Classical general equilibrium theory /


Preface xi

1 Theory of Demand 1
1.1 A Direct Approach to Demand Theory 1
1.2 Demand Theory without Transitivity 13
1.3 The Classical Theory 15
1.4 The Method of Revealed Preference 22
1.5 Market Demand Functions 25
Appendixes
A. Continuity of mx(p) 33
B. Negative Semidefiniteness of [my(p)] 34
C. Euler's Theorem for f(p) 35
D. Quasi-linear Preferences 35
E. The Law of Demand and Risk Aversion 36
F. The Strong Axiom of Revealed Preference 38
G. Group Demand Functions 40
2 Tatonnement Stability of Equilibrium 45
2.1 Excess Demand Functions 45
2.2 Market Equilibrium 50
2.3 Matrices with Quasi-dominant Diagonals 50
2.4 The Process of Tatonnement 52
2.5 Local Stability of the Tatonnement 54
2.6 Tatonnement with Expectations 64
2.7 An Economy of Firms 69
2.8 An Economy of Activities 77
2.9 Tatonnment with Trading 82
2.10 Global Stability with Gross Substitutes 89
Appendixes
A. Individual and Market Excess Demand Functions 96
B. The Gross Substitute Assumption 98
C. The Weak Axiom of Revealed Preference and Local
Stability 102
D. Stability in a Temporary Equilibrium Model 104




3 Leontief Models of Production 109
3.1 The Simple Leontief Model 109
3.2 A Simple Leontief Model of Growth 114
3.3 The Simple Model with Variable Coefficients 118
3.4 Nonsubstitution with Capital Stocks 122
3.5 Current Prices and Interest Rates 129
Appendix
Continuity of uA(s) 129
4 Comparative Statics 133
4.1 The Local Theory of Comparative Statics 133
4.2 The Morishima Case 140
4.3 Global Comparative Statics 143
4.4 Comparative Statics for the Individual Agent 145
4.5 Comparative Statics and Supermodularity 150
Appendixes
A. Local Uniqueness of Equilibrium 153
B. Jacobi's Theorem 157
C. Negative Definiteness under Constraint 158
D. Maximization under Constraint 161
E. Matrices Whose Roots Have Negative Real Parts 163
5 Pareto Optimality and the Core 165
5.1 Pareto Optimum and Competitive Equilibrium 165
5.2 Competitive Equilibrium and the Core 171
5.3 Nonemptiness of the Core 181
5.4 The Existence of Competitive Equilibrium 183
6 Existence and Uniqueness of Competitive Equilibrium 189
6.1 Existence in an Economy of Activities 189
6.2 Existence in an Economy of Firms 197
6.3 Interiority and Irreducibility 207
6.4 Existence of Competitive Equilibrium with an
Infinite Commodity Space 214
6.5 Uniqueness of Equilibrium 229
Appendix
Existence of a Zero of the Excess Demand Functions 235



7 Competitive Equilibrium over Time 239
7.1 The von Neumann Model 240
7.2 Turnpike Theorems for the von Neumann Model 244
7.3 A Generalized Ramsey Growth Model 248
7.4 Turnpike Theorems over an Infinite Horizon 255
7.5 The Generalized Ramsey Model with Discounting 259
7.6 A Turnpike Theorem for the Quasi-stationary
Model 264
7.7 The Turnpike in Competitive Equilibrium 272
Appendix
A Leontief Model with Capital Coefficients as a von
Neumann Model 293

References 301
Index of Economist Citations 309
Subject Index 311