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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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Statistics","\u002Fzh\u002Fprob-and-stats\u002F02-statistics","zh\u002Fprob-and-stats\u002F02-statistics",[1685,1691,1697,1703,1709,1715,1721],{"title":1686,"path":1687,"stem":1688,"children":1689},"第六章：抽样分布","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F01-sampling","zh\u002Fprob-and-stats\u002F02-statistics\u002F01-sampling\u002Findex",[1690],{"title":1686,"path":1687,"stem":1688},{"title":1692,"path":1693,"stem":1694,"children":1695},"第七章：区间估计","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F02-interval-estimation","zh\u002Fprob-and-stats\u002F02-statistics\u002F02-interval-estimation\u002Findex",[1696],{"title":1692,"path":1693,"stem":1694},{"title":1698,"path":1699,"stem":1700,"children":1701},"第八章：点估计理论","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F03-point-estimation","zh\u002Fprob-and-stats\u002F02-statistics\u002F03-point-estimation\u002Findex",[1702],{"title":1698,"path":1699,"stem":1700},{"title":1704,"path":1705,"stem":1706,"children":1707},"第九章：点估计方法","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F04-pe-method","zh\u002Fprob-and-stats\u002F02-statistics\u002F04-pe-method\u002Findex",[1708],{"title":1704,"path":1705,"stem":1706},{"title":1710,"path":1711,"stem":1712,"children":1713},"第十章：假设检验原理","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F05-hypothesis","zh\u002Fprob-and-stats\u002F02-statistics\u002F05-hypothesis\u002Findex",[1714],{"title":1710,"path":1711,"stem":1712},{"title":1716,"path":1717,"stem":1718,"children":1719},"第十一章：常用检验方法与选择","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F06-hypothesis-method","zh\u002Fprob-and-stats\u002F02-statistics\u002F06-hypothesis-method\u002Findex",[1720],{"title":1716,"path":1717,"stem":1718},{"title":1722,"path":1723,"stem":1724,"children":1725},"第十二章：Bootstrap 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question",[1798,1799,1800],"p",{},"When prices, income, or policy rules change, how much behaviour changes—and how much money represents the resulting welfare gain or loss?",[1793,1802,1804],{"id":1803},"learning-outcomes","Learning outcomes",[1798,1806,1807],{},"You will be able to:",[1809,1810,1811,1815,1818,1821,1824],"ul",{},[1812,1813,1814],"li",{},"derive a local comparative static from equilibrium or first-order conditions;",[1812,1816,1817],{},"decompose a price response into substitution and income effects;",[1812,1819,1820],{},"calculate compensating variation, equivalent variation, and consumer-surplus change;",[1812,1822,1823],{},"state when these measures coincide and when distribution matters;",[1812,1825,1826],{},"connect a theoretical welfare statistic to evidence and government cost.",[1793,1828,1830],{"id":1829},"_1-comparative-statics-is-a-conditional-derivative","1. Comparative statics is a conditional derivative",[1798,1832,1833],{},"If an optimum or equilibrium is characterised by",[1835,1836,1839],"span",{"className":1837},[1838],"katex-display",[1835,1840,1843,1894],{"className":1841},[1842],"katex",[1835,1844,1847],{"className":1845},[1846],"katex-mathml",[1848,1849,1852],"math",{"xmlns":1850,"display":1851},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML","block",[1853,1854,1855,1889],"semantics",{},[1856,1857,1858,1862,1867,1870,1874,1877,1880,1883,1887],"mrow",{},[1859,1860,1861],"mi",{},"F",[1863,1864,1866],"mo",{"stretchy":1865},"false","(",[1859,1868,1869],{},"z",[1863,1871,1873],{"separator":1872},"true",",",[1859,1875,1876],{},"θ",[1863,1878,1879],{"stretchy":1865},")",[1863,1881,1882],{},"=",[1884,1885,1886],"mn",{},"0",[1863,1888,1873],{"separator":1872},[1890,1891,1893],"annotation",{"encoding":1892},"application\u002Fx-tex","F(z,\\theta)=0,",[1835,1895,1898,1949],{"className":1896,"ariaHidden":1872},[1897],"katex-html",[1835,1899,1902,1907,1913,1917,1921,1925,1930,1934,1938,1942,1946],{"className":1900},[1901],"base",[1835,1903],{"className":1904,"style":1906},[1905],"strut","height:1em;vertical-align:-0.25em;",[1835,1908,1861],{"className":1909,"style":1912},[1910,1911],"mord","mathnormal","margin-right:0.1389em;",[1835,1914,1866],{"className":1915},[1916],"mopen",[1835,1918,1869],{"className":1919,"style":1920},[1910,1911],"margin-right:0.044em;",[1835,1922,1873],{"className":1923},[1924],"mpunct",[1835,1926],{"className":1927,"style":1929},[1928],"mspace","margin-right:0.1667em;",[1835,1931,1876],{"className":1932,"style":1933},[1910,1911],"margin-right:0.0278em;",[1835,1935,1879],{"className":1936},[1937],"mclose",[1835,1939],{"className":1940,"style":1941},[1928],"margin-right:0.2778em;",[1835,1943,1882],{"className":1944},[1945],"mrel",[1835,1947],{"className":1948,"style":1941},[1928],[1835,1950,1952,1956,1959],{"className":1951},[1901],[1835,1953],{"className":1954,"style":1955},[1905],"height:0.8389em;vertical-align:-0.1944em;",[1835,1957,1886],{"className":1958},[1910],[1835,1960,1873],{"className":1961},[1924],[1798,1963,1964,1965,1969],{},"and ",[1966,1967,1968],"code",{},"F_z"," is nonsingular, the implicit function theorem gives:",[1835,1971,1973],{"className":1972},[1838],[1835,1974,1976,2034],{"className":1975},[1842],[1835,1977,1979],{"className":1978},[1846],[1848,1980,1981],{"xmlns":1850,"display":1851},[1853,1982,1983,2031],{},[1856,1984,1985,2001,2003,2006,2020,2027],{},[1986,1987,1988,1995],"mfrac",{},[1856,1989,1990,1993],{},[1859,1991,1992],{},"d",[1859,1994,1869],{},[1856,1996,1997,1999],{},[1859,1998,1992],{},[1859,2000,1876],{},[1863,2002,1882],{},[1863,2004,2005],{},"−",[2007,2008,2009,2011,2013],"msubsup",{},[1859,2010,1861],{},[1859,2012,1869],{},[1856,2014,2015,2017],{},[1863,2016,2005],{},[1884,2018,2019],{},"1",[2021,2022,2023,2025],"msub",{},[1859,2024,1861],{},[1859,2026,1876],{},[1859,2028,2030],{"mathvariant":2029},"normal",".",[1890,2032,2033],{"encoding":1892},"\\frac{dz}{d\\theta}=-F_z^{-1}F_\\theta.",[1835,2035,2037,2137],{"className":2036,"ariaHidden":1872},[1897],[1835,2038,2040,2044,2128,2131,2134],{"className":2039},[1901],[1835,2041],{"className":2042,"style":2043},[1905],"height:2.0574em;vertical-align:-0.686em;",[1835,2045,2047,2051,2125],{"className":2046},[1910],[1835,2048],{"className":2049},[1916,2050],"nulldelimiter",[1835,2052,2054],{"className":2053},[1986],[1835,2055,2059,2116],{"className":2056},[2057,2058],"vlist-t","vlist-t2",[1835,2060,2063,2111],{"className":2061},[2062],"vlist-r",[1835,2064,2068,2085,2096],{"className":2065,"style":2067},[2066],"vlist","height:1.3714em;",[1835,2069,2071,2076],{"style":2070},"top:-2.314em;",[1835,2072],{"className":2073,"style":2075},[2074],"pstrut","height:3em;",[1835,2077,2079,2082],{"className":2078},[1910],[1835,2080,1992],{"className":2081},[1910,1911],[1835,2083,1876],{"className":2084,"style":1933},[1910,1911],[1835,2086,2088,2091],{"style":2087},"top:-3.23em;",[1835,2089],{"className":2090,"style":2075},[2074],[1835,2092],{"className":2093,"style":2095},[2094],"frac-line","border-bottom-width:0.04em;",[1835,2097,2099,2102],{"style":2098},"top:-3.677em;",[1835,2100],{"className":2101,"style":2075},[2074],[1835,2103,2105,2108],{"className":2104},[1910],[1835,2106,1992],{"className":2107},[1910,1911],[1835,2109,1869],{"className":2110,"style":1920},[1910,1911],[1835,2112,2115],{"className":2113},[2114],"vlist-s","​",[1835,2117,2119],{"className":2118},[2062],[1835,2120,2123],{"className":2121,"style":2122},[2066],"height:0.686em;",[1835,2124],{},[1835,2126],{"className":2127},[1937,2050],[1835,2129],{"className":2130,"style":1941},[1928],[1835,2132,1882],{"className":2133},[1945],[1835,2135],{"className":2136,"style":1941},[1928],[1835,2138,2140,2144,2147,2214,2257],{"className":2139},[1901],[1835,2141],{"className":2142,"style":2143},[1905],"height:1.1111em;vertical-align:-0.247em;",[1835,2145,2005],{"className":2146},[1910],[1835,2148,2150,2153],{"className":2149},[1910],[1835,2151,1861],{"className":2152,"style":1912},[1910,1911],[1835,2154,2157],{"className":2155},[2156],"msupsub",[1835,2158,2160,2205],{"className":2159},[2057,2058],[1835,2161,2163,2202],{"className":2162},[2062],[1835,2164,2167,2184],{"className":2165,"style":2166},[2066],"height:0.8641em;",[1835,2168,2170,2174],{"style":2169},"top:-2.453em;margin-left:-0.1389em;margin-right:0.05em;",[1835,2171],{"className":2172,"style":2173},[2074],"height:2.7em;",[1835,2175,2181],{"className":2176},[2177,2178,2179,2180],"sizing","reset-size6","size3","mtight",[1835,2182,1869],{"className":2183,"style":1920},[1910,1911,2180],[1835,2185,2187,2190],{"style":2186},"top:-3.113em;margin-right:0.05em;",[1835,2188],{"className":2189,"style":2173},[2074],[1835,2191,2193],{"className":2192},[2177,2178,2179,2180],[1835,2194,2196,2199],{"className":2195},[1910,2180],[1835,2197,2005],{"className":2198},[1910,2180],[1835,2200,2019],{"className":2201},[1910,2180],[1835,2203,2115],{"className":2204},[2114],[1835,2206,2208],{"className":2207},[2062],[1835,2209,2212],{"className":2210,"style":2211},[2066],"height:0.247em;",[1835,2213],{},[1835,2215,2217,2220],{"className":2216},[1910],[1835,2218,1861],{"className":2219,"style":1912},[1910,1911],[1835,2221,2223],{"className":2222},[2156],[1835,2224,2226,2248],{"className":2225},[2057,2058],[1835,2227,2229,2245],{"className":2228},[2062],[1835,2230,2233],{"className":2231,"style":2232},[2066],"height:0.3361em;",[1835,2234,2236,2239],{"style":2235},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[1835,2237],{"className":2238,"style":2173},[2074],[1835,2240,2242],{"className":2241},[2177,2178,2179,2180],[1835,2243,1876],{"className":2244,"style":1933},[1910,1911,2180],[1835,2246,2115],{"className":2247},[2114],[1835,2249,2251],{"className":2250},[2062],[1835,2252,2255],{"className":2253,"style":2254},[2066],"height:0.15em;",[1835,2256],{},[1835,2258,2030],{"className":2259},[1910],[1798,2261,2262,2263,2267],{},"This is a ",[2264,2265,2266],"strong",{},"local"," result. Its sign is meaningful only after stating:",[1809,2269,2270,2276,2279,2282],{},[1812,2271,2272,2273,2275],{},"what ",[1966,2274,1876],{}," changes;",[1812,2277,2278],{},"what remains fixed;",[1812,2280,2281],{},"which optimum\u002Fequilibrium is followed;",[1812,2283,2284],{},"whether a corner, discontinuity, or equilibrium switch is possible.",[2286,2287,2289],"tip",{"title":2288},"Do not differentiate before diagnosing","A price ceiling can change both a price and the allocation rule. A platform ranking rule can change demand faced by every seller. Write the post-change choice set first; then differentiate the correct system.",[1793,2291,2293],{"id":2292},"_2-slutsky-decomposition","2. Slutsky decomposition",[1798,2295,2296],{},"Marshallian demand can be written as Hicksian demand evaluated at attained utility:",[1835,2298,2300],{"className":2299},[1838],[1835,2301,2303,2366],{"className":2302},[1842],[1835,2304,2306],{"className":2305},[1846],[1848,2307,2308],{"xmlns":1850,"display":1851},[1853,2309,2310,2363],{},[1856,2311,2312,2320,2322,2324,2326,2329,2331,2333,2340,2342,2344,2346,2349,2351,2353,2355,2357,2359,2361],{},[2021,2313,2314,2317],{},[1859,2315,2316],{},"x",[1859,2318,2319],{},"i",[1863,2321,1866],{"stretchy":1865},[1859,2323,1798],{},[1863,2325,1873],{"separator":1872},[1859,2327,2328],{},"m",[1863,2330,1879],{"stretchy":1865},[1863,2332,1882],{},[2021,2334,2335,2338],{},[1859,2336,2337],{},"h",[1859,2339,2319],{},[1863,2341,1866],{"stretchy":1865},[1859,2343,1798],{},[1863,2345,1873],{"separator":1872},[1859,2347,2348],{},"v",[1863,2350,1866],{"stretchy":1865},[1859,2352,1798],{},[1863,2354,1873],{"separator":1872},[1859,2356,2328],{},[1863,2358,1879],{"stretchy":1865},[1863,2360,1879],{"stretchy":1865},[1859,2362,2030],{"mathvariant":2029},[1890,2364,2365],{"encoding":1892},"x_i(p,m)=h_i(p,v(p,m)).",[1835,2367,2369,2444],{"className":2368,"ariaHidden":1872},[1897],[1835,2370,2372,2375,2417,2420,2423,2426,2429,2432,2435,2438,2441],{"className":2371},[1901],[1835,2373],{"className":2374,"style":1906},[1905],[1835,2376,2378,2381],{"className":2377},[1910],[1835,2379,2316],{"className":2380},[1910,1911],[1835,2382,2384],{"className":2383},[2156],[1835,2385,2387,2409],{"className":2386},[2057,2058],[1835,2388,2390,2406],{"className":2389},[2062],[1835,2391,2394],{"className":2392,"style":2393},[2066],"height:0.3117em;",[1835,2395,2397,2400],{"style":2396},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1835,2398],{"className":2399,"style":2173},[2074],[1835,2401,2403],{"className":2402},[2177,2178,2179,2180],[1835,2404,2319],{"className":2405},[1910,1911,2180],[1835,2407,2115],{"className":2408},[2114],[1835,2410,2412],{"className":2411},[2062],[1835,2413,2415],{"className":2414,"style":2254},[2066],[1835,2416],{},[1835,2418,1866],{"className":2419},[1916],[1835,2421,1798],{"className":2422},[1910,1911],[1835,2424,1873],{"className":2425},[1924],[1835,2427],{"className":2428,"style":1929},[1928],[1835,2430,2328],{"className":2431},[1910,1911],[1835,2433,1879],{"className":2434},[1937],[1835,2436],{"className":2437,"style":1941},[1928],[1835,2439,1882],{"className":2440},[1945],[1835,2442],{"className":2443,"style":1941},[1928],[1835,2445,2447,2450,2490,2493,2496,2499,2502,2506,2509,2512,2515,2518,2521,2525],{"className":2446},[1901],[1835,2448],{"className":2449,"style":1906},[1905],[1835,2451,2453,2456],{"className":2452},[1910],[1835,2454,2337],{"className":2455},[1910,1911],[1835,2457,2459],{"className":2458},[2156],[1835,2460,2462,2482],{"className":2461},[2057,2058],[1835,2463,2465,2479],{"className":2464},[2062],[1835,2466,2468],{"className":2467,"style":2393},[2066],[1835,2469,2470,2473],{"style":2396},[1835,2471],{"className":2472,"style":2173},[2074],[1835,2474,2476],{"className":2475},[2177,2178,2179,2180],[1835,2477,2319],{"className":2478},[1910,1911,2180],[1835,2480,2115],{"className":2481},[2114],[1835,2483,2485],{"className":2484},[2062],[1835,2486,2488],{"className":2487,"style":2254},[2066],[1835,2489],{},[1835,2491,1866],{"className":2492},[1916],[1835,2494,1798],{"className":2495},[1910,1911],[1835,2497,1873],{"className":2498},[1924],[1835,2500],{"className":2501,"style":1929},[1928],[1835,2503,2348],{"className":2504,"style":2505},[1910,1911],"margin-right:0.0359em;",[1835,2507,1866],{"className":2508},[1916],[1835,2510,1798],{"className":2511},[1910,1911],[1835,2513,1873],{"className":2514},[1924],[1835,2516],{"className":2517,"style":1929},[1928],[1835,2519,2328],{"className":2520},[1910,1911],[1835,2522,2524],{"className":2523},[1937],"))",[1835,2526,2030],{"className":2527},[1910],[1798,2529,2530,2531,2534],{},"Differentiating with respect to price ",[1966,2532,2533],{},"p_j"," gives:",[1835,2536,2538],{"className":2537},[1838],[1835,2539,2541,2629],{"className":2540},[1842],[1835,2542,2544],{"className":2543},[1846],[1848,2545,2546],{"xmlns":1850,"display":1851},[1853,2547,2548,2626],{},[1856,2549,2550,2574,2576,2598,2600,2606,2624],{},[1986,2551,2552,2563],{},[1856,2553,2554,2557],{},[1859,2555,2556],{"mathvariant":2029},"∂",[2021,2558,2559,2561],{},[1859,2560,2316],{},[1859,2562,2319],{},[1856,2564,2565,2567],{},[1859,2566,2556],{"mathvariant":2029},[2021,2568,2569,2571],{},[1859,2570,1798],{},[1859,2572,2573],{},"j",[1863,2575,1882],{},[1986,2577,2578,2588],{},[1856,2579,2580,2582],{},[1859,2581,2556],{"mathvariant":2029},[2021,2583,2584,2586],{},[1859,2585,2337],{},[1859,2587,2319],{},[1856,2589,2590,2592],{},[1859,2591,2556],{"mathvariant":2029},[2021,2593,2594,2596],{},[1859,2595,1798],{},[1859,2597,2573],{},[1863,2599,2005],{},[2021,2601,2602,2604],{},[1859,2603,2316],{},[1859,2605,2573],{},[1986,2607,2608,2618],{},[1856,2609,2610,2612],{},[1859,2611,2556],{"mathvariant":2029},[2021,2613,2614,2616],{},[1859,2615,2316],{},[1859,2617,2319],{},[1856,2619,2620,2622],{},[1859,2621,2556],{"mathvariant":2029},[1859,2623,2328],{},[1859,2625,2030],{"mathvariant":2029},[1890,2627,2628],{"encoding":1892},"\\frac{\\partial x_i}{\\partial p_j}\n=\\frac{\\partial h_i}{\\partial p_j}\n-x_j\\frac{\\partial x_i}{\\partial m}.",[1835,2630,2632,2794,2953],{"className":2631,"ariaHidden":1872},[1897],[1835,2633,2635,2639,2785,2788,2791],{"className":2634},[1901],[1835,2636],{"className":2637,"style":2638},[1905],"height:2.3435em;vertical-align:-0.9721em;",[1835,2640,2642,2645,2782],{"className":2641},[1910],[1835,2643],{"className":2644},[1916,2050],[1835,2646,2648],{"className":2647},[1986],[1835,2649,2651,2773],{"className":2650},[2057,2058],[1835,2652,2654,2770],{"className":2653},[2062],[1835,2655,2657,2711,2719],{"className":2656,"style":2067},[2066],[1835,2658,2659,2662],{"style":2070},[1835,2660],{"className":2661,"style":2075},[2074],[1835,2663,2665,2669],{"className":2664},[1910],[1835,2666,2556],{"className":2667,"style":2668},[1910],"margin-right:0.0556em;",[1835,2670,2672,2675],{"className":2671},[1910],[1835,2673,1798],{"className":2674},[1910,1911],[1835,2676,2678],{"className":2677},[2156],[1835,2679,2681,2702],{"className":2680},[2057,2058],[1835,2682,2684,2699],{"className":2683},[2062],[1835,2685,2687],{"className":2686,"style":2393},[2066],[1835,2688,2689,2692],{"style":2396},[1835,2690],{"className":2691,"style":2173},[2074],[1835,2693,2695],{"className":2694},[2177,2178,2179,2180],[1835,2696,2573],{"className":2697,"style":2698},[1910,1911,2180],"margin-right:0.0572em;",[1835,2700,2115],{"className":2701},[2114],[1835,2703,2705],{"className":2704},[2062],[1835,2706,2709],{"className":2707,"style":2708},[2066],"height:0.2861em;",[1835,2710],{},[1835,2712,2713,2716],{"style":2087},[1835,2714],{"className":2715,"style":2075},[2074],[1835,2717],{"className":2718,"style":2095},[2094],[1835,2720,2721,2724],{"style":2098},[1835,2722],{"className":2723,"style":2075},[2074],[1835,2725,2727,2730],{"className":2726},[1910],[1835,2728,2556],{"className":2729,"style":2668},[1910],[1835,2731,2733,2736],{"className":2732},[1910],[1835,2734,2316],{"className":2735},[1910,1911],[1835,2737,2739],{"className":2738},[2156],[1835,2740,2742,2762],{"className":2741},[2057,2058],[1835,2743,2745,2759],{"className":2744},[2062],[1835,2746,2748],{"className":2747,"style":2393},[2066],[1835,2749,2750,2753],{"style":2396},[1835,2751],{"className":2752,"style":2173},[2074],[1835,2754,2756],{"className":2755},[2177,2178,2179,2180],[1835,2757,2319],{"className":2758},[1910,1911,2180],[1835,2760,2115],{"className":2761},[2114],[1835,2763,2765],{"className":2764},[2062],[1835,2766,2768],{"className":2767,"style":2254},[2066],[1835,2769],{},[1835,2771,2115],{"className":2772},[2114],[1835,2774,2776],{"className":2775},[2062],[1835,2777,2780],{"className":2778,"style":2779},[2066],"height:0.9721em;",[1835,2781],{},[1835,2783],{"className":2784},[1937,2050],[1835,2786],{"className":2787,"style":1941},[1928],[1835,2789,1882],{"className":2790},[1945],[1835,2792],{"className":2793,"style":1941},[1928],[1835,2795,2797,2800,2942,2946,2950],{"className":2796},[1901],[1835,2798],{"className":2799,"style":2638},[1905],[1835,2801,2803,2806,2939],{"className":2802},[1910],[1835,2804],{"className":2805},[1916,2050],[1835,2807,2809],{"className":2808},[1986],[1835,2810,2812,2931],{"className":2811},[2057,2058],[1835,2813,2815,2928],{"className":2814},[2062],[1835,2816,2818,2869,2877],{"className":2817,"style":2067},[2066],[1835,2819,2820,2823],{"style":2070},[1835,2821],{"className":2822,"style":2075},[2074],[1835,2824,2826,2829],{"className":2825},[1910],[1835,2827,2556],{"className":2828,"style":2668},[1910],[1835,2830,2832,2835],{"className":2831},[1910],[1835,2833,1798],{"className":2834},[1910,1911],[1835,2836,2838],{"className":2837},[2156],[1835,2839,2841,2861],{"className":2840},[2057,2058],[1835,2842,2844,2858],{"className":2843},[2062],[1835,2845,2847],{"className":2846,"style":2393},[2066],[1835,2848,2849,2852],{"style":2396},[1835,2850],{"className":2851,"style":2173},[2074],[1835,2853,2855],{"className":2854},[2177,2178,2179,2180],[1835,2856,2573],{"className":2857,"style":2698},[1910,1911,2180],[1835,2859,2115],{"className":2860},[2114],[1835,2862,2864],{"className":2863},[2062],[1835,2865,2867],{"className":2866,"style":2708},[2066],[1835,2868],{},[1835,2870,2871,2874],{"style":2087},[1835,2872],{"className":2873,"style":2075},[2074],[1835,2875],{"className":2876,"style":2095},[2094],[1835,2878,2879,2882],{"style":2098},[1835,2880],{"className":2881,"style":2075},[2074],[1835,2883,2885,2888],{"className":2884},[1910],[1835,2886,2556],{"className":2887,"style":2668},[1910],[1835,2889,2891,2894],{"className":2890},[1910],[1835,2892,2337],{"className":2893},[1910,1911],[1835,2895,2897],{"className":2896},[2156],[1835,2898,2900,2920],{"className":2899},[2057,2058],[1835,2901,2903,2917],{"className":2902},[2062],[1835,2904,2906],{"className":2905,"style":2393},[2066],[1835,2907,2908,2911],{"style":2396},[1835,2909],{"className":2910,"style":2173},[2074],[1835,2912,2914],{"className":2913},[2177,2178,2179,2180],[1835,2915,2319],{"className":2916},[1910,1911,2180],[1835,2918,2115],{"className":2919},[2114],[1835,2921,2923],{"className":2922},[2062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let ",[1966,3495,3496],{},"p_x"," rise from 1 to 4.",[1798,3499,3500],{},"Marshallian demand is:",[1835,3502,3504],{"className":3503},[1838],[1835,3505,3507,3562],{"className":3506},[1842],[1835,3508,3510],{"className":3509},[1846],[1848,3511,3512],{"xmlns":1850,"display":1851},[1853,3513,3514,3559],{},[1856,3515,3516,3518,3520,3535,3537,3539,3541,3543,3557],{},[1859,3517,2316],{},[1863,3519,1882],{},[1986,3521,3522,3524],{},[1859,3523,2328],{},[1856,3525,3526,3529],{},[1884,3527,3528],{},"2",[2021,3530,3531,3533],{},[1859,3532,1798],{},[1859,3534,2316],{},[1863,3536,1873],{"separator":1872},[1928,3538],{"width":3226},[1859,3540,3208],{},[1863,3542,1882],{},[1986,3544,3545,3547],{},[1859,3546,2328],{},[1856,3548,3549,3551],{},[1884,3550,3528],{},[2021,3552,3553,3555],{},[1859,3554,1798],{},[1859,3556,3208],{},[1859,3558,2030],{"mathvariant":2029},[1890,3560,3561],{"encoding":1892},"x=\\frac{m}{2p_x},\\qquad y=\\frac{m}{2p_y}.",[1835,3563,3565,3584,3716],{"className":3564,"ariaHidden":1872},[1897],[1835,3566,3568,3572,3575,3578,3581],{"className":3567},[1901],[1835,3569],{"className":3570,"style":3571},[1905],"height:0.4306em;",[1835,3573,2316],{"className":3574},[1910,1911],[1835,3576],{"className":3577,"style":1941},[1928],[1835,3579,1882],{"className":3580},[1945],[1835,3582],{"className":3583,"style":1941},[1928],[1835,3585,3587,3591,3695,3698,3701,3704,3707,3710,3713],{"className":3586},[1901],[1835,3588],{"className":3589,"style":3590},[1905],"height:1.988em;vertical-align:-0.8804em;",[1835,3592,3594,3597,3692],{"className":3593},[1910],[1835,3595],{"className":3596},[1916,2050],[1835,3598,3600],{"className":3599},[1986],[1835,3601,3603,3683],{"className":3602},[2057,2058],[1835,3604,3606,3680],{"className":3605},[2062],[1835,3607,3610,3661,3669],{"className":3608,"style":3609},[2066],"height:1.1076em;",[1835,3611,3612,3615],{"style":2070},[1835,3613],{"className":3614,"style":2075},[2074],[1835,3616,3618,3621],{"className":3617},[1910],[1835,3619,3528],{"className":3620},[1910],[1835,3622,3624,3627],{"className":3623},[1910],[1835,3625,1798],{"className":3626},[1910,1911],[1835,3628,3630],{"className":3629},[2156],[1835,3631,3633,3653],{"className":3632},[2057,2058],[1835,3634,3636,3650],{"className":3635},[2062],[1835,3637,3639],{"className":3638,"style":3447},[2066],[1835,3640,3641,3644],{"style":2396},[1835,3642],{"className":3643,"style":2173},[2074],[1835,3645,3647],{"className":3646},[2177,2178,2179,2180],[1835,3648,2316],{"className":3649},[1910,1911,2180],[1835,3651,2115],{"className":3652},[2114],[1835,3654,3656],{"className":3655},[2062],[1835,3657,3659],{"className":3658,"style":2254},[2066],[1835,3660],{},[1835,3662,3663,3666],{"style":2087},[1835,3664],{"className":3665,"style":2075},[2074],[1835,3667],{"className":3668,"style":2095},[2094],[1835,3670,3671,3674],{"style":2098},[1835,3672],{"className":3673,"style":2075},[2074],[1835,3675,3677],{"className":3676},[1910],[1835,3678,2328],{"className":3679},[1910,1911],[1835,3681,2115],{"className":3682},[2114],[1835,3684,3686],{"className":3685},[2062],[1835,3687,3690],{"className":3688,"style":3689},[2066],"height:0.8804em;",[1835,3691],{},[1835,3693],{"className":3694},[1937,2050],[1835,3696,1873],{"className":3697},[1924],[1835,3699],{"className":3700,"style":3382},[1928],[1835,3702],{"className":3703,"style":1929},[1928],[1835,3705,3208],{"className":3706,"style":2505},[1910,1911],[1835,3708],{"className":3709,"style":1941},[1928],[1835,3711,1882],{"className":3712},[1945],[1835,3714],{"className":3715,"style":1941},[1928],[1835,3717,3719,3723,3825],{"className":3718},[1901],[1835,3720],{"className":3721,"style":3722},[1905],"height:2.0797em;vertical-align:-0.9721em;",[1835,3724,3726,3729,3822],{"className":3725},[1910],[1835,3727],{"className":3728},[1916,2050],[1835,3730,3732],{"className":3731},[1986],[1835,3733,3735,3814],{"className":3734},[2057,2058],[1835,3736,3738,3811],{"className":3737},[2062],[1835,3739,3741,3792,3800],{"className":3740,"style":3609},[2066],[1835,3742,3743,3746],{"style":2070},[1835,3744],{"className":3745,"style":2075},[2074],[1835,3747,3749,3752],{"className":3748},[1910],[1835,3750,3528],{"className":3751},[1910],[1835,3753,3755,3758],{"className":3754},[1910],[1835,3756,1798],{"className":3757},[1910,1911],[1835,3759,3761],{"className":3760},[2156],[1835,3762,3764,3784],{"className":3763},[2057,2058],[1835,3765,3767,3781],{"className":3766},[2062],[1835,3768,3770],{"className":3769,"style":3447},[2066],[1835,3771,3772,3775],{"style":2396},[1835,3773],{"className":3774,"style":2173},[2074],[1835,3776,3778],{"className":3777},[2177,2178,2179,2180],[1835,3779,3208],{"className":3780,"style":2505},[1910,1911,2180],[1835,3782,2115],{"className":3783},[2114],[1835,3785,3787],{"className":3786},[2062],[1835,3788,3790],{"className":3789,"style":2708},[2066],[1835,3791],{},[1835,3793,3794,3797],{"style":2087},[1835,3795],{"className":3796,"style":2075},[2074],[1835,3798],{"className":3799,"style":2095},[2094],[1835,3801,3802,3805],{"style":2098},[1835,3803],{"className":3804,"style":2075},[2074],[1835,3806,3808],{"className":3807},[1910],[1835,3809,2328],{"className":3810},[1910,1911],[1835,3812,2115],{"className":3813},[2114],[1835,3815,3817],{"className":3816},[2062],[1835,3818,3820],{"className":3819,"style":2779},[2066],[1835,3821],{},[1835,3823],{"className":3824},[1937,2050],[1835,3826,2030],{"className":3827},[1910],[3108,3829,3830,3848],{},[3111,3831,3832],{},[3114,3833,3834,3837,3842,3846],{},[3117,3835,3836],{},"Environment",[3117,3838,3840],{"align":3839},"right",[1966,3841,2316],{},[3117,3843,3844],{"align":3839},[1966,3845,3208],{},[3117,3847,3152],{"align":3839},[3127,3849,3850,3865],{},[3114,3851,3852,3858,3861,3863],{},[3132,3853,3854,3855],{},"old ",[1966,3856,3857],{},"(1,1,100)",[3132,3859,3860],{"align":3839},"50",[3132,3862,3860],{"align":3839},[3132,3864,3860],{"align":3839},[3114,3866,3867,3873,3876,3878],{},[3132,3868,3869,3870],{},"new ",[1966,3871,3872],{},"(4,1,100)",[3132,3874,3875],{"align":3839},"12.5",[3132,3877,3860],{"align":3839},[3132,3879,3880],{"align":3839},"25",[1798,3882,3883,3884,3886],{},"Hicksian demand for ",[1966,3885,2316],{}," is:",[1835,3888,3890],{"className":3889},[1838],[1835,3891,3893,3943],{"className":3892},[1842],[1835,3894,3896],{"className":3895},[1846],[1848,3897,3898],{"xmlns":1850,"display":1851},[1853,3899,3900,3940],{},[1856,3901,3902,3908,3910,3912,3914,3916,3918,3920,3922,3938],{},[2021,3903,3904,3906],{},[1859,3905,2337],{},[1859,3907,2316],{},[1863,3909,1866],{"stretchy":1865},[1859,3911,1798],{},[1863,3913,1873],{"separator":1872},[1859,3915,3199],{},[1863,3917,1879],{"stretchy":1865},[1863,3919,1882],{},[1859,3921,3199],{},[3214,3923,3924],{},[1986,3925,3926,3932],{},[2021,3927,3928,3930],{},[1859,3929,1798],{},[1859,3931,3208],{},[2021,3933,3934,3936],{},[1859,3935,1798],{},[1859,3937,2316],{},[1859,3939,2030],{"mathvariant":2029},[1890,3941,3942],{"encoding":1892},"h_x(p,u)=u\\sqrt{\\frac{p_y}{p_x}}.",[1835,3944,3946,4019],{"className":3945,"ariaHidden":1872},[1897],[1835,3947,3949,3952,3992,3995,3998,4001,4004,4007,4010,4013,4016],{"className":3948},[1901],[1835,3950],{"className":3951,"style":1906},[1905],[1835,3953,3955,3958],{"className":3954},[1910],[1835,3956,2337],{"className":3957},[1910,1911],[1835,3959,3961],{"className":3960},[2156],[1835,3962,3964,3984],{"className":3963},[2057,2058],[1835,3965,3967,3981],{"className":3966},[2062],[1835,3968,3970],{"className":3969,"style":3447},[2066],[1835,3971,3972,3975],{"style":2396},[1835,3973],{"className":3974,"style":2173},[2074],[1835,3976,3978],{"className":3977},[2177,2178,2179,2180],[1835,3979,2316],{"className":3980},[1910,1911,2180],[1835,3982,2115],{"className":3983},[2114],[1835,3985,3987],{"className":3986},[2062],[1835,3988,3990],{"className":3989,"style":2254},[2066],[1835,3991],{},[1835,3993,1866],{"className":3994},[1916],[1835,3996,1798],{"className":3997},[1910,1911],[1835,3999,1873],{"className":4000},[1924],[1835,4002],{"className":4003,"style":1929},[1928],[1835,4005,3199],{"className":4006},[1910,1911],[1835,4008,1879],{"className":4009},[1937],[1835,4011],{"className":4012,"style":1941},[1928],[1835,4014,1882],{"className":4015},[1945],[1835,4017],{"className":4018,"style":1941},[1928],[1835,4020,4022,4026,4029,4219],{"className":4021},[1901],[1835,4023],{"className":4024,"style":4025},[1905],"height:2.44em;vertical-align:-0.9926em;",[1835,4027,3199],{"className":4028},[1910,1911],[1835,4030,4032],{"className":4031},[1910,3312],[1835,4033,4035,4210],{"className":4034},[2057,2058],[1835,4036,4038,4207],{"className":4037},[2062],[1835,4039,4042,4190],{"className":4040,"style":4041},[2066],"height:1.4474em;",[1835,4043,4046,4050],{"className":4044,"style":4045},[3326],"top:-4.4em;",[1835,4047],{"className":4048,"style":4049},[2074],"height:4.4em;",[1835,4051,4054],{"className":4052,"style":4053},[1910],"padding-left:1em;",[1835,4055,4057,4060,4187],{"className":4056},[1910],[1835,4058],{"className":4059},[1916,2050],[1835,4061,4063],{"className":4062},[1986],[1835,4064,4066,4179],{"className":4065},[2057,2058],[1835,4067,4069,4176],{"className":4068},[2062],[1835,4070,4072,4120,4128],{"className":4071,"style":3609},[2066],[1835,4073,4074,4077],{"style":2070},[1835,4075],{"className":4076,"style":2075},[2074],[1835,4078,4080],{"className":4079},[1910],[1835,4081,4083,4086],{"className":4082},[1910],[1835,4084,1798],{"className":4085},[1910,1911],[1835,4087,4089],{"className":4088},[2156],[1835,4090,4092,4112],{"className":4091},[2057,2058],[1835,4093,4095,4109],{"className":4094},[2062],[1835,4096,4098],{"className":4097,"style":3447},[2066],[1835,4099,4100,4103],{"style":2396},[1835,4101],{"className":4102,"style":2173},[2074],[1835,4104,4106],{"className":4105},[2177,2178,2179,2180],[1835,4107,2316],{"className":4108},[1910,1911,2180],[1835,4110,2115],{"className":4111},[2114],[1835,4113,4115],{"className":4114},[2062],[1835,4116,4118],{"className":4117,"style":2254},[2066],[1835,4119],{},[1835,4121,4122,4125],{"style":2087},[1835,4123],{"className":4124,"style":2075},[2074],[1835,4126],{"className":4127,"style":2095},[2094],[1835,4129,4130,4133],{"style":2098},[1835,4131],{"className":4132,"style":2075},[2074],[1835,4134,4136],{"className":4135},[1910],[1835,4137,4139,4142],{"className":4138},[1910],[1835,4140,1798],{"className":4141},[1910,1911],[1835,4143,4145],{"className":4144},[2156],[1835,4146,4148,4168],{"className":4147},[2057,2058],[1835,4149,4151,4165],{"className":4150},[2062],[1835,4152,4154],{"className":4153,"style":3447},[2066],[1835,4155,4156,4159],{"style":2396},[1835,4157],{"className":4158,"style":2173},[2074],[1835,4160,4162],{"className":4161},[2177,2178,2179,2180],[1835,4163,3208],{"className":4164,"style":2505},[1910,1911,2180],[1835,4166,2115],{"className":4167},[2114],[1835,4169,4171],{"className":4170},[2062],[1835,4172,4174],{"className":4173,"style":2708},[2066],[1835,4175],{},[1835,4177,2115],{"className":4178},[2114],[1835,4180,4182],{"className":4181},[2062],[1835,4183,4185],{"className":4184,"style":3689},[2066],[1835,4186],{},[1835,4188],{"className":4189},[1937,2050],[1835,4191,4193,4196],{"style":4192},"top:-3.4074em;",[1835,4194],{"className":4195,"style":4049},[2074],[1835,4197,4200],{"className":4198,"style":4199},[3350],"min-width:1.02em;height:2.48em;",[3353,4201,4204],{"xmlns":3355,"width":3356,"height":4202,"viewBox":4203,"preserveAspectRatio":3359},"2.48em","0 0 400000 2592",[3361,4205],{"d":4206},"M424,2478\nc-1.3,-0.7,-38.5,-172,-111.5,-514c-73,-342,-109.8,-513.3,-110.5,-514\nc0,-2,-10.7,14.3,-32,49c-4.7,7.3,-9.8,15.7,-15.5,25c-5.7,9.3,-9.8,16,-12.5,20\ns-5,7,-5,7c-4,-3.3,-8.3,-7.7,-13,-13s-13,-13,-13,-13s76,-122,76,-122s77,-121,77,-121\ns209,968,209,968c0,-2,84.7,-361.7,254,-1079c169.3,-717.3,254.7,-1077.7,256,-1081\nl0 -0c4,-6.7,10,-10,18,-10 H400000\nv40H1014.6\ns-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185\nc-2,6,-10,9,-24,9\nc-8,0,-12,-0.7,-12,-2z M1001 80\nh400000v40h-400000z",[1835,4208,2115],{"className":4209},[2114],[1835,4211,4213],{"className":4212},[2062],[1835,4214,4217],{"className":4215,"style":4216},[2066],"height:0.9926em;",[1835,4218],{},[1835,4220,2030],{"className":4221},[1910],[1798,4223,4224,4225,4228,4229,4232],{},"At new prices but old utility, ",[1966,4226,4227],{},"h_x=25",". The ",[2264,4230,4231],{},"Hicks decomposition"," of the finite change is therefore:",[1809,4234,4235,4246,4255],{},[1812,4236,4237,4238,4241,4242,4245],{},"substitution: ",[1966,4239,4240],{},"50 → 25",", or ",[1966,4243,4244],{},"−25",";",[1812,4247,4248,4249,4241,4252,4245],{},"purchasing-power effect: ",[1966,4250,4251],{},"25 → 12.5",[1966,4253,4254],{},"−12.5",[1812,4256,4257,4258,2030],{},"total: ",[1966,4259,4260],{},"−37.5",[1798,4262,4263],{},"The differential Slutsky equation is exact for infinitesimal changes. For a large change, Hicks and Slutsky finite compensation use different reference rules and need not produce identical intermediate bundles.",[1793,4265,4267],{"id":4266},"_4-put-a-money-value-on-the-welfare-change","4. Put a money value on the welfare change",[1798,4269,4270,4271,4274,4275,4278,4279,4282],{},"For a price increase from ",[1966,4272,4273],{},"p⁰"," to ",[1966,4276,4277],{},"p¹",", define welfare ",[2264,4280,4281],{},"losses as positive numbers",":",[1835,4284,4286],{"className":4285},[1838],[1835,4287,4289,4337],{"className":4288},[1842],[1835,4290,4292],{"className":4291},[1846],[1848,4293,4294],{"xmlns":1850,"display":1851},[1853,4295,4296,4334],{},[1856,4297,4298,4301,4304,4306,4309,4311,4318,4320,4326,4328,4330,4332],{},[1859,4299,4300],{},"C",[1859,4302,4303],{},"V",[1863,4305,1882],{},[1859,4307,4308],{},"e",[1863,4310,1866],{"stretchy":1865},[4312,4313,4314,4316],"msup",{},[1859,4315,1798],{},[1884,4317,2019],{},[1863,4319,1873],{"separator":1872},[4312,4321,4322,4324],{},[1859,4323,3199],{},[1884,4325,1886],{},[1863,4327,1879],{"stretchy":1865},[1863,4329,2005],{},[1859,4331,2328],{},[1863,4333,1873],{"separator":1872},[1890,4335,4336],{"encoding":1892},"CV=e(p^1,u^0)-m,",[1835,4338,4340,4363,4452],{"className":4339,"ariaHidden":1872},[1897],[1835,4341,4343,4347,4351,4354,4357,4360],{"className":4342},[1901],[1835,4344],{"className":4345,"style":4346},[1905],"height:0.6833em;",[1835,4348,4300],{"className":4349,"style":4350},[1910,1911],"margin-right:0.0715em;",[1835,4352,4303],{"className":4353,"style":2945},[1910,1911],[1835,4355],{"className":4356,"style":1941},[1928],[1835,4358,1882],{"className":4359},[1945],[1835,4361],{"className":4362,"style":1941},[1928],[1835,4364,4366,4370,4373,4376,4405,4408,4411,4440,4443,4446,4449],{"className":4365},[1901],[1835,4367],{"className":4368,"style":4369},[1905],"height:1.1141em;vertical-align:-0.25em;",[1835,4371,4308],{"className":4372},[1910,1911],[1835,4374,1866],{"className":4375},[1916],[1835,4377,4379,4382],{"className":4378},[1910],[1835,4380,1798],{"className":4381},[1910,1911],[1835,4383,4385],{"className":4384},[2156],[1835,4386,4388],{"className":4387},[2057],[1835,4389,4391],{"className":4390},[2062],[1835,4392,4394],{"className":4393,"style":2166},[2066],[1835,4395,4396,4399],{"style":2186},[1835,4397],{"className":4398,"style":2173},[2074],[1835,4400,4402],{"className":4401},[2177,2178,2179,2180],[1835,4403,2019],{"className":4404},[1910,2180],[1835,4406,1873],{"className":4407},[1924],[1835,4409],{"className":4410,"style":1929},[1928],[1835,4412,4414,4417],{"className":4413},[1910],[1835,4415,3199],{"className":4416},[1910,1911],[1835,4418,4420],{"className":4419},[2156],[1835,4421,4423],{"className":4422},[2057],[1835,4424,4426],{"className":4425},[2062],[1835,4427,4429],{"className":4428,"style":2166},[2066],[1835,4430,4431,4434],{"style":2186},[1835,4432],{"className":4433,"style":2173},[2074],[1835,4435,4437],{"className":4436},[2177,2178,2179,2180],[1835,4438,1886],{"className":4439},[1910,2180],[1835,4441,1879],{"className":4442},[1937],[1835,4444],{"className":4445,"style":2945},[1928],[1835,4447,2005],{"className":4448},[2949],[1835,4450],{"className":4451,"style":2945},[1928],[1835,4453,4455,4459,4462],{"className":4454},[1901],[1835,4456],{"className":4457,"style":4458},[1905],"height:0.625em;vertical-align:-0.1944em;",[1835,4460,2328],{"className":4461},[1910,1911],[1835,4463,1873],{"className":4464},[1924],[1798,4466,4467],{},"the compensation required after the change, and",[1835,4469,4471],{"className":4470},[1838],[1835,4472,4474,4519],{"className":4473},[1842],[1835,4475,4477],{"className":4476},[1846],[1848,4478,4479],{"xmlns":1850,"display":1851},[1853,4480,4481,4516],{},[1856,4482,4483,4486,4488,4490,4492,4494,4496,4498,4504,4506,4512,4514],{},[1859,4484,4485],{},"E",[1859,4487,4303],{},[1863,4489,1882],{},[1859,4491,2328],{},[1863,4493,2005],{},[1859,4495,4308],{},[1863,4497,1866],{"stretchy":1865},[4312,4499,4500,4502],{},[1859,4501,1798],{},[1884,4503,1886],{},[1863,4505,1873],{"separator":1872},[4312,4507,4508,4510],{},[1859,4509,3199],{},[1884,4511,2019],{},[1863,4513,1879],{"stretchy":1865},[1863,4515,1873],{"separator":1872},[1890,4517,4518],{"encoding":1892},"EV=m-e(p^0,u^1),",[1835,4520,4522,4544,4563],{"className":4521,"ariaHidden":1872},[1897],[1835,4523,4525,4528,4532,4535,4538,4541],{"className":4524},[1901],[1835,4526],{"className":4527,"style":4346},[1905],[1835,4529,4485],{"className":4530,"style":4531},[1910,1911],"margin-right:0.0576em;",[1835,4533,4303],{"className":4534,"style":2945},[1910,1911],[1835,4536],{"className":4537,"style":1941},[1928],[1835,4539,1882],{"className":4540},[1945],[1835,4542],{"className":4543,"style":1941},[1928],[1835,4545,4547,4551,4554,4557,4560],{"className":4546},[1901],[1835,4548],{"className":4549,"style":4550},[1905],"height:0.6667em;vertical-align:-0.0833em;",[1835,4552,2328],{"className":4553},[1910,1911],[1835,4555],{"className":4556,"style":2945},[1928],[1835,4558,2005],{"className":4559},[2949],[1835,4561],{"className":4562,"style":2945},[1928],[1835,4564,4566,4569,4572,4575,4604,4607,4610,4639,4642],{"className":4565},[1901],[1835,4567],{"className":4568,"style":4369},[1905],[1835,4570,4308],{"className":4571},[1910,1911],[1835,4573,1866],{"className":4574},[1916],[1835,4576,4578,4581],{"className":4577},[1910],[1835,4579,1798],{"className":4580},[1910,1911],[1835,4582,4584],{"className":4583},[2156],[1835,4585,4587],{"className":4586},[2057],[1835,4588,4590],{"className":4589},[2062],[1835,4591,4593],{"className":4592,"style":2166},[2066],[1835,4594,4595,4598],{"style":2186},[1835,4596],{"className":4597,"style":2173},[2074],[1835,4599,4601],{"className":4600},[2177,2178,2179,2180],[1835,4602,1886],{"className":4603},[1910,2180],[1835,4605,1873],{"className":4606},[1924],[1835,4608],{"className":4609,"style":1929},[1928],[1835,4611,4613,4616],{"className":4612},[1910],[1835,4614,3199],{"className":4615},[1910,1911],[1835,4617,4619],{"className":4618},[2156],[1835,4620,4622],{"className":4621},[2057],[1835,4623,4625],{"className":4624},[2062],[1835,4626,4628],{"className":4627,"style":2166},[2066],[1835,4629,4630,4633],{"style":2186},[1835,4631],{"className":4632,"style":2173},[2074],[1835,4634,4636],{"className":4635},[2177,2178,2179,2180],[1835,4637,2019],{"className":4638},[1910,2180],[1835,4640,1879],{"className":4641},[1937],[1835,4643,1873],{"className":4644},[1924],[1798,4646,4647],{},"the amount the consumer would pay beforehand to avoid the change.",[1798,4649,4650,4651,4654],{},"For ",[1966,4652,4653],{},"u=√(xy)",", the expenditure function 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4],[1835,5712,5714],{"className":5713},[2062],[1835,5715,5717],{"className":5716,"style":2254},[2066],[1835,5718],{},[1835,5720],{"className":5721,"style":1941},[1928],[1835,5723,1882],{"className":5724},[1945],[1835,5726],{"className":5727,"style":1941},[1928],[1835,5729,5731,5735,5738,5741,5744,5747,5750,5753,5756],{"className":5730},[1901],[1835,5732],{"className":5733,"style":5734},[1905],"height:0.6944em;",[1835,5736,3860],{"className":5737},[1910],[1835,5739],{"className":5740,"style":1929},[1928],[1835,5742,5415],{"className":5743},[5514],[1835,5745],{"className":5746,"style":1929},[1928],[1835,5748,5023],{"className":5749},[1910],[1835,5751],{"className":5752,"style":1941},[1928],[1835,5754,5423],{"className":5755},[1945],[1835,5757],{"className":5758,"style":1941},[1928],[1835,5760,5762,5765],{"className":5761},[1901],[1835,5763],{"className":5764,"style":5142},[1905],[1835,5766,5426],{"className":5767},[1910],[1798,5769,5770],{},"For this normal good and price rise:",[1835,5772,5774],{"className":5773},[1838],[1835,5775,5777,5825],{"className":5776},[1842],[1835,5778,5780],{"className":5779},[1846],[1848,5781,5782],{"xmlns":1850,"display":1851},[1853,5783,5784,5822],{},[1856,5785,5786,5788,5790,5793,5795,5797,5811,5813,5815,5817,5819],{},[1859,5787,4300],{},[1859,5789,4303],{},[1863,5791,5792],{},">",[1859,5794,5355],{"mathvariant":2029},[1859,5796,4300],{},[2021,5798,5799,5801],{},[1859,5800,5362],{},[1856,5802,5803,5805,5807,5809],{},[1859,5804,5367],{},[1859,5806,5370],{},[1859,5808,5373],{},[1859,5810,5373],{},[1863,5812,5792],{},[1859,5814,4485],{},[1859,5816,4303],{},[1863,5818,5792],{},[1884,5820,5821],{},"0.",[1890,5823,5824],{"encoding":1892},"CV>\\Delta CS_{loss}>EV>0.",[1835,5826,5828,5850,5917,5938],{"className":5827,"ariaHidden":1872},[1897],[1835,5829,5831,5835,5838,5841,5844,5847],{"className":5830},[1901],[1835,5832],{"className":5833,"style":5834},[1905],"height:0.7224em;vertical-align:-0.0391em;",[1835,5836,4300],{"className":5837,"style":4350},[1910,1911],[1835,5839,4303],{"className":5840,"style":2945},[1910,1911],[1835,5842],{"className":5843,"style":1941},[1928],[1835,5845,5792],{"className":5846},[1945],[1835,5848],{"className":5849,"style":1941},[1928],[1835,5851,5853,5856,5859,5862,5908,5911,5914],{"className":5852},[1901],[1835,5854],{"className":5855,"style":5439},[1905],[1835,5857,5355],{"className":5858},[1910],[1835,5860,4300],{"className":5861,"style":4350},[1910,1911],[1835,5863,5865,5868],{"className":5864},[1910],[1835,5866,5362],{"className":5867,"style":4531},[1910,1911],[1835,5869,5871],{"className":5870},[2156],[1835,5872,5874,5900],{"className":5873},[2057,2058],[1835,5875,5877,5897],{"className":5876},[2062],[1835,5878,5880],{"className":5879,"style":2232},[2066],[1835,5881,5882,5885],{"style":5466},[1835,5883],{"className":5884,"style":2173},[2074],[1835,5886,5888],{"className":5887},[2177,2178,2179,2180],[1835,5889,5891,5894],{"className":5890},[1910,2180],[1835,5892,5367],{"className":5893,"style":5479},[1910,1911,2180],[1835,5895,5483],{"className":5896},[1910,1911,2180],[1835,5898,2115],{"className":5899},[2114],[1835,5901,5903],{"className":5902},[2062],[1835,5904,5906],{"className":5905,"style":2254},[2066],[1835,5907],{},[1835,5909],{"className":5910,"style":1941},[1928],[1835,5912,5792],{"className":5913},[1945],[1835,5915],{"className":5916,"style":1941},[1928],[1835,5918,5920,5923,5926,5929,5932,5935],{"className":5919},[1901],[1835,5921],{"className":5922,"style":5834},[1905],[1835,5924,4485],{"className":5925,"style":4531},[1910,1911],[1835,5927,4303],{"className":5928,"style":2945},[1910,1911],[1835,5930],{"className":5931,"style":1941},[1928],[1835,5933,5792],{"className":5934},[1945],[1835,5936],{"className":5937,"style":1941},[1928],[1835,5939,5941,5944],{"className":5940},[1901],[1835,5942],{"className":5943,"style":5142},[1905],[1835,5945,5821],{"className":5946},[1910],[1798,5948,5949,5950,5953,5954,2030],{},"Earlier versions of these notes reversed the ",[1966,5951,5952],{},"CV–EV"," ordering; the reference utility makes the correct ordering clear. With quasi-linear utility and no income effect on the priced good, ",[1966,5955,5956],{},"CV = EV = ΔCS",[5958,5959],"pyodide",{"code64":5960,"layout":5961,"locale":7,"title":5962},"ZnJvbSBtYXRoIGltcG9ydCBsb2csIHNxcnQKCm0sIHAwLCBwMSwgdTAsIHUxID0gMTAwLCAxLCA0LCA1MCwgMjUKZXhwZW5kaXR1cmUgPSBsYW1iZGEgcHgsIHU6IDIgKiB1ICogc3FydChweCkKCmN2ID0gZXhwZW5kaXR1cmUocDEsIHUwKSAtIG0KZXYgPSBtIC0gZXhwZW5kaXR1cmUocDAsIHUxKQpjc19sb3NzID0gNTAgKiBsb2cocDEgLyBwMCkKCnByaW50KHsiQ1YiOiBjdiwgIkNTIGxvc3MiOiByb3VuZChjc19sb3NzLCAyKSwgIkVWIjogZXZ9KQ==","vertical","Check CV, EV, and consumer-surplus loss",[5964,5965,5967],"warning",{"title":5966},"Sign conventions differ","Some texts report a signed income change, others a positive welfare loss. State the question in words and define the sign before comparing numbers.",[1793,5969,5971],{"id":5970},"_5-from-one-consumer-to-policy-appraisal","5. From one consumer to policy appraisal",[1798,5973,5974],{},"Adding willingness to pay is defensible under quasi-linear utility or an explicit social-welfare approximation. Outside that benchmark, one pound to a low-income household and one pound to a high-income household need not carry the same social weight.",[1798,5976,5977],{},"A policy appraisal should separate:",[5979,5980,5981,5984,5987,5990,5993,5996],"ol",{},[1812,5982,5983],{},"behavioural response;",[1812,5985,5986],{},"willingness to pay or accept;",[1812,5988,5989],{},"producer and government surplus;",[1812,5991,5992],{},"external effects;",[1812,5994,5995],{},"distribution and social weights;",[1812,5997,5998],{},"implementation and fiscal spillovers.",[6000,6001,6003],"h3",{"id":6002},"marginal-value-of-public-funds","Marginal value of public funds",[1798,6005,6006],{},"One modern statistic is:",[1835,6008,6010],{"className":6009},[1838],[1835,6011,6013,6047],{"className":6012},[1842],[1835,6014,6016],{"className":6015},[1846],[1848,6017,6018],{"xmlns":1850,"display":1851},[1853,6019,6020,6044],{},[1856,6021,6022,6025,6027,6030,6032,6034,6042],{},[1859,6023,6024],{},"M",[1859,6026,4303],{},[1859,6028,6029],{},"P",[1859,6031,1861],{},[1863,6033,1882],{},[1986,6035,6036,6039],{},[5398,6037,6038],{},"recipients’ willingness to pay",[5398,6040,6041],{},"net government cost",[1859,6043,2030],{"mathvariant":2029},[1890,6045,6046],{"encoding":1892},"MVPF=\\frac{\\text{recipients' willingness to pay}}\n{\\text{net government cost}}.",[1835,6048,6050,6078],{"className":6049,"ariaHidden":1872},[1897],[1835,6051,6053,6056,6060,6063,6066,6069,6072,6075],{"className":6052},[1901],[1835,6054],{"className":6055,"style":4346},[1905],[1835,6057,6024],{"className":6058,"style":6059},[1910,1911],"margin-right:0.109em;",[1835,6061,4303],{"className":6062,"style":2945},[1910,1911],[1835,6064,6029],{"className":6065,"style":1912},[1910,1911],[1835,6067,1861],{"className":6068,"style":1912},[1910,1911],[1835,6070],{"className":6071,"style":1941},[1928],[1835,6073,1882],{"className":6074},[1945],[1835,6076],{"className":6077,"style":1941},[1928],[1835,6079,6081,6085,6154],{"className":6080},[1901],[1835,6082],{"className":6083,"style":6084},[1905],"height:2.2519em;vertical-align:-0.8804em;",[1835,6086,6088,6091,6151],{"className":6087},[1910],[1835,6089],{"className":6090},[1916,2050],[1835,6092,6094],{"className":6093},[1986],[1835,6095,6097,6143],{"className":6096},[2057,2058],[1835,6098,6100,6140],{"className":6099},[2062],[1835,6101,6103,6118,6126],{"className":6102,"style":2067},[2066],[1835,6104,6105,6108],{"style":2070},[1835,6106],{"className":6107,"style":2075},[2074],[1835,6109,6111],{"className":6110},[1910],[1835,6112,6115],{"className":6113},[1910,6114],"text",[1835,6116,6041],{"className":6117},[1910],[1835,6119,6120,6123],{"style":2087},[1835,6121],{"className":6122,"style":2075},[2074],[1835,6124],{"className":6125,"style":2095},[2094],[1835,6127,6128,6131],{"style":2098},[1835,6129],{"className":6130,"style":2075},[2074],[1835,6132,6134],{"className":6133},[1910],[1835,6135,6137],{"className":6136},[1910,6114],[1835,6138,6038],{"className":6139},[1910],[1835,6141,2115],{"className":6142},[2114],[1835,6144,6146],{"className":6145},[2062],[1835,6147,6149],{"className":6148,"style":3689},[2066],[1835,6150],{},[1835,6152],{"className":6153},[1937,2050],[1835,6155,2030],{"className":6156},[1910],[1798,6158,6159,6160,6166],{},"The denominator includes behavioural fiscal effects, not only the programme's sticker cost. A 2025 guide explains its use for marginal tax-policy comparisons while emphasising that the question and spending margin must be defined carefully (",[3245,6161,6165],{"href":6162,"rel":6163},"https:\u002F\u002Fdoi.org\u002F10.1007\u002Fs10797-024-09860-x",[6164],"nofollow","Bastani, 2025","). It is not a complete social welfare function and does not eliminate distributional judgment.",[1793,6168,6170],{"id":6169},"_6-worked-policy-a-transit-fare-increase","6. Worked policy: a transit fare increase",[1798,6172,6173,6174,6177],{},"A city raises a fare from £2 to £3. A commuter's monthly trip demand is ",[1966,6175,6176],{},"q(p)=60−10p"," over this range.",[1809,6179,6180,6183],{},[1812,6181,6182],{},"trips fall from 40 to 30;",[1812,6184,6185],{},"consumer-surplus loss is the trapezoid:",[1835,6187,6189],{"className":6188},[1838],[1835,6190,6192,6240],{"className":6191},[1842],[1835,6193,6195],{"className":6194},[1846],[1848,6196,6197],{"xmlns":1850,"display":1851},[1853,6198,6199,6237],{},[1856,6200,6201,6216,6218,6221,6223,6225,6227,6229,6232,6235],{},[1986,6202,6203,6214],{},[1856,6204,6205,6208,6211],{},[1884,6206,6207],{},"40",[1863,6209,6210],{},"+",[1884,6212,6213],{},"30",[1884,6215,3528],{},[1863,6217,1866],{"stretchy":1865},[1884,6219,6220],{},"3",[1863,6222,2005],{},[1884,6224,3528],{},[1863,6226,1879],{"stretchy":1865},[1863,6228,1882],{},[1859,6230,6231],{"mathvariant":2029},"£",[1884,6233,6234],{},"35",[1863,6236,4245],{"separator":1872},[1890,6238,6239],{"encoding":1892},"\\frac{40+30}{2}(3-2)=£35;",[1835,6241,6243,6339,6360],{"className":6242,"ariaHidden":1872},[1897],[1835,6244,6246,6250,6324,6327,6330,6333,6336],{"className":6245},[1901],[1835,6247],{"className":6248,"style":6249},[1905],"height:2.0074em;vertical-align:-0.686em;",[1835,6251,6253,6256,6321],{"className":6252},[1910],[1835,6254],{"className":6255},[1916,2050],[1835,6257,6259],{"className":6258},[1986],[1835,6260,6262,6313],{"className":6261},[2057,2058],[1835,6263,6265,6310],{"className":6264},[2062],[1835,6266,6268,6279,6287],{"className":6267,"style":5591},[2066],[1835,6269,6270,6273],{"style":2070},[1835,6271],{"className":6272,"style":2075},[2074],[1835,6274,6276],{"className":6275},[1910],[1835,6277,3528],{"className":6278},[1910],[1835,6280,6281,6284],{"style":2087},[1835,6282],{"className":6283,"style":2075},[2074],[1835,6285],{"className":6286,"style":2095},[2094],[1835,6288,6289,6292],{"style":2098},[1835,6290],{"className":6291,"style":2075},[2074],[1835,6293,6295,6298,6301,6304,6307],{"className":6294},[1910],[1835,6296,6207],{"className":6297},[1910],[1835,6299],{"className":6300,"style":2945},[1928],[1835,6302,6210],{"className":6303},[2949],[1835,6305],{"className":6306,"style":2945},[1928],[1835,6308,6213],{"className":6309},[1910],[1835,6311,2115],{"className":6312},[2114],[1835,6314,6316],{"className":6315},[2062],[1835,6317,6319],{"className":6318,"style":2122},[2066],[1835,6320],{},[1835,6322],{"className":6323},[1937,2050],[1835,6325,1866],{"className":6326},[1916],[1835,6328,6220],{"className":6329},[1910],[1835,6331],{"className":6332,"style":2945},[1928],[1835,6334,2005],{"className":6335},[2949],[1835,6337],{"className":6338,"style":2945},[1928],[1835,6340,6342,6345,6348,6351,6354,6357],{"className":6341},[1901],[1835,6343],{"className":6344,"style":1906},[1905],[1835,6346,3528],{"className":6347},[1910],[1835,6349,1879],{"className":6350},[1937],[1835,6352],{"className":6353,"style":1941},[1928],[1835,6355,1882],{"className":6356},[1945],[1835,6358],{"className":6359,"style":1941},[1928],[1835,6361,6363,6367,6371],{"className":6362},[1901],[1835,6364],{"className":6365,"style":6366},[1905],"height:0.8889em;vertical-align:-0.1944em;",[1835,6368,6370],{"className":6369},[1910],"£35",[1835,6372,4245],{"className":6373},[1924],[1809,6375,6376],{},[1812,6377,6378,6379,4274,6382,2030],{},"fare revenue changes from ",[1966,6380,6381],{},"2×40=£80",[1966,6383,6384],{},"3×30=£90",[1798,6386,6387],{},"The £10 revenue gain is not the commuter's full welfare loss. Nor does the partial-equilibrium calculation include congestion, operator cost, crowding, service quality, low-income incidence, or substitution to cars.",[1793,6389,6391],{"id":6390},"_7-evidence-discipline","7. Evidence discipline",[1798,6393,6394],{},"Hicksian demand is rarely observed directly. Researchers combine demand estimation, experiments or quasi-experiments, price variation, and assumptions about utility or market structure. Welfare results can be sensitive to:",[1809,6396,6397,6400,6403,6406,6409],{},[1812,6398,6399],{},"which consumers are represented;",[1812,6401,6402],{},"intensive versus extensive margins;",[1812,6404,6405],{},"equilibrium price responses;",[1812,6407,6408],{},"quality and product entry;",[1812,6410,6411],{},"extrapolation beyond observed variation.",[1798,6413,6414],{},"A precise estimate under a restrictive model is not automatically a complete welfare judgment.",[1793,6416,6418],{"id":6417},"practice","Practice",[5979,6420,6421,6427,6434,6437,6440],{},[1812,6422,6423,6424,2030],{},"Derive the Slutsky equation from ",[1966,6425,6426],{},"x(p,m)=h(p,v(p,m))",[1812,6428,6429,6430,6433],{},"Repeat the worked example for ",[1966,6431,6432],{},"p_x: 1 → 2"," and compare the three losses.",[1812,6435,6436],{},"Show why quasi-linearity removes the income effect on the non-numeraire good, subject to an interior solution.",[1812,6438,6439],{},"Evaluate a £1 per-trip subsidy using consumer surplus, fiscal cost, congestion, and distribution.",[1812,6441,6442],{},"Give one case where a local derivative gives the wrong intuition for a large policy change.",[1793,6444,6446],{"id":6445},"quick-check","Quick check",[1809,6448,6449,6452,6455,6465,6468],{},[1812,6450,6451],{},"Comparative statics is conditional on an equilibrium and “other things equal.”",[1812,6453,6454],{},"Substitution holds utility fixed; ordinary demand holds income fixed.",[1812,6456,6457,6460,6461,6464],{},[1966,6458,6459],{},"CV"," and ",[1966,6462,6463],{},"EV"," answer different counterfactual compensation questions.",[1812,6466,6467],{},"Consumer surplus is exact only under particular preference conditions.",[1812,6469,6470],{},"Welfare appraisal requires incidence, external effects, and a normative criterion.",[1798,6472,6473,6476,6477,2030],{},[2264,6474,6475],{},"Next:"," ",[3245,6478,6480],{"href":6479},"..\u002F03-uncertainty\u002F","value risky prospects and design insurance",{"title":10,"searchDepth":6482,"depth":6482,"links":6483},2,[6484,6485,6486,6487,6488,6489,6490,6494,6495,6496,6497],{"id":1795,"depth":6482,"text":1796},{"id":1803,"depth":6482,"text":1804},{"id":1829,"depth":6482,"text":1830},{"id":2292,"depth":6482,"text":2293},{"id":3177,"depth":6482,"text":3178},{"id":4266,"depth":6482,"text":4267},{"id":5970,"depth":6482,"text":5971,"children":6491},[6492],{"id":6002,"depth":6493,"text":6003},3,{"id":6169,"depth":6482,"text":6170},{"id":6390,"depth":6482,"text":6391},{"id":6417,"depth":6482,"text":6418},{"id":6445,"depth":6482,"text":6446},"Implicit derivatives, Slutsky decomposition, compensating and equivalent variation, surplus, incidence, and empirical welfare.","md",null,{},true,{"title":733,"description":6498},"Km-u0hlMhvAWRNYKI8eVm0tAraFVOHsfJIoeGfufkyo",[6506,6508],{"title":727,"path":728,"stem":729,"description":6507,"children":-1},"Consumer and producer choice, value functions, envelope results, demand properties, and revealed-preference tests.",{"title":739,"path":740,"stem":741,"description":6509,"children":-1},"Expected utility, certainty equivalents, risk aversion, insurance, portfolio choice, ambiguity, and climate-risk evidence.",1785754732236]