General Equilibrium Analysis of Production

The scope of the general equilibrium (GE) theory has so far been limited to The Walrasian tradition. Indeed, The theories of competitive equilibria and The core are nothing but the modern mathematical analysis of the economic ideas due to Walras, Edgeworth and Pareto. Consequently, recent books in this field are inclined to be heavily technical and mathematical. On the other hand, The modern GE theory has not completed the study of increasing returns and monopolistic competition, which belong to The alternative important stream of economic thought, namely the Marshallian tradition. This book aims to fill this gap, by proving the existence of a competitive equilibrium with increasing returns coming from externalities in a dynamic economy and a monopolistically competitive equilibrium with the technologies exhibiting increasing returns coming from a large set-up cost. Also intended as a basic graduate textbook on GE theory, it contains all the basic results and mathematical techniques in this field, such as measure theory, manifold theory and Banach space theory. A unique feature of the book compared to classical monographs on GE is its emphasis on the historical nature of the subject, and not only the mathematical nature. Students are expected to learn that those mathematically formidable techniques are indeed necessary for tackling many economic problems which have been significant not only in the mathematical or technical context, but also in the historical and traditional context.

Preface	p. vii
Introduction	p. 1
From the 19th Century to the 1940s	p. 1
After the 1950s; Existence of Equilibrium and Core Limit Theorem	p. 7
The Local Uniqueness and Stability of Equilibria	p. 7
Markets with a Continuum of Traders	p. 9
Increasing Returns and Monopolistic Competition	p. 11
Markets with Infinitely Many Commodities	p. 13
The Organization of the Book	p. 14
Notes	p. 15
Classical Exchange Economies	p. 19
Commodities and Markets	p. 19
The Preference of a Consumer	p. 22
The Demand of a Consumer	p. 24
The Demand Theory	p. 31
Competitive Equilibria of a Classical Exchange Economy	p. 34
A Limit Theorem of the Core of a Classical Exchange Economy	p. 40
Nash Equilibria and the Core of Games	p. 45
The Local Uniqueness of Equilibria	p. 51
Notes	p. 60
Economies With a Continuum of Traders	p. 63
Markets with a Measure Space of Consumers	p. 63
Spaces of Preferences	p. 65
Existence of Competitive Equilibria	p. 69
The Equivalence of the Core and Equilibria	p. 81
Exchange Economies with a Non-Convex Consumption Set	p. 85
Production Economies with a Non-Convex Consumption Set	p. 94
On The Law of Demand	p. 103
Notes	p. 106
Production Economies with Increasing Returns	p. 109
Classical Production Economies with Competitive Firms	p. 109
Core of an Economy with Increasing Returns	p. 117
Production Economies with External Increasing Returns	p. 124
Pareto Optimally and Tax Policies	p. 130
Notes	p. 139
Economies With Infinitely Many Commodities	p. 141
Markets with Infinitely Many Commodities	p. 141
Exchange Economies with Infinite Time Horizon	p. 145
Exchange Economies with Differentiated Commodities	p. 155
Exchange Economies on a General Banach Space	p. 160
Infinite Time Horizon Economies with External Increasing Returns	p. 169
On the Differentiability of Demand	p. 177
Notes	p. 181
Economies With Monopolistically Competitive Firms	p. 183
Monopolistically Competitive Markets	p. 183
Existence of Equilibria with Pricing Rules	p. 188
Monopolistically Competitive Equilibria Under Convex Technologies	p. 195
Monopolistically Competitive Equilibria with Fixed Costs	p. 201
Notes	p. 208
Convex Sets and Functions	p. 211
Elements of General Topology	p. 215
Metric Spaces	p. 219
Continuity of Correspondences	p. 223
Differential Calculus and Manifolds	p. 229
Spaces of Closed Sets	p. 239
Measure and Integration	p. 243
Banach Spaces and Related Topics	p. 253
Notes	p. 261
References	p. 263
Index	p. 269
Table of Contents provided by Ingram. All Rights Reserved.

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General Equilibrium Analysis of Production and Increasing Returns

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