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The Theory of General Economic Equilibrium : A Differentiable Approach - Andreu Mas-Colell

The Theory of General Economic Equilibrium

A Differentiable Approach

Hardcover Published: 26th September 1985
ISBN: 9780521265140
Number Of Pages: 392

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Andreu Mas-Colell has been doing pioneering work using differential topology in the analysis of general equilibrium. This work is regarded as outstanding and one of the major contributions to the development of rigorous economic theory in the last twenty years. The articles he has written have been difficult and technically demanding. In this book he brings this work together to show its scope and its power. He presents the analysis in a way which makes it accessible to the broader range of economic theorists and advanced students. This book has been long awaited as a seminal contribution to the subject.

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'This thorough and lucid account of the use of differential methods in general equilibrium theory since 1970 is the most important new book in mathematical economics in over a decade.' Journal of Economic Literature

Prefacep. xi
Glossaryp. xiii
Introductionp. 1
Modern general equilibrium theory and the calculusp. 1
The return of the differentiability approachp. 2
Object and content of the bookp. 3
Topics and techniques not coveredp. 5
Reference conventions and sourcesp. 5
Mathematicsp. 6
Point-set topology and metric spacesp. 7
Some definitionsp. 7
Compactness and connectednessp. 8
Metric spacesp. 9
The Baire propertyp. 10
The space of subsets of a metric spacep. 10
Correspondencesp. 11
Zorn's lemmap. 11
Reference notesp. 11
Linear algebrap. 12
Linear spacesp. 12
Linear functionsp. 13
Matricesp. 13
Determinantsp. 14
Scalar products and orthogonalityp. 15
Eigenvalues and definite matricesp. 16
Quadratic formsp. 18
Reference notesp. 18
Differential calculusp. 18
Definitionsp. 18
Basic properties of the derivativep. 19
Implicit function theoremsp. 20
Gradients and second derivativesp. 21
Reference notesp. 21
Smooth optimizationp. 22
First-order necessary conditionsp. 22
Second-order conditionsp. 22
Reference notesp. 22
Measures and integralsp. 23
Measuresp. 23
Integralsp. 23
Convergence of measures on a metric spacep. 24
Continuity propertiesp. 25
Integrals and derivativesp. 25
Reference notesp. 26
Convex sets and functionsp. 27
Convex setsp. 27
Supporting propertiesp. 28
Convex and concave functionsp. 29
Reference notesp. 30
Lipschitzian functionsp. 31
Definitions and basic propertiesp. 31
The generalized Jacobianp. 31
Reference notesp. 32
Differentiable manifoldsp. 33
Definitions and examplesp. 33
Functions on manifoldsp. 36
Curvaturep. 39
Technical miscellaneap. 40
Reference notesp. 41
Transversality theoryp. 42
The measure of the set of critical valuesp. 42
Transversalityp. 43
Miscellaneap. 45
Reference notesp. 45
Degrees, indices, and fixed pointsp. 45
Preliminariesp. 45
The degree of a functionp. 46
Vector fields and fixed pointsp. 47
Reference notesp. 50
Function spacesp. 50
Definitions and basic propertiesp. 50
Compact sets and measures on function spacesp. 51
Reference notesp. 52
Averages of setsp. 52
Sums of setsp. 52
Partial sumsp. 53
Reference notesp. 55
Preferences, utility, and demandp. 57
Introductionp. 57
Definitionsp. 58
Smooth preferencesp. 61
Spaces of smooth preferencesp. 69
Regular and critical pointsp. 75
Smooth, convex preferencesp. 78
Differentiable demandp. 84
Approximation theoryp. 89
Demand theory without preferencesp. 91
Reference notesp. 94
Production setsp. 96
Introductionp. 96
Production sets and efficient productionsp. 96
From individual to aggregate production setsp. 98
Some derived constructionsp. 99
Some differentiability facts and relationsp. 102
Smoothness hypothesesp. 107
Some examplesp. 109
Perturbations of production setsp. 112
Reference notesp. 113
Optimality and price equilibriump. 114
Introductionp. 114
Optimality and price equilibrium: general theoryp. 114
First-order necessary conditions for an optimump. 128
Second-order conditions for an optimump. 135
General propositions on approximate price supportabilityp. 144
The structure of the set of optimum allocationsp. 153
Reference notesp. 164
Exchange economiesp. 166
Introductionp. 166
Exchange economies and exchange price equilibriump. 167
Regular exchange equilibrium and regular exchange economiesp. 175
Properties of regular equilibriap. 184
The equilibrium set of an economy and the index theorem for regular economiesp. 188
Proof and discussion of the index theoremp. 201
Special classes of economies and the uniqueness of equilibriap. 215
The equilibrium set: global analysisp. 222
Reference notesp. 241
Production economiesp. 245
Introductionp. 245
Production economiesp. 245
Equilibrium and regular equilibriump. 247
Regular equilibrium in constant returns economiesp. 249
The index theoremp. 252
Special classes of economies and the uniqueness of equilibriump. 256
Reference notesp. 261
Exchange economies with many tradersp. 263
Introductionp. 263
Properties of Walrasian allocationsp. 264
Core allocations in continuum exchange economiesp. 269
Core allocations in exchange economies with a finite number of tradersp. 273
Anonymous optimal allocations in continuum exchange economiesp. 298
No-surplus allocations in continuum exchange economiesp. 310
Reference notesp. 313
Genericity analysisp. 316
Introductionp. 316
The generic point of viewp. 316
The mathematical theoryp. 319
Generic demandp. 322
Generic production setsp. 330
Generic optimap. 332
Genericity of regular economiesp. 336
Generic properties of the equilibrium manifoldp. 342
Reference notesp. 351
Referencesp. 353
Name indexp. 365
Subject indexp. 369
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521265140
ISBN-10: 0521265142
Series: Cambridge Studies in American Literature and Culture
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 392
Published: 26th September 1985
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.86 x 15.24  x 2.54
Weight (kg): 0.74

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