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Overview
Yves Balasko offers an extensive, up-to-date look at the standard theory of general equilibrium, to which he has been a major contributor. This book explains how the equilibrium manifold approach can be usefully applied to the general equilibrium model, from basic consumer theory and exchange economies to models with private ownership of production. Balasko examines properties of the standard general equilibrium model that are beyond traditional existence and optimality. He applies the theory of smooth manifolds and mappings to the multiplicity of equilibrium solutions and related discontinuities of market prices. The economic concepts and differential topology methods presented in this book are accessible, clear, and relevant, and no prior knowledge of economic theory is necessary.
General Equilibrium Theory of Value offers a comprehensive foundation for the most current models of economic theory and is ideally suited for graduate economics students, advanced undergraduates in mathematics, and researchers in the field.
Product Details
ISBN-13: | 9780691146799 |
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Publisher: | Princeton University Press |
Publication date: | 08/14/2011 |
Edition description: | New Edition |
Pages: | 192 |
Product dimensions: | 6.30(w) x 9.30(h) x 0.90(d) |
About the Author
Table of Contents
Preface xi
CHAPTER 1: Goods and Prices 11.1 Introduction 11.2 Goods 11.3 Prices 21.4 Relative Prices 21.5 Price Normalization 31.6 Notes and Comments 4
CHAPTER 2: Preferences and Utility 52.1 Consumption Sets 52.2 Binary Relations 62.3 Consumers’ Preferences 82.4 Smooth Utility Functions 142.5 Conclusion 182.6 Notes and Comments 18
CHAPTER 3: Demand Functions 193.1 Introduction 193.2 Constrained Utility Maximization 193.3 The Individual Demand Function 233.4 Properties of Demand Functions in D 243.5 Demand-based Consumer Theory 313.6 Conclusion 363.7 Notes and Comments 36
CHAPTER 4: The Exchange Model 374.1 Introduction 374.2 The Sets E, Er, and Ec of m-tuples of Demand Functions Defining the Exchange Model 384.3 The Exchange Model 394.4 Equilibrium Equation 394.5 The Equilibrium Manifold and the Natural Projection 414.6 The Smooth Equilibrium Manifold 424.7 Smoothness of the Natural Projection 444.8 Critical and Regular Points and Values 444.9 Notes and Comments 46
CHAPTER 5: The Equilibrium Manifold 475.1 Introduction 475.2 Global Properties and Their Interest 475.3 The No-trade Equilibria 495.4 The Fibers of the Equilibrium Manifold 505.5 The Equilibrium Manifold as a Collection of Linear Fibers Parameterized by the No-trade Equilibria 525.6 A Picture of the Equilibrium Manifold 535.7 Diffeomorphism with R_m 535.8 Conclusion 545.9 Notes and Comments 55
CHAPTER 6: Applications of the Global Coordinate System 566.1 Introduction 566.2 Coordinate System (A) 566.3 Coordinate System (B) 576.4 Formulas of the Natural Projection 576.5 The Jacobian Matrix of Aggregate Excess Demand 586.6 Conclusion 616.7 Notes and Comments 61
CHAPTER 7: The Broad Picture 627.1 Introduction 627.2 Properness 627.3 Smooth Selection at a Regular Equilibrium 637.4 The Equilibrium Manifold over Regular Economies 647.5 Genericity of Regular Economies 677.6 The Degrees of the Natural Projection 697.7 Conclusion 727.8 Notes and Comments 73
CHAPTER 8: The Fine Picture 748.1 Introduction 748.2 Aggregate Demand at a No-trade Equilibrium 748.3 Regularity of the No-trade Equilibria 758.4 The Set of Equilibrium Allocations 758.5 Economies with a Unique Equilibrium 788.6 Degree of the Natural Projection 798.7 The Set of Regular Equilibria 798.8 Conclusion 818.9 Notes and Comments 81
CHAPTER 9: Production with Decreasing Returns 829.1 Introduction 829.2 Production Sets: Definitions 829.3 Production Sets: Main Properties 849.4 The Firm’s Objective Function 899.5 The Strict Decreasing Returns to Scale Firm 909.6 The Net Supply Function as a Primitive Concept 929.7 Conclusion 949.8 Notes and Comments 95
CHAPTER 10: Equilibrium with Decreasing Returns 9610.1 Introduction 9610.2 The General Equilibrium Model with Private Ownership of Decreasing Returns to Scale Firms 9610.3 Production Adjusted Demand Functions 9810.4 The Equivalent Exchange Model 10110.5 Properness of the Natural Projection 10310.6 Conclusion 10710.7 Notes and Comments 107
CHAPTER 11: Production with Constant Returns 10811.1 Introduction 10811.2 Production Sets 10911.3 The Net Supply Correspondence 11211.4 Three Examples 11511.5 Net Supply Correspondence of a Smooth Constant Returns to Scale Firm 11811.6 The Graph of the Net Supply Correspondence 12011.7 Conclusion 12311.8 Notes and Comments 123
CHAPTER 12: Equilibrium with Constant Returns 12412.1 Introduction 12412.2 Decreasing and Constant Returns: General Case 12412.3 Constant Returns: Reduced Form 12512.4 Equilibria of the Model N 12612.5 The Equilibrium Manifold Approach 12612.6 The Equilibrium Manifold for the Model N 12712.7 The Natural Projection 13312.8 Regular and Critical Equilibria 13412.9 Degrees of the Natural Projection 13712.10 Regular and Singular Economies 13812.11 Uniqueness of Equilibrium over ?(T) 13912.12 The Natural Projection as a Finite Covering of the Set of Regular Economies 14112.13 Values of the Natural Projection Degrees 14312.14 Conclusion 14412.15 Notes and Comments 144Postscript 145
APPENDIX A: Notation 149A.1 Points, Vectors, Inner Product 149A.2 Gradient 149A.3 Second-Order Derivatives and the Hessian Matrix of a Smooth Function 150
APPENDIX B: Point-set Topology 151B.1 Proper Maps 151
APPENDIX C: Smooth Manifolds 152C.1 The Implicit Function Theorem 152C.2 Smooth Manifolds and Submanifolds 152C.3 Smooth Mappings, Immersions, and Submersions 153
APPENDIX D: Singularities of Smooth Maps 155D.1 Critical and Regular Points 155D.2 Singular and Regular Values 155D.3 Sard’s Theorem 156D.4 The Regular Value Theorem 156D.5 The Case where dimX = dimY 156D.6 Coverings 157D.7 Surjectivity of Maps with Non-Zero Modulo 2 Degree 157
APPENDIX E: Convexity 159E.1 Convex and Strictly Convex Sets 159E.2 Quasi-concave Functions 159E.3 Smooth Quasi-concavity and Second-Order Derivatives 162E.4 Bordered Hessian of a Smoothly Quasi-concave Function 164E.5 Recession Cone of a Convex Set 165
APPENDIX F: Miscellany 166F.1 Dimension of Semi-algebraic Sets 166References 167Index 171
What People are Saying About This
"Balasko provides a clear, thorough, and completely up-to-date look at the basic economic model of supply and demand, in which values are determined through the interaction of individual preferences, endowments, and technologies. This will be an excellent text for advanced graduate students in economic theory, an introduction for mathematics students with an interest in applications of differential topology, and a must-have reference for researchers in general equilibrium theory."—Karl Shell, Cornell University"This book performs a valuable pedagogical service for the economics profession by providing a detailed development of general equilibrium theory that will be accessible to graduate students of economics."—Stephen E. Spear, Carnegie Mellon University