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| Preface | |
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| Consumer Choice: The Basics | |
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| Proving Most of Proposition 1.2, and More | |
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| The No-Better-Than Sets and Utility Representations | |
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| Strict Preference and Indifference | |
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| Infinite Sets and Utility Representations | |
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| Choice from Infinite Sets | |
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| Equivalent Utility Representations | |
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| Commentary | |
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| Bibliographic Notes | |
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| Problems | |
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| Monotonicity | |
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| Convexity | |
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| Continuity | |
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| Indifference Curve Diagrams | |
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| Weak and Additive Separability | |
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| Quasi-linearity | |
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| Homotheticity | |
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| Bibliographic Notes | |
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| Problems | |
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| The Consumer's Problem | |
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| Basic Facts about the CP | |
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| The Marshallian Demand Correspondence and Indirect Utility Function | |
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| Solving the CP with Calculus | |
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| Bibliographic Notes | |
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| Problems | |
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| An Example and Basic Ideas | |
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| GARP and Afriat's Theorem | |
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| Comparative Statics and the Own-Price Effect | |
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| Bibliographic Notes | |
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| Problems | |
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| Two Models and Three Representations | |
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| The Mixture-Space Theorem | |
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| States of Nature and Subjective Expected Utility | |
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| Subjective and Objective Probability and the Harsanyi Doctrine | |
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| Empirical and Theoretical Critiques | |
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| Bibliographic Notes | |
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| Problems | |
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| Properties of Utility Functions for Money | |
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| Induced Preferences for Income | |
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| Demand for Insurance and Risky Assets | |
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| Bibliographic Notes | |
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| Problems | |
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| The Standard Strategic Approach | |
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| Dynamic Programming | |
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| Testable Restrictions of the Standard Model | |
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| Three Alternatives to the Standard Model | |
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| Bibliographic Notes | |
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| Problems | |
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| Arrow's Theorem | |
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| What Do We Give Up? | |
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| Efficiency | |
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| Identifying the Pareto Frontier: Utility Imputations and Bergsonian Social Utility Functionals | |
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| Syndicate Theory and Efficient Risk Sharing: Applying Proposition 8.10 | |
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| Efficiency? | |
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| Bibliographic Notes | |
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| Problems | |
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| The Production-Possibility Set | |
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| Profit Maximization | |
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| Basics of the Firm's Profit-Maximization Problem | |
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| Afriat's Theorem for Firms | |
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| From Profit Functions to Production-Possibility Sets | |
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| How Many Production-Possibility Sets Give the Same Profit Function? | |
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| What Is Going On Here, Mathematically? | |
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| Differentiability of the Profit Function | |
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| Cost Minimization and Input-Requirement Sets | |
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| Why DoWe Care? | |
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| Bibilographic Notes | |
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| Problems | |
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| Defining the EMP | |
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| Basic Analysis of the EMP | |
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| Hicksian Demand and the Expenditure Function | |
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| Properties of the Expenditure Function | |
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| How Many Continuous Utility Functions | |
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| Give the Same Expenditure Function? | |
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| Recovering Continuous Utility Functions from Expenditure Functions | |
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| Is an Alleged Expenditure Function Really an Expenditure Function? | |
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| Connecting the CP and the EMP | |
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| Bibliographic Notes | |
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| Problems | |
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| Roy's Identity and the Slutsky Equation | |
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| Differentiability of Indirect Utility | |
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| Duality of Utility and Indirect Utility | |
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| Differentiability of Marshallian Demand | |
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| Integrability | |
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| Complements and Substitutes | |
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| Integrability and Revealed Preference | |
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| Bibliographic Notes | |
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| Problems | |
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| Producer Surplus | |
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| Consumer Surplus | |
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| Bibliographic Notes | |
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| Problems | |
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| Aggregating Firms | |
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| Aggregating Consumers | |
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| Convexification through Aggregation | |
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| Bibliographic Notes | |
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| Problems | |
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| Definitions | |
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| Basic Properties ofWalrasian Equilibrium | |
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| The Edgeworth Box | |
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| Existence ofWalrasian Equilibria | |
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| The Set of Equilibria for a Fixed Economy | |
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| The Equilibrium Correspondence | |
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| Bibliographic Notes | |
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| Problems | |
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| The First Theorem ofWelfare Economics | |
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| The Second Theorem ofWelfare Economics | |
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| Walrasian Equilibria Are in the Core | |
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| In a Large Enough Economy, Every Core Allocation Is a Walrasian-Equilibrium Allocation | |
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| Externalities and Lindahl Equilibrium | |
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| Bibliographic Notes | |
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| Problems | |
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| A Framework for Time and Uncertainty | |
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| General Equilibrium with Time and Uncertainty | |
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| Equilibria of Plans, Prices, and Price Expectations: I. Pure Exchange with Contingent Claims | |
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| EPPPE: II. Complex Financial Securities and Complete Markets | |
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| EPPPE: III. Complex Securities with Real Dividends and Complete Markets | |
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| Incomplete Markets | |
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| Firms | |
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| Bibliographic Notes | |
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| Problems | |
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| About the Appendices | |
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| Mathematical Induction | |
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| Some Simple Real Analysis | |
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| The Setting | |
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| Distance, Neighborhoods, and Open and Closed Sets | |
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| Sequences and Limits | |
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| Boundedness, (Completeness), and Compactness | |
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| Continuous Functions | |
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| Simply Connected Sets and the Intermediate-Value Theorem | |
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| Suprema and Infima; Maxes and Mins | |
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| The Maximum of a Continuous Function on a Compact Set | |
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| Lims Sup and Inf | |
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| Upper and Lower Semi-continuous Functions | |
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| Convexity | |
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| Convex Sets | |
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| The Separating- and Supporting-Hyperplane Theorems | |
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| The Support-Function Theorem | |
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| Concave and Convex Functions | |
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| Quasi-concavity and Quasi-convexity | |
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| Supergradients and Subgradients | |
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| Concave and Convex Functions and Calculus | |
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| Correspondences | |
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| Functions and Correspondences | |
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| Continuity of Correspondences | |
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| Singleton-Valued Correspondences and Continuity | |
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| Parametric Constrained Optimization Problems and Berge's Theorem | |
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| Why this Terminology? | |
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| Constrained Optimization | |
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| Dynamic Programming | |
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| Several Examples | |
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| A General Formulation | |
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| Bellman's Equation | |
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| Conserving and Unimprovable Strategies | |
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| Additive Rewards | |
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| States of the System | |
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| Solving Finite-Horizon Problems | |
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| Infinite-Horizon Problems and Stationarity | |
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| Solving Infinite-Horizon (Stationary) Problems with Unimprovability | |
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| Policy Iteration (and Transience) | |
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| Value Iteration | |
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| Examples | |
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| Things Not Covered Here: Other Optimality Criteria; Continuous Time and Control Theory | |
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| Multi-armed Bandits and Complexity | |
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| Four More Problems You Can Solve | |
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| The Implicit Function Theorem | |
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| Fixed-Point Theory | |
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| References | |
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| Index | |