Preface xiii
Chapter One. Choice, Preference, and Utility 1
1.1. Consumer Choice: The Basics 1
1.2. Proving Most of Proposition 1.2, and More 5
1.3. The No-Better-Than Sets and Utility Representations 7
1.4. Strict Preference and Indifference 9
1.5. Infinite Sets and Utility Representations 10
1.6. Choice from Infinite Sets 15
1.7. Equivalent Utility Representations 17
1.8. Commentary 18
Bibliographic Notes 23
Problems 23
Chapter Two. Structural Properties of Preferences and Utility Functions 30
2.1. Monotonicity 31
2.2. Convexity 32
2.3. Continuity 35
2.4. Indifference Curve Diagrams 38
2.5. Weak and Additive Separability 39
2.6. Quasi-linearity 43
2.7. Homotheticity 44
Bibliographic Notes 45
Problems 45
Chapter Three. Basics of Consumer Demand 50
3.1. The Consumer''s Problem 50
3.2. Basic Facts about the CP 52
3.3. The Marshallian Demand Correspondence and Indirect Utility Function 54
3.4. Solving the CP with Calculus 56
Bibliographic Notes 63
Problems 64
Chapter Four. Revealed Preference and Afriat''s Theorem 67
4.1. An Example and Basic Ideas 67
4.2. GARP and Afriat''s Theorem 70
4.3. Comparative Statics and the Own-Price Effect 74
Bibliographic Notes 77
Problems 78
Chapter Five. Choice under Uncertainty 79
5.1. Two Models and Three Representations 79
5.2. The Mixture-Space Theorem 89
5.3. States of Nature and Subjective Expected Utility 101
5.4. Subjective and Objective Probability and the Harsanyi Doctrine 108
5.5. Empirical and Theoretical Critiques 110
Bibliographic Notes 116
Problems 116
Chapter Six. Utility for Money 123
6.1. Properties of Utility Functions for Money 123
6.2. Induced Preferences for Income 134
6.3. Demand for Insurance and Risky Assets 138
Bibliographic Notes 140
Problems 140
Chapter Seven. Dynamic Choice 148
7.1. The Standard Strategic Approach 149
7.2. Dynamic Programming 152
7.3. Testable Restrictions of the Standard Model 153
7.4. Three Alternatives to the Standard Model 156
Bibliographic Notes 161
Problems 161
Chapter Eight. Social Choice and Efficiency 166
8.1. Arrow''s Theorem 166
8.2. What Do We Give Up? 172
8.3. Efficiency 175
8.4. Identifying the Pareto Frontier: Utility Imputations and Bergsonian Social Utility Functionals 176
8.5. Syndicate Theory and Efficient Risk Sharing: Applying Proposition 8.10 184
8.6. Efficiency? 192
Bibliographic Notes 194
Problems 194
Chapter Nine. Competitive and Profit-Maximizing Firms 197
9.1. The Production-Possibility Set 198
9.2. Profit Maximization 199
9.3. Basics of the Firm''s Profit-Maximization Problem 201
9.4. Afriat''s Theorem for Firms 207
9.5. From Profit Functions to Production-Possibility Sets 211
9.6. How Many Production-Possibility Sets Give the Same Profit Function? 213
9.7. What Is Going On Here, Mathematically? 216
9.8. Differentiability of the Profit Function 219
9.9. Cost Minimization and Input-Requirement Sets 222
9.10. Why DoWe Care? 228
Bibilographic Notes 229
Problems 229
Chapter Ten. The Expenditure-Minimization Problem 233
10.1. Defining the EMP 233
10.2. Basic Analysis of the EMP 235
10.3. Hicksian Demand and the Expenditure Function 236
10.4. Properties of the Expenditure Function 238
10.5. How Many Continuous Utility Functions
Give the Same Expenditure Function? 240
10.6. Recovering Continuous Utility Functions from Expenditure Functions 247
10.7. Is an Alleged Expenditure Function Really an Expenditure Function? 248
10.8. Connecting the CP and the EMP 254
Bibliographic Notes 255
Problems 255
Chapter Eleven. Classic Demand Theory 258
11.1. Roy''s Identity and the Slutsky Equation 258
11.2. Differentiability of Indirect Utility 262
11.3. Duality of Utility and Indirect Utility 269
11.4. Differentiability of Marshallian Demand 274
11.5. Integrability 279
11.6. Complements and Substitutes 283
11.7. Integrability and Revealed Preference 284
Bibliographic Notes 286
Problems 287
Chapter Twelve. Producer and Consumer Surplus 289
12.1. Producer Surplus 289
12.2. Consumer Surplus 296
Bibliographic Notes 304
Problems 304
Chapter Thirteen. Aggregating Firms and Consumers 306
13.1. Aggregating Firms 307
13.2. Aggregating Consumers 310
13.3. Convexification through Aggregation 318
Bibliographic Notes 326
Problems 326
Chapter Fourteen. General Equilibrium 329
14.1. Definitions 329
14.2. Basic Properties ofWalrasian Equilibrium 333
14.3. The Edgeworth Box 335
14.4. Existence ofWalrasian Equilibria 338
14.5. The Set of Equilibria for a Fixed Economy 351
14.6. The Equilibrium Correspondence 354
Bibliographic Notes 354
Problems 355
Chapter Fifteen. General Equilibrium, Efficiency, and the Core 358
15.1. The First Theorem ofWelfare Economics 359
15.2. The Second Theorem ofWelfare Economics 362
15.3. Walrasian Equilibria Are in the Core 366
15.4. In a Large Enough Economy, Every Core Allocation Is a Walrasian-Equilibrium Allocation 370
15.5. Externalities and Lindahl Equilibrium 380
Bibliographic Notes 383
Problems 383
Chapter Sixteen. General Equilibrium, Time, and Uncertainty 386
16.1. A Framework for Time and Uncertainty 386
16.2. General Equilibrium with Time and Uncertainty 389
16.3. Equilibria of Plans, Prices, and Price Expectations: I. Pure Exchange with Contingent Claims 392
16.4. EPPPE: II. Complex Financial Securities and Complete Markets 402
16.5. EPPPE: III. Complex Securities with Real Dividends and Complete Markets 418
16.6. Incomplete Markets 419
16.7. Firms 424
Bibliographic Notes 431
Problems 432
About the Appendices 437
Appendix One: Mathematical Induction 439
Appendix Two: Some Simple Real Analysis 441
A2.1. The Setting 441
A2.2. Distance, Neighborhoods, and Open and Closed Sets 441
A2.3. Sequences and Limits 445
A2.4. Boundedness, (Completeness), and Compactness 446
A2.5. Continuous Functions 447
A2.6. Simply Connected Sets and the Intermediate-Value Theorem 448
A2.7. Suprema and Infima; Maxes and Mins 448
A2.8. The Maximum of a Continuous Function on a Compact Set 449
A2.9. Lims Sup and Inf 450
A2.10. Upper and Lower Semi-continuous Functions 451
Appendix Three: Convexity 452
A3.1. Convex Sets 452
A3.2. The Separating- and Supporting-Hyperplane Theorems 457
A3.3. The Support-Function Theorem 459
A3.4. Concave and Convex Functions 461
A3.5. Quasi-concavity and Quasi-convexity 463
A3.6. Supergradients and Subgradients 466
A3.7. Concave and Convex Functions and Calculus 468
Appendix Four: Correspondences 469
A4.1. Functions and Correspondences 470
A4.2. Continuity of Correspondences 471
A4.3. Singleton-Valued Correspondences and Continuity 474
A4.4. Parametric Constrained Optimization Problems and Berge''s Theorem 475
A4.5. Why this Terminology? 477
Appendix Five: Constrained Optimization 479
Appendix Six: Dynamic Programming 485
A6.1. Several Examples 485
A6.2. A General Formulation 489
A6.3. Bellman''s Equation 494
A6.4. Conserving and Unimprovable Strategies 496
A6.5. Additive Rewards 501
A6.6. States of the System 504
A6.7. Solving Finite-Horizon Problems 506
A6.8. Infinite-Horizon Problems and Stationarity 509
A6.9. Solving Infinite-Horizon (Stationary) Problems with Unimprovability 512
A6.10. Policy Iteration (and Transience) 516
A6.11. Value Iteration 518
A6.12. Examples 521
A6.13. Things Not Covered Here: Other Optimality Criteria; Continuous Time and Control Theory 527
A6.14. Multi-armed Bandits and Complexity 528
A6.15. Four More Problems You Can Solve 530
Appendix Seven: The Implicit Function Theorem 534
Appendix Eight: Fixed-Point Theory 535
References 543
Index 551
