General Equilibrium Theory: An Introduction

Contents......Page 8
List of illustrations......Page 14
Introduction to the second edition......Page 16
 Notation......Page 20
Preface to the second edition......Page 22
Preface to the first edition......Page 24
Table of notation......Page 26
Table of assumptions......Page 30
A General equilibrium theory: Getting acquainted......Page 32
1.1 Partial and general equilibrium: Development of the field......Page 34
1.2 The role of mathematics......Page 38
1.3 History of general equilibrium theory......Page 39
1.4 Bibliographic note......Page 41
2 An elementary general equilibrium model: The Robinson Crusoe economy......Page 43
2.1 Centralized allocation......Page 45
2.2 Decentralized allocation......Page 47
2.3 Pareto efficiency of the competitive equilibrium allocation......Page 54
 Exercises......Page 55
3 The Edgeworth box......Page 62
3.1 Geometry of the Edgeworth box......Page 63
3.2 Calculating an efficient allocation......Page 66
3.3 A competitive market solution in the Edgeworth box......Page 68
 Exercises......Page 71
4 Integrating production and multiple consumption decisions......Page 75
4.2 Technical efficiency......Page 77
4.3 Pareto efficiency......Page 79
 Exercises......Page 81
5 Existence of general equilibrium in an economy with an excess demand function......Page 89
 Exercises......Page 95
B Mathematics......Page 98
6 Logic and set theory......Page 100
6.1 Quasi-orderings......Page 102
 Exercises......Page 104
7 RN: Real N-dimensional Euclidean space......Page 106
7.1 Continuous functions......Page 113
 Exercises......Page 116
8 Convex sets, separation theorems, and nonconvex sets in RN......Page 122
8.1 Separation theorems......Page 123
8.2.1 Nonconvex sets and their convex hulls......Page 126
8.2.3 Measuring nonconvexity, the Shapley-Folkman Theorem......Page 127
 Exercises......Page 128
9 The Brouwer Fixed-Point Theorem......Page 130
 Exercises......Page 137
C An economy with bounded production technology......Page 140
10.2 The formal structure of pure economic theory......Page 143
10.3 Markets, commodities, and prices......Page 144
 Exercise......Page 145
11.1 Firms and production technology......Page 146
11.2 The form of production technology......Page 147
11.3 Strictly convex production technology......Page 148
11.5 Attainable production plans......Page 151
 Exercises......Page 152
12.2 Consumption sets......Page 155
12.3 Representation of i: Existence of a continuous utility function......Page 160
12.4 Choice and boundedness of budget sets, B̃i(p)......Page 162
12.5 Demand behavior under strict convexity......Page 165
 Exercises......Page 168
13.1 Firms, profits, and household income......Page 173
13.2 Excess demand and Walras\'s Law......Page 174
 Exercises......Page 176
14.1 Existence of equilibrium......Page 178
 Exercises......Page 183
D An economy with unbounded production technology......Page 192
15.1 Unbounded production technology......Page 195
15.2 Boundedness of the attainable set......Page 196
15.3 An artificially bounded supply function......Page 200
 Exercises......Page 203
16.2 Choice in an unbounded budget set......Page 205
16.3 Demand behavior under strict convexity......Page 208
 Exercise......Page 210
17.2 Profits......Page 211
17.4 Excess demand and Walras\'s Law......Page 212
 Exercises......Page 215
18.1 General equilibrium......Page 216
18.2 An artificially restricted economy......Page 217
18.3 General equilibrium of the unrestricted economy......Page 218
18.4 The Uzawa Equivalence Theorem......Page 221
 Exercises......Page 224
E Welfare economics and the scope of markets......Page 234
19.1 Pareto efficiency......Page 236
19.2 First Fundamental Theorem of Welfare Economics......Page 237
19.3 Second Fundamental Theorem of Welfare Economics......Page 240
 Exercises......Page 245
20.1 Introduction......Page 256
20.2 Time: Futures markets......Page 258
20.3 Uncertainty: Arrow-Debreu contingent commodity markets......Page 264
20.4 Uncertainty: Arrow securities markets......Page 269
20.5 Conclusion: The missing markets......Page 272
20.6 Bibliographic note......Page 273
 Exercises......Page 274
F Bargaining and equilibrium: The core......Page 280
21.1 Bargaining and competition......Page 282
21.2 The core of a pure exchange economy......Page 283
21.3 The competitive equilibrium allocation is in the core......Page 285
 Exercise......Page 286
22.1 Replication: A large economy......Page 287
22.2 Equal treatment......Page 288
22.3 Core convergence in a large economy......Page 290
22.4 A large economy without replication......Page 294
22.5 Interpreting the core convergence result......Page 298
22.6 Bibliographic note......Page 299
 Exercises......Page 300
G An economy with supply and demand correspondences......Page 306
23.2 Upper hemicontinuity......Page 310
23.3 Lower hemicontinuity......Page 313
23.4 Continuous correspondence......Page 315
23.6 Optimization subject to constraint......Page 316
23.7 Kakutani Fixed-Point Theorem......Page 318
 Exercises......Page 322
24.1 General equilibrium with set-valued supply and demand......Page 324
24.2 Production with a (weakly) convex production technology......Page 325
24.3 Households......Page 329
24.4 The market economy......Page 335
24.5 The artificially restricted economy......Page 338
24.6 Existence of competitive equilibrium......Page 339
 Exercises......Page 341
25.1 U-shaped cost curves and concentrated preferences......Page 343
25.2.1 Nonconvex technology and supply......Page 344
25.3.1 Convexified technology and supply......Page 345
25.3.2 Artificial convex preferences and demand......Page 346
25.4 Approximate equilibrium......Page 348
25.5 Bibliographic note......Page 350
 Exercises......Page 351
H Standing on the shoulders of giants......Page 354
26.1 Large economies......Page 356
26.2 Anything goes!......Page 358
26.3 Regular economies and the determinacy of equilibrium......Page 359
26.4 General equilibrium with incomplete markets......Page 360
26.5 Computing general equilibrium......Page 361
26.6 Bibliographic note......Page 362
27.1 Overview and summary......Page 363
27.2 Bibliographic note......Page 364
 Exercises......Page 365
Bibliography......Page 366
Index......Page 372