[2190],[2061,28711,28713],{"className":28712,"style":2370},[2194],[2061,28714,28715,28718],{"style":2302},[2061,28716],{"className":28717,"style":2203},[2202],[2061,28719,28721],{"className":28720},[2207,2208,2209,2210],[2061,28722,2134],{"className":28723},[2169,2210],[2061,28725,2218],{"className":28726},[2217],[2061,28728,28730],{"className":28729},[2190],[2061,28731,28733],{"className":28732,"style":2225},[2194],[2061,28734],{},"，却没有检查角点解、完全替代和完全互补的情形。",[1808,28737,28738],{},"把效用数值当成幸福的绝对单位。序数效用只保留排序，单调变换不改变偏好。",[1808,28740,28741],{},"混淆马歇尔需求和希克斯需求：前者固定收入，后者固定效用。",[1808,28743,28744,28745,28774],{},"拉格朗日乘子算出来后不解释。UMP 中的 ",[2061,28746,28748,28762],{"className":28747},[2068],[2061,28749,28751],{"className":28750},[2072],[2074,28752,28753],{"xmlns":2076},[2079,28754,28755,28759],{},[2082,28756,28757],{},[2085,28758,8630],{},[2149,28760,28761],{"encoding":2151},"\\lambda",[2061,28763,28765],{"className":28764,"ariaHidden":2126},[2156],[2061,28766,28768,28771],{"className":28767},[2160],[2061,28769],{"className":28770,"style":2805},[2164],[2061,28772,8630],{"className":28773},[2169,2170]," 可以理解为一元钱带来的边际效用。",[1847,28776,28777],{"id":28777},"自测题",[1860,28779,28780,29080,29083,29086,29089],{},[1808,28781,28782,28783,29079],{},"对 ",[2061,28784,28786,28848],{"className":28785},[2068],[2061,28787,28789],{"className":28788},[2072],[2074,28790,28791],{"xmlns":2076},[2079,28792,28793,28845],{},[2082,28794,28795,28797,28799,28805,28807,28813,28815,28817,28831],{},[2085,28796,2005],{},[2097,28798,2114],{"stretchy":2113},[2089,28800,28801,28803],{},[2085,28802,2119],{},[2121,28804,2123],{},[2097,28806,2127],{"separator":2126},[2089,28808,28809,28811],{},[2085,28810,2119],{},[2121,28812,2134],{},[2097,28814,2137],{"stretchy":2113},[2097,28816,2099],{},[2500,28818,28819,28821,28823],{},[2085,28820,2119],{},[2121,28822,2123],{},[2082,28824,28825,28827,28829],{},[2121,28826,2123],{},[2085,28828,3215],{"mathvariant":2107},[2121,28830,2134],{},[2500,28832,28833,28835,28837],{},[2085,28834,2119],{},[2121,28836,2134],{},[2082,28838,28839,28841,28843],{},[2121,28840,2123],{},[2085,28842,3215],{"mathvariant":2107},[2121,28844,2134],{},[2149,28846,28847],{"encoding":2151},"U(x_1,x_2)=x_1^{1\u002F2}x_2^{1\u002F2}",[2061,28849,28851,28961],{"className":28850,"ariaHidden":2126},[2156],[2061,28852,28854,28857,28860,28863,28903,28906,28909,28949,28952,28955,28958],{"className":28853},[2160],[2061,28855],{"className":28856,"style":4634},[2164],[2061,28858,2005],{"className":28859,"style":2171},[2169,2170],[2061,28861,2114],{"className":28862},[2253],[2061,28864,28866,28869],{"className":28865},[2169],[2061,28867,2119],{"className":28868},[2169,2170],[2061,28870,28872],{"className":28871},[2181],[2061,28873,28875,28895],{"className":28874},[2185,2186],[2061,28876,28878,28892],{"className":28877},[2190],[2061,28879,28881],{"className":28880,"style":2370},[2194],[2061,28882,28883,28886],{"style":2302},[2061,28884],{"className":28885,"style":2203},[2202],[2061,28887,28889],{"className":28888},[2207,2208,2209,2210],[2061,28890,2123],{"className":28891},[2169,2210],[2061,28893,2218],{"className":28894},[2217],[2061,28896,28898],{"className":28897},[2190],[2061,28899,28901],{"className":28900,"style":2225},[2194],[2061,28902],{},[2061,28904,2127],{"className":28905},[2396],[2061,28907],{"className":28908,"style":2400},[2231],[2061,28910,28912,28915],{"className":28911},[2169],[2061,28913,2119],{"className":28914},[2169,2170],[2061,28916,28918],{"className":28917},[2181],[2061,28919,28921,28941],{"className":28920},[2185,2186],[2061,28922,28924,28938],{"className":28923},[2190],[2061,28925,28927],{"className":28926,"style":2370},[2194],[2061,28928,28929,28932],{"style":2302},[2061,28930],{"className":28931,"style":2203},[2202],[2061,28933,28935],{"className":28934},[2207,2208,2209,2210],[2061,28936,2134],{"className":28937},[2169,2210],[2061,28939,2218],{"className":28940},[2217],[2061,28942,28944],{"className":28943},[2190],[2061,28945,28947],{"className":28946,"style":2225},[2194],[2061,28948],{},[2061,28950,2137],{"className":28951},[2444],[2061,28953],{"className":28954,"style":2232},[2231],[2061,28956,2099],{"className":28957},[2236],[2061,28959],{"className":28960,"style":2232},[2231],[2061,28962,28964,28968,29025],{"className":28963},[2160],[2061,28965],{"className":28966,"style":28967},[2164],"height:1.3111em;vertical-align:-0.2663em;",[2061,28969,28971,28974],{"className":28970},[2169],[2061,28972,2119],{"className":28973},[2169,2170],[2061,28975,28977],{"className":28976},[2181],[2061,28978,28980,29017],{"className":28979},[2185,2186],[2061,28981,28983,29014],{"className":28982},[2190],[2061,28984,28987,28998],{"className":28985,"style":28986},[2194],"height:1.0448em;",[2061,28988,28989,28992],{"style":4826},[2061,28990],{"className":28991,"style":2203},[2202],[2061,28993,28995],{"className":28994},[2207,2208,2209,2210],[2061,28996,2123],{"className":28997},[2169,2210],[2061,28999,29001,29004],{"style":29000},"top:-3.2198em;margin-right:0.05em;",[2061,29002],{"className":29003,"style":2203},[2202],[2061,29005,29007],{"className":29006},[2207,2208,2209,2210],[2061,29008,29010],{"className":29009},[2169,2210],[2061,29011,29013],{"className":29012},[2169,2210],"1\u002F2",[2061,29015,2218],{"className":29016},[2217],[2061,29018,29020],{"className":29019},[2190],[2061,29021,29023],{"className":29022,"style":4861},[2194],[2061,29024],{},[2061,29026,29028,29031],{"className":29027},[2169],[2061,29029,2119],{"className":29030},[2169,2170],[2061,29032,29034],{"className":29033},[2181],[2061,29035,29037,29071],{"className":29036},[2185,2186],[2061,29038,29040,29068],{"className":29039},[2190],[2061,29041,29043,29054],{"className":29042,"style":28986},[2194],[2061,29044,29045,29048],{"style":4826},[2061,29046],{"className":29047,"style":2203},[2202],[2061,29049,29051],{"className":29050},[2207,2208,2209,2210],[2061,29052,2134],{"className":29053},[2169,2210],[2061,29055,29056,29059],{"style":29000},[2061,29057],{"className":29058,"style":2203},[2202],[2061,29060,29062],{"className":29061},[2207,2208,2209,2210],[2061,29063,29065],{"className":29064},[2169,2210],[2061,29066,29013],{"className":29067},[2169,2210],[2061,29069,2218],{"className":29070},[2217],[2061,29072,29074],{"className":29073},[2190],[2061,29075,29077],{"className":29076,"style":4861},[2194],[2061,29078],{},"，写出预算约束并推导马歇尔需求。",[1808,29081,29082],{},"为什么完全互补品的最优点通常在“折角”而不是切点？",[1808,29084,29085],{},"用一句话解释谢泼德引理为什么等于“价格的边际变化乘以需求量”。",[1808,29087,29088],{},"如果所有价格和收入同时翻倍，需求会不会变？这体现了什么性质？",[1808,29090,29091],{},"构造一个违反传递性的偏好例子，并说明它为什么会造成选择困难。",[1847,29093,29094],{"id":29094},"下一步学习提示",[1798,29096,29097],{},"做完本章后，请至少独立求解一个柯布-道格拉斯、一个完全替代和一个完全互补的需求问题。进入下一章时，把注意力从“最优点在哪里”转到“价格或收入变化后，最优点怎样移动”。",[1798,29099,29100,29103,29104,29106],{},[1865,29101,29102],{},"下一章预告",": 我们将学习如何利用这些工具进行",[1865,29105,24942],{},"——当价格或收入发生变化时，需求和福利会如何变化？斯勒茨基方程将替代效应和收入效应分离，为我们提供深刻的洞见。",{"title":10,"searchDepth":29108,"depth":29108,"links":29109},2,[29110,29111,29112,29118,29123,29129,29130,29134,29140,29145,29150,29151,29152],{"id":1796,"depth":29108,"text":1796},{"id":1834,"depth":29108,"text":1835},{"id":1844,"depth":29108,"text":1845,"children":29113},[29114,29116,29117],{"id":1849,"depth":29115,"text":1850},3,{"id":1937,"depth":29115,"text":1938},{"id":1970,"depth":29115,"text":1971},{"id":7149,"depth":29108,"text":7150,"children":29119},[29120,29121,29122],{"id":7153,"depth":29115,"text":7154},{"id":7432,"depth":29115,"text":7433},{"id":8586,"depth":29115,"text":8587},{"id":11451,"depth":29108,"text":11452,"children":29124},[29125,29126,29127,29128],{"id":11455,"depth":29115,"text":11456},{"id":13216,"depth":29115,"text":13217},{"id":13696,"depth":29115,"text":13697},{"id":14077,"depth":29115,"text":14078},{"id":14089,"depth":29108,"text":14089},{"id":14137,"depth":29108,"text":14138,"children":29131},[29132,29133],{"id":14141,"depth":29115,"text":14142},{"id":20917,"depth":29115,"text":20918},{"id":22878,"depth":29108,"text":22879,"children":29135},[29136,29137,29138,29139],{"id":22882,"depth":29115,"text":22883},{"id":23661,"depth":29115,"text":23662},{"id":24167,"depth":29115,"text":24168},{"id":24494,"depth":29115,"text":24495},{"id":24912,"depth":29108,"text":24913,"children":29141},[29142,29143,29144],{"id":24916,"depth":29115,"text":24917},{"id":24946,"depth":29115,"text":24947},{"id":25979,"depth":29115,"text":25980},{"id":26492,"depth":29108,"text":26493,"children":29146},[29147,29148,29149],{"id":26496,"depth":29115,"text":26497},{"id":26990,"depth":29115,"text":26991},{"id":27525,"depth":29115,"text":27526},{"id":28342,"depth":29108,"text":28343},{"id":28396,"depth":29108,"text":28397},{"id":28445,"depth":29108,"text":28445,"children":29153},[29154,29155,29156],{"id":28576,"depth":29115,"text":28576},{"id":28777,"depth":29115,"text":28777},{"id":29094,"depth":29115,"text":29094},"偏好、效用最大化、支出最小化、对偶理论与需求函数","md",null,{},true,{"title":1554,"description":29157},"hUKZ1i6O_cnHZ-BPUGG1TSNC2dGU4Wa3X3y2c6fWDzk",[29165,29167],{"title":1548,"path":1549,"stem":1550,"description":29166,"children":-1},"高级微观经济学笔记，覆盖消费者理论、福利分析、不确定性、博弈、信息经济学和市场设计。",{"title":1560,"path":1561,"stem":1562,"description":29168,"children":-1},"斯勒茨基方程、替代效应与收入效应、福利变化的精确测量",1785754752746]