Classical general equilibrium theory

✍ Scribed by Lionel W. McKenzie

• Publisher: MIT Press
• Year: 2002
• Tongue: English
• Leaves: 333
• Category: Library

✦ Synopsis

Although general equilibrium theory originated in the late nineteenth century, modern elaboration and development of the theory began only in the 1930s and 1940s. This book focuses on the version of the theory developed in the second half of the twentieth century, referred to by Lionel McKenzie as the classical general equilibrium theory. McKenzie offers detailed and rigorous treatment of the classical model, giving step-by-step proofs of the basic theorems. In many cases he elaborates on the individual steps to give a fuller understanding of the underlying principles. His goal is to provide readers with a true mastery of the methodology so that they can derive new results that will further enrich their thinking about general equilibrium theory. Special attention is given to the McKenzie model, in which it is not assumed that the number of firms is given but rather that technologies or activities are available to any agents who can supply the resources they require. The McKenzie model is used to establish the turnpike theorems of optimal and competitive capital accumulation.

✦ Table of Contents

Contents......Page 8
Preface......Page 12
1.1 A Direct Approach to Demand Theory......Page 16
1.2 Demand Theory without Transitivity......Page 28
1.3 The Classical Theory......Page 30
1.4 The Method of Revealed Preference......Page 37
1.5 Market Demand Functions......Page 40
A. Continuity of msub(x)......Page 48
B. Negative Semidefiniteness of [msub(ij)]......Page 49
D. Quasi-linear Preferences......Page 50
E. The Law of Demand and Risk Aversion......Page 51
F. The Strong Axiom of Revealed Preference......Page 53
G. Group Demand Functions......Page 55
2.1 Excess Demand Functions......Page 60
2.3 Matrices with Quasi-dominant Diagonals......Page 65
2.4 The Process of Tâtonnement......Page 67
2.5 Local Stability of the Tâtonnement......Page 69
2.6 Tâtonnement with Expectations......Page 79
2.7 An Economy of Firms......Page 84
2.8 An Economy of Activities......Page 92
2.9 Tâtonnment with Trading......Page 97
2.10 Global Stability with Gross Substitutes......Page 104
A. Individual and Market Excess Demand Functions......Page 111
B. The Gross Substitute Assumption......Page 113
C. The Weak Axiom of Revealed Preference and Local Stability......Page 117
D. Stability in a Temporary Equilibrium Model......Page 119
3.1 The Simple Leontief Model......Page 124
3.2 A Simple Leontief Model of Growth......Page 129
3.3 The Simple Model with Variable Coefficients......Page 133
3.4 Nonsubstitution with Capital Stocks......Page 137
Continuity of μsub(A)......Page 144
4.1 The Local Theory of Comparative Statics......Page 148
4.2 The Morishima Case......Page 155
4.3 Global Comparative Statics......Page 158
4.4 Comparative Statics for the Individual Agent......Page 160
4.5 Comparative Statics and Supermodularity......Page 165
A. Local Uniqueness of Equilibrium......Page 168
B. Jacobi’s Theorem......Page 172
C. Negative Definiteness under Constraint......Page 173
D. Maximization under Constraint......Page 176
E. Matrices Whose Roots Have Negative Real Parts......Page 178
5.1 Pareto Optimum and Competitive Equilibrium......Page 180
5.2 Competitive Equilibrium and the Core......Page 186
5.3 Nonemptiness of the Core......Page 196
5.4 The Existence of Competitive Equilibrium......Page 198
6.1 Existence in an Economy of Activities......Page 204
6.2 Existence in an Economy of Firms......Page 212
6.3 Interiority and Irreducibility......Page 222
6.4 Existence of Competitive Equilibrium with an Infinite Commodity Space......Page 229
6.5 Uniqueness of Equilibrium......Page 244
Existence of a Zero of the Excess Demand Functions......Page 250
7 Competitive Equilibrium over Time......Page 254
7.1 The von Neumann Model......Page 255
7.2 Turnpike Theorems for the von Neumann Model......Page 259
7.3 A Generalized Ramsey Growth Model......Page 263
7.4 Turnpike Theorems over an Infinite Horizon......Page 270
7.5 The Generalized Ramsey Model with Discounting......Page 274
7.6 A Turnpike Theorem for the Quasi-stationary Model......Page 279
7.7 The Turnpike in Competitive Equilibrium......Page 287
A Leontief Model with Capital Coefficients as a von Neumann Model......Page 308
References......Page 316
S......Page 324
Y......Page 325
C......Page 326
D......Page 327
E......Page 328
L......Page 329
P......Page 330
S......Page 331
U......Page 332
Z......Page 333