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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",{},"Can decentralised choices be mutually feasible in every market, and what assumptions connect competitive equilibrium to social efficiency?",[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",{},"define feasibility, Pareto efficiency, and Walrasian equilibrium;",[1812,1816,1817],{},"solve a two-consumer, two-good exchange economy;",[1812,1819,1820],{},"state and qualify both fundamental welfare theorems;",[1812,1822,1823],{},"distinguish existence, uniqueness, stability, efficiency, and fairness;",[1812,1825,1826],{},"explain how production networks transmit local shocks.",[1793,1828,1830],{"id":1829},"_1-from-one-budget-to-an-economy","1. From one budget to an economy",[1798,1832,1833,1834,1838,1839,1842,1843,1846],{},"Consumer ",[1835,1836,1837],"code",{},"i"," has preferences ",[1835,1840,1841],{},"u_i",", endowment ",[1835,1844,1845],{},"ω_i",", and demand:",[1848,1849,1852],"span",{"className":1850},[1851],"katex-display",[1848,1853,1856,1984],{"className":1854},[1855],"katex",[1848,1857,1860],{"className":1858},[1859],"katex-mathml",[1861,1862,1865],"math",{"xmlns":1863,"display":1864},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML","block",[1866,1867,1868,1979],"semantics",{},[1869,1870,1871,1880,1885,1887,1890,1893,1896,1899,1924,1927,1934,1936,1942,1944,1947,1949,1952,1958,1961,1963,1965,1972,1975],"mrow",{},[1872,1873,1874,1878],"msub",{},[1875,1876,1877],"mi",{},"x",[1875,1879,1837],{},[1881,1882,1884],"mo",{"stretchy":1883},"false","(",[1875,1886,1798],{},[1881,1888,1889],{"stretchy":1883},")",[1881,1891,1892],{},"∈",[1875,1894,1895],{},"arg",[1881,1897,1898],{},"⁡",[1900,1901,1902,1909],"munder",{},[1869,1903,1904,1907],{},[1875,1905,1906],{},"max",[1881,1908,1898],{},[1869,1910,1911,1917,1920],{},[1872,1912,1913,1915],{},[1875,1914,1877],{},[1875,1916,1837],{},[1881,1918,1919],{},"≥",[1921,1922,1923],"mn",{},"0",[1881,1925,1926],{"stretchy":1883},"{",[1872,1928,1929,1932],{},[1875,1930,1931],{},"u",[1875,1933,1837],{},[1881,1935,1884],{"stretchy":1883},[1872,1937,1938,1940],{},[1875,1939,1877],{},[1875,1941,1837],{},[1881,1943,1889],{"stretchy":1883},[1881,1945,1946],{},":",[1875,1948,1798],{},[1881,1950,1951],{},"⋅",[1872,1953,1954,1956],{},[1875,1955,1877],{},[1875,1957,1837],{},[1881,1959,1960],{},"≤",[1875,1962,1798],{},[1881,1964,1951],{},[1872,1966,1967,1970],{},[1875,1968,1969],{},"ω",[1875,1971,1837],{},[1881,1973,1974],{"stretchy":1883},"}",[1875,1976,1978],{"mathvariant":1977},"normal",".",[1980,1981,1983],"annotation",{"encoding":1982},"application\u002Fx-tex","x_i(p)\\in\\arg\\max_{x_i\\ge0}\n\\{u_i(x_i):p\\cdot x_i\\le p\\cdot\\omega_i\\}.",[1848,1985,1989,2079,2299,2320,2376,2394],{"className":1986,"ariaHidden":1988},[1987],"katex-html","true",[1848,1990,1993,1998,2056,2060,2063,2067,2072,2076],{"className":1991},[1992],"base",[1848,1994],{"className":1995,"style":1997},[1996],"strut","height:1em;vertical-align:-0.25em;",[1848,1999,2002,2006],{"className":2000},[2001],"mord",[1848,2003,1877],{"className":2004},[2001,2005],"mathnormal",[1848,2007,2010],{"className":2008},[2009],"msupsub",[1848,2011,2015,2047],{"className":2012},[2013,2014],"vlist-t","vlist-t2",[1848,2016,2019,2042],{"className":2017},[2018],"vlist-r",[1848,2020,2024],{"className":2021,"style":2023},[2022],"vlist","height:0.3117em;",[1848,2025,2027,2032],{"style":2026},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1848,2028],{"className":2029,"style":2031},[2030],"pstrut","height:2.7em;",[1848,2033,2039],{"className":2034},[2035,2036,2037,2038],"sizing","reset-size6","size3","mtight",[1848,2040,1837],{"className":2041},[2001,2005,2038],[1848,2043,2046],{"className":2044},[2045],"vlist-s","​",[1848,2048,2050],{"className":2049},[2018],[1848,2051,2054],{"className":2052,"style":2053},[2022],"height:0.15em;",[1848,2055],{},[1848,2057,1884],{"className":2058},[2059],"mopen",[1848,2061,1798],{"className":2062},[2001,2005],[1848,2064,1889],{"className":2065},[2066],"mclose",[1848,2068],{"className":2069,"style":2071},[2070],"mspace","margin-right:0.2778em;",[1848,2073,1892],{"className":2074},[2075],"mrel",[1848,2077],{"className":2078,"style":2071},[2070],[1848,2080,2082,2086,2095,2099,2201,2204,2244,2247,2287,2290,2293,2296],{"className":2081},[1992],[1848,2083],{"className":2084,"style":2085},[1996],"height:1.5672em;vertical-align:-0.8172em;",[1848,2087,2090,2091],{"className":2088},[2089],"mop","ar",[1848,2092,2094],{"style":2093},"margin-right:0.0139em;","g",[1848,2096],{"className":2097,"style":2098},[2070],"margin-right:0.1667em;",[1848,2100,2103],{"className":2101},[2089,2102],"op-limits",[1848,2104,2106,2192],{"className":2105},[2013,2014],[1848,2107,2109,2189],{"className":2108},[2018],[1848,2110,2113,2178],{"className":2111,"style":2112},[2022],"height:0.4306em;",[1848,2114,2116,2120],{"style":2115},"top:-2.3829em;margin-left:0em;",[1848,2117],{"className":2118,"style":2119},[2030],"height:3em;",[1848,2121,2123],{"className":2122},[2035,2036,2037,2038],[1848,2124,2126,2172,2175],{"className":2125},[2001,2038],[1848,2127,2129,2132],{"className":2128},[2001,2038],[1848,2130,1877],{"className":2131},[2001,2005,2038],[1848,2133,2135],{"className":2134},[2009],[1848,2136,2138,2163],{"className":2137},[2013,2014],[1848,2139,2141,2160],{"className":2140},[2018],[1848,2142,2145],{"className":2143,"style":2144},[2022],"height:0.3281em;",[1848,2146,2148,2152],{"style":2147},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[1848,2149],{"className":2150,"style":2151},[2030],"height:2.5em;",[1848,2153,2157],{"className":2154},[2035,2155,2156,2038],"reset-size3","size1",[1848,2158,1837],{"className":2159},[2001,2005,2038],[1848,2161,2046],{"className":2162},[2045],[1848,2164,2166],{"className":2165},[2018],[1848,2167,2170],{"className":2168,"style":2169},[2022],"height:0.143em;",[1848,2171],{},[1848,2173,1919],{"className":2174},[2075,2038],[1848,2176,1923],{"className":2177},[2001,2038],[1848,2179,2181,2184],{"style":2180},"top:-3em;",[1848,2182],{"className":2183,"style":2119},[2030],[1848,2185,2186],{},[1848,2187,1906],{"className":2188},[2089],[1848,2190,2046],{"className":2191},[2045],[1848,2193,2195],{"className":2194},[2018],[1848,2196,2199],{"className":2197,"style":2198},[2022],"height:0.8172em;",[1848,2200],{},[1848,2202,1926],{"className":2203},[2059],[1848,2205,2207,2210],{"className":2206},[2001],[1848,2208,1931],{"className":2209},[2001,2005],[1848,2211,2213],{"className":2212},[2009],[1848,2214,2216,2236],{"className":2215},[2013,2014],[1848,2217,2219,2233],{"className":2218},[2018],[1848,2220,2222],{"className":2221,"style":2023},[2022],[1848,2223,2224,2227],{"style":2026},[1848,2225],{"className":2226,"style":2031},[2030],[1848,2228,2230],{"className":2229},[2035,2036,2037,2038],[1848,2231,1837],{"className":2232},[2001,2005,2038],[1848,2234,2046],{"className":2235},[2045],[1848,2237,2239],{"className":2238},[2018],[1848,2240,2242],{"className":2241,"style":2053},[2022],[1848,2243],{},[1848,2245,1884],{"className":2246},[2059],[1848,2248,2250,2253],{"className":2249},[2001],[1848,2251,1877],{"className":2252},[2001,2005],[1848,2254,2256],{"className":2255},[2009],[1848,2257,2259,2279],{"className":2258},[2013,2014],[1848,2260,2262,2276],{"className":2261},[2018],[1848,2263,2265],{"className":2264,"style":2023},[2022],[1848,2266,2267,2270],{"style":2026},[1848,2268],{"className":2269,"style":2031},[2030],[1848,2271,2273],{"className":2272},[2035,2036,2037,2038],[1848,2274,1837],{"className":2275},[2001,2005,2038],[1848,2277,2046],{"className":2278},[2045],[1848,2280,2282],{"className":2281},[2018],[1848,2283,2285],{"className":2284,"style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allocation is feasible when:",[1848,2452,2454],{"className":2453},[1851],[1848,2455,2457,2498],{"className":2456},[1855],[1848,2458,2460],{"className":2459},[1859],[1861,2461,2462],{"xmlns":1863,"display":1864},[1866,2463,2464,2495],{},[1869,2465,2466,2473,2479,2481,2487,2493],{},[1900,2467,2468,2471],{},[1881,2469,2470],{},"∑",[1875,2472,1837],{},[1872,2474,2475,2477],{},[1875,2476,1877],{},[1875,2478,1837],{},[1881,2480,1960],{},[1900,2482,2483,2485],{},[1881,2484,2470],{},[1875,2486,1837],{},[1872,2488,2489,2491],{},[1875,2490,1969],{},[1875,2492,1837],{},[1875,2494,1978],{"mathvariant":1977},[1980,2496,2497],{"encoding":1982},"\\sum_i x_i\\le\\sum_i\\omega_i.",[1848,2499,2501,2611],{"className":2500,"ariaHidden":1988},[1987],[1848,2502,2504,2508,2559,2562,2602,2605,2608],{"className":2503},[1992],[1848,2505],{"className":2506,"style":2507},[1996],"height:2.3277em;vertical-align:-1.2777em;",[1848,2509,2511],{"className":2510},[2089,2102],[1848,2512,2514,2550],{"className":2513},[2013,2014],[1848,2515,2517,2547],{"className":2516},[2018],[1848,2518,2521,2534],{"className":2519,"style":2520},[2022],"height:1.05em;",[1848,2522,2524,2528],{"style":2523},"top:-1.8723em;margin-left:0em;",[1848,2525],{"className":2526,"style":2527},[2030],"height:3.05em;",[1848,2529,2531],{"className":2530},[2035,2036,2037,2038],[1848,2532,1837],{"className":2533},[2001,2005,2038],[1848,2535,2537,2540],{"style":2536},"top:-3.05em;",[1848,2538],{"className":2539,"style":2527},[2030],[1848,2541,2542],{},[1848,2543,2470],{"className":2544},[2089,2545,2546],"op-symbol","large-op",[1848,2548,2046],{"className":2549},[2045],[1848,2551,2553],{"className":2552},[2018],[1848,2554,2557],{"className":2555,"style":2556},[2022],"height:1.2777em;",[1848,2558],{},[1848,2560],{"className":2561,"style":2098},[2070],[1848,2563,2565,2568],{"className":2564},[2001],[1848,2566,1877],{"className":2567},[2001,2005],[1848,2569,2571],{"className":2570},[2009],[1848,2572,2574,2594],{"className":2573},[2013,2014],[1848,2575,2577,2591],{"className":2576},[2018],[1848,2578,2580],{"className":2579,"style":2023},[2022],[1848,2581,2582,2585],{"style":2026},[1848,2583],{"className":2584,"style":2031},[2030],[1848,2586,2588],{"className":2587},[2035,2036,2037,2038],[1848,2589,1837],{"className":2590},[2001,2005,2038],[1848,2592,2046],{"className":2593},[2045],[1848,2595,2597],{"className":2596},[2018],[1848,2598,2600],{"className":2599,"style":2053},[2022],[1848,2601],{},[1848,2603],{"className":2604,"style":2071},[2070],[1848,2606,1960],{"className":2607},[2075],[1848,2609],{"className":2610,"style":2071},[2070],[1848,2612,2614,2617,2661,2664,2704],{"className":2613},[1992],[1848,2615],{"className":2616,"style":2507},[1996],[1848,2618,2620],{"className":2619},[2089,2102],[1848,2621,2623,2653],{"className":2622},[2013,2014],[1848,2624,2626,2650],{"className":2625},[2018],[1848,2627,2629,2640],{"className":2628,"style":2520},[2022],[1848,2630,2631,2634],{"style":2523},[1848,2632],{"className":2633,"style":2527},[2030],[1848,2635,2637],{"className":2636},[2035,2036,2037,2038],[1848,2638,1837],{"className":2639},[2001,2005,2038],[1848,2641,2642,2645],{"style":2536},[1848,2643],{"className":2644,"style":2527},[2030],[1848,2646,2647],{},[1848,2648,2470],{"className":2649},[2089,2545,2546],[1848,2651,2046],{"className":2652},[2045],[1848,2654,2656],{"className":2655},[2018],[1848,2657,2659],{"className":2658,"style":2556},[2022],[1848,2660],{},[1848,2662],{"className":2663,"style":2098},[2070],[1848,2665,2667,2670],{"className":2666},[2001],[1848,2668,1969],{"className":2669,"style":2406},[2001,2005],[1848,2671,2673],{"className":2672},[2009],[1848,2674,2676,2696],{"className":2675},[2013,2014],[1848,2677,2679,2693],{"className":2678},[2018],[1848,2680,2682],{"className":2681,"style":2023},[2022],[1848,2683,2684,2687],{"style":2421},[1848,2685],{"className":2686,"style":2031},[2030],[1848,2688,2690],{"className":2689},[2035,2036,2037,2038],[1848,2691,1837],{"className":2692},[2001,2005,2038],[1848,2694,2046],{"className":2695},[2045],[1848,2697,2699],{"className":2698},[2018],[1848,2700,2702],{"className":2701,"style":2053},[2022],[1848,2703],{},[1848,2705,1978],{"className":2706},[2001],[1798,2708,2709,2710,2713,2714,2717],{},"A Walrasian equilibrium is a price vector ",[1835,2711,2712],{},"p*"," and allocation ",[1835,2715,2716],{},"x*"," such that:",[2719,2720,2721,2727],"ol",{},[1812,2722,2723,2724,2726],{},"every consumer optimises at ",[1835,2725,2712],{},";",[1812,2728,2729],{},"every market clears:",[1848,2731,2733],{"className":2732},[1851],[1848,2734,2736,2781],{"className":2735},[1855],[1848,2737,2739],{"className":2738},[1859],[1861,2740,2741],{"xmlns":1863,"display":1864},[1866,2742,2743,2778],{},[1869,2744,2745,2751,2761,2764,2770,2776],{},[1900,2746,2747,2749],{},[1881,2748,2470],{},[1875,2750,1837],{},[2752,2753,2754,2756,2758],"msubsup",{},[1875,2755,1877],{},[1875,2757,1837],{},[1881,2759,2760],{},"∗",[1881,2762,2763],{},"=",[1900,2765,2766,2768],{},[1881,2767,2470],{},[1875,2769,1837],{},[1872,2771,2772,2774],{},[1875,2773,1969],{},[1875,2775,1837],{},[1875,2777,1978],{"mathvariant":1977},[1980,2779,2780],{"encoding":1982},"\\sum_i x_i^*=\\sum_i\\omega_i.",[1848,2782,2784,2901],{"className":2783,"ariaHidden":1988},[1987],[1848,2785,2787,2790,2834,2837,2892,2895,2898],{"className":2786},[1992],[1848,2788],{"className":2789,"style":2507},[1996],[1848,2791,2793],{"className":2792},[2089,2102],[1848,2794,2796,2826],{"className":2795},[2013,2014],[1848,2797,2799,2823],{"className":2798},[2018],[1848,2800,2802,2813],{"className":2801,"style":2520},[2022],[1848,2803,2804,2807],{"style":2523},[1848,2805],{"className":2806,"style":2527},[2030],[1848,2808,2810],{"className":2809},[2035,2036,2037,2038],[1848,2811,1837],{"className":2812},[2001,2005,2038],[1848,2814,2815,2818],{"style":2536},[1848,2816],{"className":2817,"style":2527},[2030],[1848,2819,2820],{},[1848,2821,2470],{"className":2822},[2089,2545,2546],[1848,2824,2046],{"className":2825},[2045],[1848,2827,2829],{"className":2828},[2018],[1848,2830,2832],{"className":2831,"style":2556},[2022],[1848,2833],{},[1848,2835],{"className":2836,"style":2098},[2070],[1848,2838,2840,2843],{"className":2839},[2001],[1848,2841,1877],{"className":2842},[2001,2005],[1848,2844,2846],{"className":2845},[2009],[1848,2847,2849,2883],{"className":2848},[2013,2014],[1848,2850,2852,2880],{"className":2851},[2018],[1848,2853,2856,2868],{"className":2854,"style":2855},[2022],"height:0.7387em;",[1848,2857,2859,2862],{"style":2858},"top:-2.453em;margin-left:0em;margin-right:0.05em;",[1848,2860],{"className":2861,"style":2031},[2030],[1848,2863,2865],{"className":2864},[2035,2036,2037,2038],[1848,2866,1837],{"className":2867},[2001,2005,2038],[1848,2869,2871,2874],{"style":2870},"top:-3.113em;margin-right:0.05em;",[1848,2872],{"className":2873,"style":2031},[2030],[1848,2875,2877],{"className":2876},[2035,2036,2037,2038],[1848,2878,2760],{"className":2879},[2316,2038],[1848,2881,2046],{"className":2882},[2045],[1848,2884,2886],{"className":2885},[2018],[1848,2887,2890],{"className":2888,"style":2889},[2022],"height:0.247em;",[1848,2891],{},[1848,2893],{"className":2894,"style":2071},[2070],[1848,2896,2763],{"className":2897},[2075],[1848,2899],{"className":2900,"style":2071},[2070],[1848,2902,2904,2907,2951,2954,2994],{"className":2903},[1992],[1848,2905],{"className":2906,"style":2507},[1996],[1848,2908,2910],{"className":2909},[2089,2102],[1848,2911,2913,2943],{"className":2912},[2013,2014],[1848,2914,2916,2940],{"className":2915},[2018],[1848,2917,2919,2930],{"className":2918,"style":2520},[2022],[1848,2920,2921,2924],{"style":2523},[1848,2922],{"className":2923,"style":2527},[2030],[1848,2925,2927],{"className":2926},[2035,2036,2037,2038],[1848,2928,1837],{"className":2929},[2001,2005,2038],[1848,2931,2932,2935],{"style":2536},[1848,2933],{"className":2934,"style":2527},[2030],[1848,2936,2937],{},[1848,2938,2470],{"className":2939},[2089,2545,2546],[1848,2941,2046],{"className":2942},[2045],[1848,2944,2946],{"className":2945},[2018],[1848,2947,2949],{"className":2948,"style":2556},[2022],[1848,2950],{},[1848,2952],{"className":2953,"style":2098},[2070],[1848,2955,2957,2960],{"className":2956},[2001],[1848,2958,1969],{"className":2959,"style":2406},[2001,2005],[1848,2961,2963],{"className":2962},[2009],[1848,2964,2966,2986],{"className":2965},[2013,2014],[1848,2967,2969,2983],{"className":2968},[2018],[1848,2970,2972],{"className":2971,"style":2023},[2022],[1848,2973,2974,2977],{"style":2421},[1848,2975],{"className":2976,"style":2031},[2030],[1848,2978,2980],{"className":2979},[2035,2036,2037,2038],[1848,2981,1837],{"className":2982},[2001,2005,2038],[1848,2984,2046],{"className":2985},[2045],[1848,2987,2989],{"className":2988},[2018],[1848,2990,2992],{"className":2991,"style":2053},[2022],[1848,2993],{},[1848,2995,1978],{"className":2996},[2001],[1798,2998,2999],{},"Prices coordinate plans; they do not create resources.",[3001,3002],"mermaid-diagram",{"code64":3003,"locale":7},"Zmxvd2NoYXJ0IExSCiAgUFtQcmljZXNdIC0tPiBCW0J1ZGdldCB2YWx1ZXMgb2YgZW5kb3dtZW50c10KICBCIC0tPiBEW0luZGl2aWR1YWwgZGVtYW5kc10KICBEIC0tPiBaW0FnZ3JlZ2F0ZSBleGNlc3MgZGVtYW5kXQogIFogLS0+IFA=",[1793,3005,3007],{"id":3006},"_2-edgeworth-box-logic","2. Edgeworth-box logic",[1798,3009,3010],{},"For two consumers and two goods, the Edgeworth box contains every feasible division of total endowment. An allocation is Pareto efficient if no feasible reallocation makes one consumer better off without making the other worse off.",[1798,3012,3013],{},"At a regular interior efficient allocation:",[1848,3015,3017],{"className":3016},[1851],[1848,3018,3020,3061],{"className":3019},[1855],[1848,3021,3023],{"className":3022},[1859],[1861,3024,3025],{"xmlns":1863,"display":1864},[1866,3026,3027,3058],{},[1869,3028,3029,3032,3035,3043,3045,3047,3049,3056],{},[1875,3030,3031],{},"M",[1875,3033,3034],{},"R",[1872,3036,3037,3040],{},[1875,3038,3039],{},"S",[1875,3041,3042],{},"A",[1881,3044,2763],{},[1875,3046,3031],{},[1875,3048,3034],{},[1872,3050,3051,3053],{},[1875,3052,3039],{},[1875,3054,3055],{},"B",[1875,3057,1978],{"mathvariant":1977},[1980,3059,3060],{"encoding":1982},"MRS_A=MRS_B.",[1848,3062,3064,3131],{"className":3063,"ariaHidden":1988},[1987],[1848,3065,3067,3071,3075,3079,3122,3125,3128],{"className":3066},[1992],[1848,3068],{"className":3069,"style":3070},[1996],"height:0.8333em;vertical-align:-0.15em;",[1848,3072,3031],{"className":3073,"style":3074},[2001,2005],"margin-right:0.109em;",[1848,3076,3034],{"className":3077,"style":3078},[2001,2005],"margin-right:0.0077em;",[1848,3080,3082,3086],{"className":3081},[2001],[1848,3083,3039],{"className":3084,"style":3085},[2001,2005],"margin-right:0.0576em;",[1848,3087,3089],{"className":3088},[2009],[1848,3090,3092,3114],{"className":3091},[2013,2014],[1848,3093,3095,3111],{"className":3094},[2018],[1848,3096,3099],{"className":3097,"style":3098},[2022],"height:0.3283em;",[1848,3100,3102,3105],{"style":3101},"top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;",[1848,3103],{"className":3104,"style":2031},[2030],[1848,3106,3108],{"className":3107},[2035,2036,2037,2038],[1848,3109,3042],{"className":3110},[2001,2005,2038],[1848,3112,2046],{"className":3113},[2045],[1848,3115,3117],{"className":3116},[2018],[1848,3118,3120],{"className":3119,"style":2053},[2022],[1848,3121],{},[1848,3123],{"className":3124,"style":2071},[2070],[1848,3126,2763],{"className":3127},[2075],[1848,3129],{"className":3130,"style":2071},[2070],[1848,3132,3134,3137,3140,3143,3184],{"className":3133},[1992],[1848,3135],{"className":3136,"style":3070},[1996],[1848,3138,3031],{"className":3139,"style":3074},[2001,2005],[1848,3141,3034],{"className":3142,"style":3078},[2001,2005],[1848,3144,3146,3149],{"className":3145},[2001],[1848,3147,3039],{"className":3148,"style":3085},[2001,2005],[1848,3150,3152],{"className":3151},[2009],[1848,3153,3155,3176],{"className":3154},[2013,2014],[1848,3156,3158,3173],{"className":3157},[2018],[1848,3159,3161],{"className":3160,"style":3098},[2022],[1848,3162,3163,3166],{"style":3101},[1848,3164],{"className":3165,"style":2031},[2030],[1848,3167,3169],{"className":3168},[2035,2036,2037,2038],[1848,3170,3055],{"className":3171,"style":3172},[2001,2005,2038],"margin-right:0.0502em;",[1848,3174,2046],{"className":3175},[2045],[1848,3177,3179],{"className":3178},[2018],[1848,3180,3182],{"className":3181,"style":2053},[2022],[1848,3183],{},[1848,3185,1978],{"className":3186},[2001],[1798,3188,3189,3190,3194],{},"Otherwise, the consumers value a marginal trade differently and both can gain. The set of efficient allocations is the ",[3191,3192,3193],"strong",{},"contract curve",". Efficiency does not select one point on it.",[1793,3196,3198],{"id":3197},"_3-worked-competitive-equilibrium","3. Worked competitive equilibrium",[1798,3200,3201,3202,3205],{},"Let total resources be ",[1835,3203,3204],{},"(10,10)",". Endowments are:",[1848,3207,3209],{"className":3208},[1851],[1848,3210,3212,3270],{"className":3211},[1855],[1848,3213,3215],{"className":3214},[1859],[1861,3216,3217],{"xmlns":1863,"display":1864},[1866,3218,3219,3267],{},[1869,3220,3221,3227,3229,3231,3234,3237,3240,3242,3244,3247,3253,3255,3257,3259,3261,3263,3265],{},[1872,3222,3223,3225],{},[1875,3224,1969],{},[1875,3226,3042],{},[1881,3228,2763],{},[1881,3230,1884],{"stretchy":1883},[1921,3232,3233],{},"8",[1881,3235,3236],{"separator":1988},",",[1921,3238,3239],{},"2",[1881,3241,1889],{"stretchy":1883},[1881,3243,3236],{"separator":1988},[2070,3245],{"width":3246},"2em",[1872,3248,3249,3251],{},[1875,3250,1969],{},[1875,3252,3055],{},[1881,3254,2763],{},[1881,3256,1884],{"stretchy":1883},[1921,3258,3239],{},[1881,3260,3236],{"separator":1988},[1921,3262,3233],{},[1881,3264,1889],{"stretchy":1883},[1881,3266,3236],{"separator":1988},[1980,3268,3269],{"encoding":1982},"\\omega_A=(8,2),\\qquad \\omega_B=(2,8),",[1848,3271,3273,3329,3413],{"className":3272,"ariaHidden":1988},[1987],[1848,3274,3276,3280,3320,3323,3326],{"className":3275},[1992],[1848,3277],{"className":3278,"style":3279},[1996],"height:0.5806em;vertical-align:-0.15em;",[1848,3281,3283,3286],{"className":3282},[2001],[1848,3284,1969],{"className":3285,"style":2406},[2001,2005],[1848,3287,3289],{"className":3288},[2009],[1848,3290,3292,3312],{"className":3291},[2013,2014],[1848,3293,3295,3309],{"className":3294},[2018],[1848,3296,3298],{"className":3297,"style":3098},[2022],[1848,3299,3300,3303],{"style":2421},[1848,3301],{"className":3302,"style":2031},[2030],[1848,3304,3306],{"className":3305},[2035,2036,2037,2038],[1848,3307,3042],{"className":3308},[2001,2005,2038],[1848,3310,2046],{"className":3311},[2045],[1848,3313,3315],{"className":3314},[2018],[1848,3316,3318],{"className":3317,"style":2053},[2022],[1848,3319],{},[1848,3321],{"className":3322,"style":2071},[2070],[1848,3324,2763],{"className":3325},[2075],[1848,3327],{"className":3328,"style":2071},[2070],[1848,3330,3332,3335,3338,3341,3345,3348,3351,3354,3357,3361,3364,3404,3407,3410],{"className":3331},[1992],[1848,3333],{"className":3334,"style":1997},[1996],[1848,3336,1884],{"className":3337},[2059],[1848,3339,3233],{"className":3340},[2001],[1848,3342,3236],{"className":3343},[3344],"mpunct",[1848,3346],{"className":3347,"style":2098},[2070],[1848,3349,3239],{"className":3350},[2001],[1848,3352,1889],{"className":3353},[2066],[1848,3355,3236],{"className":3356},[3344],[1848,3358],{"className":3359,"style":3360},[2070],"margin-right:2em;",[1848,3362],{"className":3363,"style":2098},[2070],[1848,3365,3367,3370],{"className":3366},[2001],[1848,3368,1969],{"className":3369,"style":2406},[2001,2005],[1848,3371,3373],{"className":3372},[2009],[1848,3374,3376,3396],{"className":3375},[2013,2014],[1848,3377,3379,3393],{"className":3378},[2018],[1848,3380,3382],{"className":3381,"style":3098},[2022],[1848,3383,3384,3387],{"style":2421},[1848,3385],{"className":3386,"style":2031},[2030],[1848,3388,3390],{"className":3389},[2035,2036,2037,2038],[1848,3391,3055],{"className":3392,"style":3172},[2001,2005,2038],[1848,3394,2046],{"className":3395},[2045],[1848,3397,3399],{"className":3398},[2018],[1848,3400,3402],{"className":3401,"style":2053},[2022],[1848,3403],{},[1848,3405],{"className":3406,"style":2071},[2070],[1848,3408,2763],{"className":3409},[2075],[1848,3411],{"className":3412,"style":2071},[2070],[1848,3414,3416,3419,3422,3425,3428,3431,3434,3437],{"className":3415},[1992],[1848,3417],{"className":3418,"style":1997},[1996],[1848,3420,1884],{"className":3421},[2059],[1848,3423,3239],{"className":3424},[2001],[1848,3426,3236],{"className":3427},[3344],[1848,3429],{"className":3430,"style":2098},[2070],[1848,3432,3233],{"className":3433},[2001],[1848,3435,1889],{"className":3436},[2066],[1848,3438,3236],{"className":3439},[3344],[1798,3441,3442,3443,3446,3447,3450,3451,1978],{},"and both consumers have ",[1835,3444,3445],{},"u_i(x,y)=√(xy)",". Normalise ",[1835,3448,3449],{},"p_y=1"," and write ",[1835,3452,3453],{},"p_x=p",[1798,3455,3456],{},"Incomes are:",[1848,3458,3460],{"className":3459},[1851],[1848,3461,3463,3514],{"className":3462},[1855],[1848,3464,3466],{"className":3465},[1859],[1861,3467,3468],{"xmlns":1863,"display":1864},[1866,3469,3470,3511],{},[1869,3471,3472,3479,3481,3483,3485,3488,3490,3492,3494,3500,3502,3504,3506,3508],{},[1872,3473,3474,3477],{},[1875,3475,3476],{},"m",[1875,3478,3042],{},[1881,3480,2763],{},[1921,3482,3233],{},[1875,3484,1798],{},[1881,3486,3487],{},"+",[1921,3489,3239],{},[1881,3491,3236],{"separator":1988},[2070,3493],{"width":3246},[1872,3495,3496,3498],{},[1875,3497,3476],{},[1875,3499,3055],{},[1881,3501,2763],{},[1921,3503,3239],{},[1875,3505,1798],{},[1881,3507,3487],{},[1921,3509,3510],{},"8.",[1980,3512,3513],{"encoding":1982},"m_A=8p+2,\\qquad m_B=2p+8.",[1848,3515,3517,3572,3594,3661,3682],{"className":3516,"ariaHidden":1988},[1987],[1848,3518,3520,3523,3563,3566,3569],{"className":3519},[1992],[1848,3521],{"className":3522,"style":3279},[1996],[1848,3524,3526,3529],{"className":3525},[2001],[1848,3527,3476],{"className":3528},[2001,2005],[1848,3530,3532],{"className":3531},[2009],[1848,3533,3535,3555],{"className":3534},[2013,2014],[1848,3536,3538,3552],{"className":3537},[2018],[1848,3539,3541],{"className":3540,"style":3098},[2022],[1848,3542,3543,3546],{"style":2026},[1848,3544],{"className":3545,"style":2031},[2030],[1848,3547,3549],{"className":3548},[2035,2036,2037,2038],[1848,3550,3042],{"className":3551},[2001,2005,2038],[1848,3553,2046],{"className":3554},[2045],[1848,3556,3558],{"className":3557},[2018],[1848,3559,3561],{"className":3560,"style":2053},[2022],[1848,3562],{},[1848,3564],{"className":3565,"style":2071},[2070],[1848,3567,2763],{"className":3568},[2075],[1848,3570],{"className":3571,"style":2071},[2070],[1848,3573,3575,3579,3582,3585,3588,3591],{"className":3574},[1992],[1848,3576],{"className":3577,"style":3578},[1996],"height:0.8389em;vertical-align:-0.1944em;",[1848,3580,3233],{"className":3581},[2001],[1848,3583,1798],{"className":3584},[2001,2005],[1848,3586],{"className":3587,"style":2312},[2070],[1848,3589,3487],{"className":3590},[2316],[1848,3592],{"className":3593,"style":2312},[2070],[1848,3595,3597,3600,3603,3606,3609,3612,3652,3655,3658],{"className":3596},[1992],[1848,3598],{"className":3599,"style":3578},[1996],[1848,3601,3239],{"className":3602},[2001],[1848,3604,3236],{"className":3605},[3344],[1848,3607],{"className":3608,"style":3360},[2070],[1848,3610],{"className":3611,"style":2098},[2070],[1848,3613,3615,3618],{"className":3614},[2001],[1848,3616,3476],{"className":3617},[2001,2005],[1848,3619,3621],{"className":3620},[2009],[1848,3622,3624,3644],{"className":3623},[2013,2014],[1848,3625,3627,3641],{"className":3626},[2018],[1848,3628,3630],{"className":3629,"style":3098},[2022],[1848,3631,3632,3635],{"style":2026},[1848,3633],{"className":3634,"style":2031},[2030],[1848,3636,3638],{"className":3637},[2035,2036,2037,2038],[1848,3639,3055],{"className":3640,"style":3172},[2001,2005,2038],[1848,3642,2046],{"className":3643},[2045],[1848,3645,3647],{"className":3646},[2018],[1848,3648,3650],{"className":3649,"style":2053},[2022],[1848,3651],{},[1848,3653],{"className":3654,"style":2071},[2070],[1848,3656,2763],{"className":3657},[2075],[1848,3659],{"className":3660,"style":2071},[2070],[1848,3662,3664,3667,3670,3673,3676,3679],{"className":3663},[1992],[1848,3665],{"className":3666,"style":3578},[1996],[1848,3668,3239],{"className":3669},[2001],[1848,3671,1798],{"className":3672},[2001,2005],[1848,3674],{"className":3675,"style":2312},[2070],[1848,3677,3487],{"className":3678},[2316],[1848,3680],{"className":3681,"style":2312},[2070],[1848,3683,3685,3689],{"className":3684},[1992],[1848,3686],{"className":3687,"style":3688},[1996],"height:0.6444em;",[1848,3690,3510],{"className":3691},[2001],[1798,3693,3694,3695,3697],{},"Each spends half of income on each good, so aggregate demand for ",[1835,3696,1877],{}," is:",[1848,3699,3701],{"className":3700},[1851],[1848,3702,3704,3793],{"className":3703},[1855],[1848,3705,3707],{"className":3706},[1859],[1861,3708,3709],{"xmlns":1863,"display":1864},[1866,3710,3711,3790],{},[1869,3712,3713,3719,3721,3727,3729,3754,3756,3775,3777,3780,3782,3788],{},[1872,3714,3715,3717],{},[1875,3716,1877],{},[1875,3718,3042],{},[1881,3720,3487],{},[1872,3722,3723,3725],{},[1875,3724,1877],{},[1875,3726,3055],{},[1881,3728,2763],{},[3730,3731,3732,3748],"mfrac",{},[1869,3733,3734,3740,3742],{},[1872,3735,3736,3738],{},[1875,3737,3476],{},[1875,3739,3042],{},[1881,3741,3487],{},[1872,3743,3744,3746],{},[1875,3745,3476],{},[1875,3747,3055],{},[1869,3749,3750,3752],{},[1921,3751,3239],{},[1875,3753,1798],{},[1881,3755,2763],{},[3730,3757,3758,3769],{},[1869,3759,3760,3763,3765,3767],{},[1921,3761,3762],{},"10",[1875,3764,1798],{},[1881,3766,3487],{},[1921,3768,3762],{},[1869,3770,3771,3773],{},[1921,3772,3239],{},[1875,3774,1798],{},[1881,3776,2763],{},[1921,3778,3779],{},"5",[1881,3781,3487],{},[3730,3783,3784,3786],{},[1921,3785,3779],{},[1875,3787,1798],{},[1875,3789,1978],{"mathvariant":1977},[1980,3791,3792],{"encoding":1982},"x_A+x_B=\\frac{m_A+m_B}{2p}\n=\\frac{10p+10}{2p}=5+\\frac5p.",[1848,3794,3796,3852,3907,4082,4179,4198],{"className":3795,"ariaHidden":1988},[1987],[1848,3797,3799,3803,3843,3846,3849],{"className":3798},[1992],[1848,3800],{"className":3801,"style":3802},[1996],"height:0.7333em;vertical-align:-0.15em;",[1848,3804,3806,3809],{"className":3805},[2001],[1848,3807,1877],{"className":3808},[2001,2005],[1848,3810,3812],{"className":3811},[2009],[1848,3813,3815,3835],{"className":3814},[2013,2014],[1848,3816,3818,3832],{"className":3817},[2018],[1848,3819,3821],{"className":3820,"style":3098},[2022],[1848,3822,3823,3826],{"style":2026},[1848,3824],{"className":3825,"style":2031},[2030],[1848,3827,3829],{"className":3828},[2035,2036,2037,2038],[1848,3830,3042],{"className":3831},[2001,2005,2038],[1848,3833,2046],{"className":3834},[2045],[1848,3836,3838],{"className":3837},[2018],[1848,3839,3841],{"className":3840,"style":2053},[2022],[1848,3842],{},[1848,3844],{"className":3845,"style":2312},[2070],[1848,3847,3487],{"className":3848},[2316],[1848,3850],{"className":3851,"style":2312},[2070],[1848,3853,3855,3858,3898,3901,3904],{"className":3854},[1992],[1848,3856],{"className":3857,"style":3279},[1996],[1848,3859,3861,3864],{"className":3860},[2001],[1848,3862,1877],{"className":3863},[2001,2005],[1848,3865,3867],{"className":3866},[2009],[1848,3868,3870,3890],{"className":3869},[2013,2014],[1848,3871,3873,3887],{"className":3872},[2018],[1848,3874,3876],{"className":3875,"style":3098},[2022],[1848,3877,3878,3881],{"style":2026},[1848,3879],{"className":3880,"style":2031},[2030],[1848,3882,3884],{"className":3883},[2035,2036,2037,2038],[1848,3885,3055],{"className":3886,"style":3172},[2001,2005,2038],[1848,3888,2046],{"className":3889},[2045],[1848,3891,3893],{"className":3892},[2018],[1848,3894,3896],{"className":3895,"style":2053},[2022],[1848,3897],{},[1848,3899],{"className":3900,"style":2071},[2070],[1848,3902,2763],{"className":3903},[2075],[1848,3905],{"className":3906,"style":2071},[2070],[1848,3908,3910,3914,4073,4076,4079],{"className":3909},[1992],[1848,3911],{"className":3912,"style":3913},[1996],"height:2.1408em;vertical-align:-0.8804em;",[1848,3915,3917,3921,4070],{"className":3916},[2001],[1848,3918],{"className":3919},[2059,3920],"nulldelimiter",[1848,3922,3924],{"className":3923},[3730],[1848,3925,3927,4061],{"className":3926},[2013,2014],[1848,3928,3930,4058],{"className":3929},[2018],[1848,3931,3934,3949,3960],{"className":3932,"style":3933},[2022],"height:1.2603em;",[1848,3935,3937,3940],{"style":3936},"top:-2.314em;",[1848,3938],{"className":3939,"style":2119},[2030],[1848,3941,3943,3946],{"className":3942},[2001],[1848,3944,3239],{"className":3945},[2001],[1848,3947,1798],{"className":3948},[2001,2005],[1848,3950,3952,3955],{"style":3951},"top:-3.23em;",[1848,3953],{"className":3954,"style":2119},[2030],[1848,3956],{"className":3957,"style":3959},[3958],"frac-line","border-bottom-width:0.04em;",[1848,3961,3963,3966],{"style":3962},"top:-3.677em;",[1848,3964],{"className":3965,"style":2119},[2030],[1848,3967,3969,4009,4012,4015,4018],{"className":3968},[2001],[1848,3970,3972,3975],{"className":3971},[2001],[1848,3973,3476],{"className":3974},[2001,2005],[1848,3976,3978],{"className":3977},[2009],[1848,3979,3981,4001],{"className":3980},[2013,2014],[1848,3982,3984,3998],{"className":3983},[2018],[1848,3985,3987],{"className":3986,"style":3098},[2022],[1848,3988,3989,3992],{"style":2026},[1848,3990],{"className":3991,"style":2031},[2030],[1848,3993,3995],{"className":3994},[2035,2036,2037,2038],[1848,3996,3042],{"className":3997},[2001,2005,2038],[1848,3999,2046],{"className":4000},[2045],[1848,4002,4004],{"className":4003},[2018],[1848,4005,4007],{"className":4006,"style":2053},[2022],[1848,4008],{},[1848,4010],{"className":4011,"style":2312},[2070],[1848,4013,3487],{"className":4014},[2316],[1848,4016],{"className":4017,"style":2312},[2070],[1848,4019,4021,4024],{"className":4020},[2001],[1848,4022,3476],{"className":4023},[2001,2005],[1848,4025,4027],{"className":4026},[2009],[1848,4028,4030,4050],{"className":4029},[2013,2014],[1848,4031,4033,4047],{"className":4032},[2018],[1848,4034,4036],{"className":4035,"style":3098},[2022],[1848,4037,4038,4041],{"style":2026},[1848,4039],{"className":4040,"style":2031},[2030],[1848,4042,4044],{"className":4043},[2035,2036,2037,2038],[1848,4045,3055],{"className":4046,"style":3172},[2001,2005,2038],[1848,4048,2046],{"className":4049},[2045],[1848,4051,4053],{"className":4052},[2018],[1848,4054,4056],{"className":4055,"style":2053},[2022],[1848,4057],{},[1848,4059,2046],{"className":4060},[2045],[1848,4062,4064],{"className":4063},[2018],[1848,4065,4068],{"className":4066,"style":4067},[2022],"height:0.8804em;",[1848,4069],{},[1848,4071],{"className":4072},[2066,3920],[1848,4074],{"className":4075,"style":2071},[2070],[1848,4077,2763],{"className":4078},[2075],[1848,4080],{"className":4081,"style":2071},[2070],[1848,4083,4085,4089,4170,4173,4176],{"className":4084},[1992],[1848,4086],{"className":4087,"style":4088},[1996],"height:2.2019em;vertical-align:-0.8804em;",[1848,4090,4092,4095,4167],{"className":4091},[2001],[1848,4093],{"className":4094},[2059,3920],[1848,4096,4098],{"className":4097},[3730],[1848,4099,4101,4159],{"className":4100},[2013,2014],[1848,4102,4104,4156],{"className":4103},[2018],[1848,4105,4108,4122,4130],{"className":4106,"style":4107},[2022],"height:1.3214em;",[1848,4109,4110,4113],{"style":3936},[1848,4111],{"className":4112,"style":2119},[2030],[1848,4114,4116,4119],{"className":4115},[2001],[1848,4117,3239],{"className":4118},[2001],[1848,4120,1798],{"className":4121},[2001,2005],[1848,4123,4124,4127],{"style":3951},[1848,4125],{"className":4126,"style":2119},[2030],[1848,4128],{"className":4129,"style":3959},[3958],[1848,4131,4132,4135],{"style":3962},[1848,4133],{"className":4134,"style":2119},[2030],[1848,4136,4138,4141,4144,4147,4150,4153],{"className":4137},[2001],[1848,4139,3762],{"className":4140},[2001],[1848,4142,1798],{"className":4143},[2001,2005],[1848,4145],{"className":4146,"style":2312},[2070],[1848,4148,3487],{"className":4149},[2316],[1848,4151],{"className":4152,"style":2312},[2070],[1848,4154,3762],{"className":4155},[2001],[1848,4157,2046],{"className":4158},[2045],[1848,4160,4162],{"className":4161},[2018],[1848,4163,4165],{"className":4164,"style":4067},[2022],[1848,4166],{},[1848,4168],{"className":4169},[2066,3920],[1848,4171],{"className":4172,"style":2071},[2070],[1848,4174,2763],{"className":4175},[2075],[1848,4177],{"className":4178,"style":2071},[2070],[1848,4180,4182,4186,4189,4192,4195],{"className":4181},[1992],[1848,4183],{"className":4184,"style":4185},[1996],"height:0.7278em;vertical-align:-0.0833em;",[1848,4187,3779],{"className":4188},[2001],[1848,4190],{"className":4191,"style":2312},[2070],[1848,4193,3487],{"className":4194},[2316],[1848,4196],{"className":4197,"style":2312},[2070],[1848,4199,4201,4204,4266],{"className":4200},[1992],[1848,4202],{"className":4203,"style":4088},[1996],[1848,4205,4207,4210,4263],{"className":4206},[2001],[1848,4208],{"className":4209},[2059,3920],[1848,4211,4213],{"className":4212},[3730],[1848,4214,4216,4255],{"className":4215},[2013,2014],[1848,4217,4219,4252],{"className":4218},[2018],[1848,4220,4222,4233,4241],{"className":4221,"style":4107},[2022],[1848,4223,4224,4227],{"style":3936},[1848,4225],{"className":4226,"style":2119},[2030],[1848,4228,4230],{"className":4229},[2001],[1848,4231,1798],{"className":4232},[2001,2005],[1848,4234,4235,4238],{"style":3951},[1848,4236],{"className":4237,"style":2119},[2030],[1848,4239],{"className":4240,"style":3959},[3958],[1848,4242,4243,4246],{"style":3962},[1848,4244],{"className":4245,"style":2119},[2030],[1848,4247,4249],{"className":4248},[2001],[1848,4250,3779],{"className":4251},[2001],[1848,4253,2046],{"className":4254},[2045],[1848,4256,4258],{"className":4257},[2018],[1848,4259,4261],{"className":4260,"style":4067},[2022],[1848,4262],{},[1848,4264],{"className":4265},[2066,3920],[1848,4267,1978],{"className":4268},[2001],[1798,4270,4271,4272,4275,4276,4279,4280,1978],{},"Market clearing requires ",[1835,4273,4274],{},"5+5\u002Fp=10",", hence ",[1835,4277,4278],{},"p*=1",". Each income is 10 and each demands ",[1835,4281,4282],{},"(5,5)",[4284,4285,4286,4305],"table",{},[4287,4288,4289],"thead",{},[4290,4291,4292,4296,4299,4302],"tr",{},[4293,4294,4295],"th",{},"Consumer",[4293,4297,4298],{},"Endowment",[4293,4300,4301],{},"Equilibrium bundle",[4293,4303,4304],{},"Net trade",[4306,4307,4308,4331],"tbody",{},[4290,4309,4310,4313,4318,4322],{},[4311,4312,3042],"td",{},[4311,4314,4315],{},[1835,4316,4317],{},"(8,2)",[4311,4319,4320],{},[1835,4321,4282],{},[4311,4323,4324,4325,4327,4328],{},"sells 3 units of ",[1835,4326,1877],{},", buys 3 of ",[1835,4329,4330],{},"y",[4290,4332,4333,4335,4340,4344],{},[4311,4334,3055],{},[4311,4336,4337],{},[1835,4338,4339],{},"(2,8)",[4311,4341,4342],{},[1835,4343,4282],{},[4311,4345,4346,4347,4349,4350],{},"buys 3 units of ",[1835,4348,1877],{},", sells 3 of ",[1835,4351,4330],{},[1798,4353,4354],{},"Both optimise, trade balances in value, and aggregate demand equals resources.",[1793,4356,4358],{"id":4357},"_4-walras-law-reducesbut-does-not-solvethe-system","4. Walras' law reduces—but does not solve—the system",[1798,4360,4361],{},"Aggregate excess demand is:",[1848,4363,4365],{"className":4364},[1851],[1848,4366,4368,4426],{"className":4367},[1855],[1848,4369,4371],{"className":4370},[1859],[1861,4372,4373],{"xmlns":1863,"display":1864},[1866,4374,4375,4423],{},[1869,4376,4377,4380,4382,4384,4386,4388,4394,4400,4402,4404,4406,4409,4415,4421],{},[1875,4378,4379],{},"z",[1881,4381,1884],{"stretchy":1883},[1875,4383,1798],{},[1881,4385,1889],{"stretchy":1883},[1881,4387,2763],{},[1900,4389,4390,4392],{},[1881,4391,2470],{},[1875,4393,1837],{},[1872,4395,4396,4398],{},[1875,4397,1877],{},[1875,4399,1837],{},[1881,4401,1884],{"stretchy":1883},[1875,4403,1798],{},[1881,4405,1889],{"stretchy":1883},[1881,4407,4408],{},"−",[1900,4410,4411,4413],{},[1881,4412,2470],{},[1875,4414,1837],{},[1872,4416,4417,4419],{},[1875,4418,1969],{},[1875,4420,1837],{},[1875,4422,1978],{"mathvariant":1977},[1980,4424,4425],{"encoding":1982},"z(p)=\\sum_i x_i(p)-\\sum_i\\omega_i.",[1848,4427,4429,4457,4568],{"className":4428,"ariaHidden":1988},[1987],[1848,4430,4432,4435,4439,4442,4445,4448,4451,4454],{"className":4431},[1992],[1848,4433],{"className":4434,"style":1997},[1996],[1848,4436,4379],{"className":4437,"style":4438},[2001,2005],"margin-right:0.044em;",[1848,4440,1884],{"className":4441},[2059],[1848,4443,1798],{"className":4444},[2001,2005],[1848,4446,1889],{"className":4447},[2066],[1848,4449],{"className":4450,"style":2071},[2070],[1848,4452,2763],{"className":4453},[2075],[1848,4455],{"className":4456,"style":2071},[2070],[1848,4458,4460,4463,4507,4510,4550,4553,4556,4559,4562,4565],{"className":4459},[1992],[1848,4461],{"className":4462,"style":2507},[1996],[1848,4464,4466],{"className":4465},[2089,2102],[1848,4467,4469,4499],{"className":4468},[2013,2014],[1848,4470,4472,4496],{"className":4471},[2018],[1848,4473,4475,4486],{"className":4474,"style":2520},[2022],[1848,4476,4477,4480],{"style":2523},[1848,4478],{"className":4479,"style":2527},[2030],[1848,4481,4483],{"className":4482},[2035,2036,2037,2038],[1848,4484,1837],{"className":4485},[2001,2005,2038],[1848,4487,4488,4491],{"style":2536},[1848,4489],{"className":4490,"style":2527},[2030],[1848,4492,4493],{},[1848,4494,2470],{"className":4495},[2089,2545,2546],[1848,4497,2046],{"className":4498},[2045],[1848,4500,4502],{"className":4501},[2018],[1848,4503,4505],{"className":4504,"style":2556},[2022],[1848,4506],{},[1848,4508],{"className":4509,"style":2098},[2070],[1848,4511,4513,4516],{"className":4512},[2001],[1848,4514,1877],{"className":4515},[2001,2005],[1848,4517,4519],{"className":4518},[2009],[1848,4520,4522,4542],{"className":4521},[2013,2014],[1848,4523,4525,4539],{"className":4524},[2018],[1848,4526,4528],{"className":4527,"style":2023},[2022],[1848,4529,4530,4533],{"style":2026},[1848,4531],{"className":4532,"style":2031},[2030],[1848,4534,4536],{"className":4535},[2035,2036,2037,2038],[1848,4537,1837],{"className":4538},[2001,2005,2038],[1848,4540,2046],{"className":4541},[2045],[1848,4543,4545],{"className":4544},[2018],[1848,4546,4548],{"className":4547,"style":2053},[2022],[1848,4549],{},[1848,4551,1884],{"className":4552},[2059],[1848,4554,1798],{"className":4555},[2001,2005],[1848,4557,1889],{"className":4558},[2066],[1848,4560],{"className":4561,"style":2312},[2070],[1848,4563,4408],{"className":4564},[2316],[1848,4566],{"className":4567,"style":2312},[2070],[1848,4569,4571,4574,4618,4621,4661],{"className":4570},[1992],[1848,4572],{"className":4573,"style":2507},[1996],[1848,4575,4577],{"className":4576},[2089,2102],[1848,4578,4580,4610],{"className":4579},[2013,2014],[1848,4581,4583,4607],{"className":4582},[2018],[1848,4584,4586,4597],{"className":4585,"style":2520},[2022],[1848,4587,4588,4591],{"style":2523},[1848,4589],{"className":4590,"style":2527},[2030],[1848,4592,4594],{"className":4593},[2035,2036,2037,2038],[1848,4595,1837],{"className":4596},[2001,2005,2038],[1848,4598,4599,4602],{"style":2536},[1848,4600],{"className":4601,"style":2527},[2030],[1848,4603,4604],{},[1848,4605,2470],{"className":4606},[2089,2545,2546],[1848,4608,2046],{"className":4609},[2045],[1848,4611,4613],{"className":4612},[2018],[1848,4614,4616],{"className":4615,"style":2556},[2022],[1848,4617],{},[1848,4619],{"className":4620,"style":2098},[2070],[1848,4622,4624,4627],{"className":4623},[2001],[1848,4625,1969],{"className":4626,"style":2406},[2001,2005],[1848,4628,4630],{"className":4629},[2009],[1848,4631,4633,4653],{"className":4632},[2013,2014],[1848,4634,4636,4650],{"className":4635},[2018],[1848,4637,4639],{"className":4638,"style":2023},[2022],[1848,4640,4641,4644],{"style":2421},[1848,4642],{"className":4643,"style":2031},[2030],[1848,4645,4647],{"className":4646},[2035,2036,2037,2038],[1848,4648,1837],{"className":4649},[2001,2005,2038],[1848,4651,2046],{"className":4652},[2045],[1848,4654,4656],{"className":4655},[2018],[1848,4657,4659],{"className":4658,"style":2053},[2022],[1848,4660],{},[1848,4662,1978],{"className":4663},[2001],[1798,4665,4666],{},"If every budget satisfies Walras' law, then:",[1848,4668,4670],{"className":4669},[1851],[1848,4671,4673,4702],{"className":4672},[1855],[1848,4674,4676],{"className":4675},[1859],[1861,4677,4678],{"xmlns":1863,"display":1864},[1866,4679,4680,4699],{},[1869,4681,4682,4684,4686,4688,4690,4692,4694,4696],{},[1875,4683,1798],{},[1881,4685,1951],{},[1875,4687,4379],{},[1881,4689,1884],{"stretchy":1883},[1875,4691,1798],{},[1881,4693,1889],{"stretchy":1883},[1881,4695,2763],{},[1921,4697,4698],{},"0.",[1980,4700,4701],{"encoding":1982},"p\\cdot z(p)=0.",[1848,4703,4705,4723,4750],{"className":4704,"ariaHidden":1988},[1987],[1848,4706,4708,4711,4714,4717,4720],{"className":4707},[1992],[1848,4709],{"className":4710,"style":2305},[1996],[1848,4712,1798],{"className":4713},[2001,2005],[1848,4715],{"className":4716,"style":2312},[2070],[1848,4718,1951],{"className":4719},[2316],[1848,4721],{"className":4722,"style":2312},[2070],[1848,4724,4726,4729,4732,4735,4738,4741,4744,4747],{"className":4725},[1992],[1848,4727],{"className":4728,"style":1997},[1996],[1848,4730,4379],{"className":4731,"style":4438},[2001,2005],[1848,4733,1884],{"className":4734},[2059],[1848,4736,1798],{"className":4737},[2001,2005],[1848,4739,1889],{"className":4740},[2066],[1848,4742],{"className":4743,"style":2071},[2070],[1848,4745,2763],{"className":4746},[2075],[1848,4748],{"className":4749,"style":2071},[2070],[1848,4751,4753,4756],{"className":4752},[1992],[1848,4754],{"className":4755,"style":3688},[1996],[1848,4757,4698],{"className":4758},[2001],[1798,4760,4761],{},"Therefore, if all but one market clear and the omitted good has a positive price, the last clears too. Walras' law is an accounting restriction; it does not prove that an equilibrium exists, is unique, or is stable under price adjustment.",[1793,4763,4765],{"id":4764},"_5-the-welfare-theoremsand-their-assumptions","5. The welfare theorems—and their assumptions",[4767,4768,4770],"h3",{"id":4769},"first-welfare-theorem","First welfare theorem",[1798,4772,4773],{},"Under local nonsatiation and a complete competitive-market environment, a Walrasian equilibrium is Pareto efficient.",[1798,4775,4776],{},"The result can fail with:",[1809,4778,4779,4782,4785,4788,4791],{},[1812,4780,4781],{},"externalities or public goods;",[1812,4783,4784],{},"market power;",[1812,4786,4787],{},"asymmetric information;",[1812,4789,4790],{},"missing state-contingent markets;",[1812,4792,4793],{},"non-convex technologies or other institutional constraints.",[4767,4795,4797],{"id":4796},"second-welfare-theorem","Second welfare theorem",[1798,4799,4800],{},"With convex preferences and production sets plus suitable regularity, a Pareto-efficient allocation can be decentralised as a competitive equilibrium after appropriate lump-sum redistribution of endowments.",[1798,4802,4803],{},"This separates, in theory, distribution from price-based allocation. In practice, lump-sum transfers may be unavailable because type, wealth, or earning ability is private; taxes then change incentives.",[4805,4806,4808],"warning",{"title":4807},"Pareto efficiency is deliberately incomplete","An allocation where one person owns almost everything can be Pareto efficient. The criterion rules out unambiguous waste; it does not encode equality, rights, desert, or priority to the worse-off.",[1793,4810,4812],{"id":4811},"_6-existence-uniqueness-and-stability-are-different-claims","6. Existence, uniqueness, and stability are different claims",[1809,4814,4815,4821,4827,4833],{},[1812,4816,4817,4820],{},[3191,4818,4819],{},"Existence:"," at least one price vector clears markets.",[1812,4822,4823,4826],{},[3191,4824,4825],{},"Uniqueness:"," only one relative-price equilibrium exists.",[1812,4828,4829,4832],{},[3191,4830,4831],{},"Local stability:"," small deviations trigger forces that return to it.",[1812,4834,4835,4838],{},[3191,4836,4837],{},"Global stability:"," adjustment converges from a wide set of starting prices.",[1798,4840,4841],{},"Continuity, convexity, and bounded feasible sets help establish existence through a fixed-point argument. Gross-substitutes conditions can support uniqueness and price adjustment. Standard preference assumptions alone do not guarantee either.",[1793,4843,4845],{"id":4844},"_7-add-firms-and-production","7. Add firms and production",[1798,4847,4848,4849,4852,4853,4856,4857,4860],{},"Firms choose net output ",[1835,4850,4851],{},"y_j"," from production set ",[1835,4854,4855],{},"Y_j"," to maximise ",[1835,4858,4859],{},"p·y_j",". Consumers own firm profits. Feasibility becomes:",[1848,4862,4864],{"className":4863},[1851],[1848,4865,4867,4922],{"className":4866},[1855],[1848,4868,4870],{"className":4869},[1859],[1861,4871,4872],{"xmlns":1863,"display":1864},[1866,4873,4874,4919],{},[1869,4875,4876,4882,4888,4890,4896,4902,4904,4911,4917],{},[1900,4877,4878,4880],{},[1881,4879,2470],{},[1875,4881,1837],{},[1872,4883,4884,4886],{},[1875,4885,1877],{},[1875,4887,1837],{},[1881,4889,1960],{},[1900,4891,4892,4894],{},[1881,4893,2470],{},[1875,4895,1837],{},[1872,4897,4898,4900],{},[1875,4899,1969],{},[1875,4901,1837],{},[1881,4903,3487],{},[1900,4905,4906,4908],{},[1881,4907,2470],{},[1875,4909,4910],{},"j",[1872,4912,4913,4915],{},[1875,4914,4330],{},[1875,4916,4910],{},[1875,4918,1978],{"mathvariant":1977},[1980,4920,4921],{"encoding":1982},"\\sum_i x_i\\le\\sum_i\\omega_i+\\sum_j y_j.",[1848,4923,4925,5027,5129],{"className":4924,"ariaHidden":1988},[1987],[1848,4926,4928,4931,4975,4978,5018,5021,5024],{"className":4927},[1992],[1848,4929],{"className":4930,"style":2507},[1996],[1848,4932,4934],{"className":4933},[2089,2102],[1848,4935,4937,4967],{"className":4936},[2013,2014],[1848,4938,4940,4964],{"className":4939},[2018],[1848,4941,4943,4954],{"className":4942,"style":2520},[2022],[1848,4944,4945,4948],{"style":2523},[1848,4946],{"className":4947,"style":2527},[2030],[1848,4949,4951],{"className":4950},[2035,2036,2037,2038],[1848,4952,1837],{"className":4953},[2001,2005,2038],[1848,4955,4956,4959],{"style":2536},[1848,4957],{"className":4958,"style":2527},[2030],[1848,4960,4961],{},[1848,4962,2470],{"className":4963},[2089,2545,2546],[1848,4965,2046],{"className":4966},[2045],[1848,4968,4970],{"className":4969},[2018],[1848,4971,4973],{"className":4972,"style":2556},[2022],[1848,4974],{},[1848,4976],{"className":4977,"style":2098},[2070],[1848,4979,4981,4984],{"className":4980},[2001],[1848,4982,1877],{"className":4983},[2001,2005],[1848,4985,4987],{"className":4986},[2009],[1848,4988,4990,5010],{"className":4989},[2013,2014],[1848,4991,4993,5007],{"className":4992},[2018],[1848,4994,4996],{"className":4995,"style":2023},[2022],[1848,4997,4998,5001],{"style":2026},[1848,4999],{"className":5000,"style":2031},[2030],[1848,5002,5004],{"className":5003},[2035,2036,2037,2038],[1848,5005,1837],{"className":5006},[2001,2005,2038],[1848,5008,2046],{"className":5009},[2045],[1848,5011,5013],{"className":5012},[2018],[1848,5014,5016],{"className":5015,"style":2053},[2022],[1848,5017],{},[1848,5019],{"className":5020,"style":2071},[2070],[1848,5022,1960],{"className":5023},[2075],[1848,5025],{"className":5026,"style":2071},[2070],[1848,5028,5030,5033,5077,5080,5120,5123,5126],{"className":5029},[1992],[1848,5031],{"className":5032,"style":2507},[1996],[1848,5034,5036],{"className":5035},[2089,2102],[1848,5037,5039,5069],{"className":5038},[2013,2014],[1848,5040,5042,5066],{"className":5041},[2018],[1848,5043,5045,5056],{"className":5044,"style":2520},[2022],[1848,5046,5047,5050],{"style":2523},[1848,5048],{"className":5049,"style":2527},[2030],[1848,5051,5053],{"className":5052},[2035,2036,2037,2038],[1848,5054,1837],{"className":5055},[2001,2005,2038],[1848,5057,5058,5061],{"style":2536},[1848,5059],{"className":5060,"style":2527},[2030],[1848,5062,5063],{},[1848,5064,2470],{"className":5065},[2089,2545,2546],[1848,5067,2046],{"className":5068},[2045],[1848,5070,5072],{"className":5071},[2018],[1848,5073,5075],{"className":5074,"style":2556},[2022],[1848,5076],{},[1848,5078],{"className":5079,"style":2098},[2070],[1848,5081,5083,5086],{"className":5082},[2001],[1848,5084,1969],{"className":5085,"style":2406},[2001,2005],[1848,5087,5089],{"className":5088},[2009],[1848,5090,5092,5112],{"className":5091},[2013,2014],[1848,5093,5095,5109],{"className":5094},[2018],[1848,5096,5098],{"className":5097,"style":2023},[2022],[1848,5099,5100,5103],{"style":2421},[1848,5101],{"className":5102,"style":2031},[2030],[1848,5104,5106],{"className":5105},[2035,2036,2037,2038],[1848,5107,1837],{"className":5108},[2001,2005,2038],[1848,5110,2046],{"className":5111},[2045],[1848,5113,5115],{"className":5114},[2018],[1848,5116,5118],{"className":5117,"style":2053},[2022],[1848,5119],{},[1848,5121],{"className":5122,"style":2312},[2070],[1848,5124,3487],{"className":5125},[2316],[1848,5127],{"className":5128,"style":2312},[2070],[1848,5130,5132,5136,5182,5185,5226],{"className":5131},[1992],[1848,5133],{"className":5134,"style":5135},[1996],"height:2.4638em;vertical-align:-1.4138em;",[1848,5137,5139],{"className":5138},[2089,2102],[1848,5140,5142,5173],{"className":5141},[2013,2014],[1848,5143,5145,5170],{"className":5144},[2018],[1848,5146,5148,5160],{"className":5147,"style":2520},[2022],[1848,5149,5150,5153],{"style":2523},[1848,5151],{"className":5152,"style":2527},[2030],[1848,5154,5156],{"className":5155},[2035,2036,2037,2038],[1848,5157,4910],{"className":5158,"style":5159},[2001,2005,2038],"margin-right:0.0572em;",[1848,5161,5162,5165],{"style":2536},[1848,5163],{"className":5164,"style":2527},[2030],[1848,5166,5167],{},[1848,5168,2470],{"className":5169},[2089,2545,2546],[1848,5171,2046],{"className":5172},[2045],[1848,5174,5176],{"className":5175},[2018],[1848,5177,5180],{"className":5178,"style":5179},[2022],"height:1.4138em;",[1848,5181],{},[1848,5183],{"className":5184,"style":2098},[2070],[1848,5186,5188,5191],{"className":5187},[2001],[1848,5189,4330],{"className":5190,"style":2406},[2001,2005],[1848,5192,5194],{"className":5193},[2009],[1848,5195,5197,5217],{"className":5196},[2013,2014],[1848,5198,5200,5214],{"className":5199},[2018],[1848,5201,5203],{"className":5202,"style":2023},[2022],[1848,5204,5205,5208],{"style":2421},[1848,5206],{"className":5207,"style":2031},[2030],[1848,5209,5211],{"className":5210},[2035,2036,2037,2038],[1848,5212,4910],{"className":5213,"style":5159},[2001,2005,2038],[1848,5215,2046],{"className":5216},[2045],[1848,5218,5220],{"className":5219},[2018],[1848,5221,5224],{"className":5222,"style":5223},[2022],"height:0.2861em;",[1848,5225],{},[1848,5227,1978],{"className":5228},[2001],[1798,5230,5231],{},"At an interior efficient allocation with production:",[1848,5233,5235],{"className":5234},[1851],[1848,5236,5238,5267],{"className":5237},[1855],[1848,5239,5241],{"className":5240},[1859],[1861,5242,5243],{"xmlns":1863,"display":1864},[1866,5244,5245,5264],{},[1869,5246,5247,5249,5251,5253,5255,5257,5259,5262],{},[1875,5248,3031],{},[1875,5250,3034],{},[1875,5252,3039],{},[1881,5254,2763],{},[1875,5256,3031],{},[1875,5258,3034],{},[1875,5260,5261],{},"T",[1881,5263,3236],{"separator":1988},[1980,5265,5266],{"encoding":1982},"MRS=MRT,",[1848,5268,5270,5295],{"className":5269,"ariaHidden":1988},[1987],[1848,5271,5273,5277,5280,5283,5286,5289,5292],{"className":5272},[1992],[1848,5274],{"className":5275,"style":5276},[1996],"height:0.6833em;",[1848,5278,3031],{"className":5279,"style":3074},[2001,2005],[1848,5281,3034],{"className":5282,"style":3078},[2001,2005],[1848,5284,3039],{"className":5285,"style":3085},[2001,2005],[1848,5287],{"className":5288,"style":2071},[2070],[1848,5290,2763],{"className":5291},[2075],[1848,5293],{"className":5294,"style":2071},[2070],[1848,5296,5298,5302,5305,5308,5312],{"className":5297},[1992],[1848,5299],{"className":5300,"style":5301},[1996],"height:0.8778em;vertical-align:-0.1944em;",[1848,5303,3031],{"className":5304,"style":3074},[2001,2005],[1848,5306,3034],{"className":5307,"style":3078},[2001,2005],[1848,5309,5261],{"className":5310,"style":5311},[2001,2005],"margin-right:0.1389em;",[1848,5313,3236],{"className":5314},[3344],[1798,5316,5317],{},"so consumers' willingness to substitute goods equals the economy's marginal transformation rate. Distortions anywhere in the production chain can alter prices and quantities elsewhere.",[1793,5319,5321],{"id":5320},"_8-current-extension-production-networks","8. Current extension: production networks",[1798,5323,5324,5325,5332],{},"Baqaee and Farhi study trade economies with international production networks and wedge-like distortions such as markups, tariffs, and nominal rigidities (",[5326,5327,5331],"a",{"href":5328,"rel":5329},"https:\u002F\u002Fdoi.org\u002F10.3982\u002FECTA17513",[5330],"nofollow","2024","). Their framework shows why a sector's sales share alone need not measure the full welfare effect of a shock: substitution, input-output links, and distortions generate general-equilibrium propagation.",[1798,5334,5335],{},"Use the paper as a conceptual warning. A supply disruption at a small upstream input can matter through network position, while a large gross-output sector need not create an equally large welfare loss. Exact effects require an estimated network and elasticities; the theorem is not a universal multiplier.",[1793,5337,5339],{"id":5338},"_9-partial-versus-general-equilibrium","9. Partial versus general equilibrium",[4284,5341,5342,5355],{},[4287,5343,5344],{},[4290,5345,5346,5349,5352],{},[4293,5347,5348],{},"Question",[4293,5350,5351],{},"Partial equilibrium may suffice",[4293,5353,5354],{},"General equilibrium is needed",[4306,5356,5357,5368,5379,5390],{},[4290,5358,5359,5362,5365],{},[4311,5360,5361],{},"small tax in one minor market",[4311,5363,5364],{},"other prices\u002Fincomes nearly fixed",[4311,5366,5367],{},"tax changes wages, profits, or linked input prices",[4290,5369,5370,5373,5376],{},[4311,5371,5372],{},"local transport project",[4311,5374,5375],{},"narrow users and routes",[4311,5377,5378],{},"land prices, location, and labour markets adjust",[4290,5380,5381,5384,5387],{},[4311,5382,5383],{},"carbon price",[4311,5385,5386],{},"one fuel response",[4311,5388,5389],{},"energy, production networks, trade, and revenue recycling",[4290,5391,5392,5395,5398],{},[4311,5393,5394],{},"AI compute shortage",[4311,5396,5397],{},"one service price",[4311,5399,5400],{},"cloud, chips, energy, entry, and downstream innovation",[1798,5402,5403],{},"The choice is about the counterfactual, not prestige: use the smallest model that contains the important feedbacks.",[1793,5405,5407],{"id":5406},"practice","Practice",[2719,5409,5410,5420,5430,5433,5436],{},[1812,5411,5412,5413,5416,5417,1978],{},"Resolve the worked economy when A's endowment becomes ",[1835,5414,5415],{},"(9,1)"," and B's ",[1835,5418,5419],{},"(1,9)",[1812,5421,5422,5423,5426,5427,1978],{},"Find the contract-curve condition when ",[1835,5424,5425],{},"u_A=x_Ay_A"," and ",[1835,5428,5429],{},"u_B=x_B²y_B",[1812,5431,5432],{},"Give an efficient but highly unequal allocation.",[1812,5434,5435],{},"Identify which welfare-theorem assumption fails in pollution, monopoly, and hidden-action insurance.",[1812,5437,5438],{},"Draw a three-sector input network and trace one upstream productivity shock.",[1793,5440,5442],{"id":5441},"quick-check","Quick check",[1809,5444,5445,5448,5451,5454,5457],{},[1812,5446,5447],{},"Equilibrium requires optimisation and simultaneous feasibility.",[1812,5449,5450],{},"Equal MRS is an interior efficiency condition, not a fairness rule.",[1812,5452,5453],{},"Walras' law is accounting; existence and stability need more.",[1812,5455,5456],{},"The welfare theorems are conditional institutional results.",[1812,5458,5459],{},"Networks turn local shocks into economy-wide price and quantity changes.",[1798,5461,5462,5465,5466,1978],{},[3191,5463,5464],{},"Next:"," ",[5326,5467,5469],{"href":5468},"..\u002F05-game-theory\u002F","replace price-taking with strategic interaction",{"title":10,"searchDepth":5471,"depth":5471,"links":5472},2,[5473,5474,5475,5476,5477,5478,5479,5484,5485,5486,5487,5488,5489],{"id":1795,"depth":5471,"text":1796},{"id":1803,"depth":5471,"text":1804},{"id":1829,"depth":5471,"text":1830},{"id":3006,"depth":5471,"text":3007},{"id":3197,"depth":5471,"text":3198},{"id":4357,"depth":5471,"text":4358},{"id":4764,"depth":5471,"text":4765,"children":5480},[5481,5483],{"id":4769,"depth":5482,"text":4770},3,{"id":4796,"depth":5482,"text":4797},{"id":4811,"depth":5471,"text":4812},{"id":4844,"depth":5471,"text":4845},{"id":5320,"depth":5471,"text":5321},{"id":5338,"depth":5471,"text":5339},{"id":5406,"depth":5471,"text":5407},{"id":5441,"depth":5471,"text":5442},"Exchange economies, Walrasian equilibrium, Pareto efficiency, welfare theorems, existence, distribution, production, and network propagation.","md",null,{},true,{"title":745,"description":5490},"mFzYhf3dQ0F7ONuGC9ZP-T4oydDbh0GeTg0eJBmrzsE",[5498,5500],{"title":739,"path":740,"stem":741,"description":5499,"children":-1},"Expected utility, certainty equivalents, risk aversion, insurance, portfolio choice, ambiguity, and climate-risk evidence.",{"title":751,"path":752,"stem":753,"description":5501,"children":-1},"Best responses, Nash equilibrium, mixed strategies, backward induction, credibility, repeated interaction, and Bayesian games.",1785754732475]