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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 | |