Introduction to Equilibrium Analysis, Volume 6

Preface

Chapter 1. An Introductory Outline

1. Introduction

2. Basic Example

3. Improving by Cooperation

4. Decentralization by Prices

5. Coincidence of Two Themes

6. Conjuring Trick

7. Limit Economies and Insignificance

8. From Limits to Limiting Results

9. Back to Walras

10. Less Well Behaved Individuals

11. Forewarned is Forearmed

Chapter 2. Exchange Economies

1. Introduction

2. Commodity Space

3. Agents' Characteristics

4. Economies

5. Appendix

Chapter 3. The Core of a Game

1. Introduction

2. Balancedness

3. Non-Classical Exchange Economies

4. Appendix

Chapter 4. Large Economies

1. Introduction

2. Prices and Demand

3. Walras Equilibrium

4. Economies with a Continuum of Agents

Chapter 5. Limit Theorems for the Core

1. Limit Theorem for Replica Economies

2. Limit Theorems for Type Economies

3. Uniform Boundedness of Core Allocations

4. Asymptotic Equal Treatment for Most

5. Asymptotic Equal Treatment for All

6. Proof of Limit Theorem 5.2

7. Emergence of Prices

8. Alternative Proof for Section 6

Chapter 6. Existence of Competitive Equilibria

1. Introduction

2. Individual Demand

3. Total Demand

4. Equilibria for Strongly Conve Preferences

5. Equilibria for Economies with Convex Preferences

6. Equilibria without Convexity of Preferences

7. Conclusions

8. Appendix

Mathematical Appendix I: Topological Concepts in Rl

1. Convergence of R1

2. Closed and Open Sets

Mathematical Appendix II: Separation Theorems

Mathematical Appendix III: Continuous Correspondences

1. Introduction

2. Upper Hemi-Continuous Correspondences

3. Lower Hemi-Continuous Correspondences

4. Continuous Correspondences

Mathematical Appendix IV: Fixed Point Theorems

List of Mathematical Symbols

References

Author Index

Subject Index

Advanced Textbooks in Economics, Volume 6: Introduction to Equilibrium Analysis: Variations on Themes by Edgeworth and Walras focuses on the approaches developed and instituted by Edgeworth and Walras in the study of equilibrium analysis. The book first underscores exchange economies, core of a game, and large economies. Discussions focus on economies with a continuum of agents, Walras equilibrium, prices and demand, balancedness, and commodity space. The manuscript then ponders on limit theorems for the core and existence of competitive equilibria. Topics include equilibria without convexity of preferences, existence of equilibria for economies with convex preferences, individual demand, emergence of prices, asymptotic equal treatment for most, uniform boundedness of core allocations, and limit theorems for type and replica economies. The publication examines continuous, upper, and lower hemi-continuous correspondences, fixed point theorems, and separation of convex sets. The book is a vital source of data for economists and researchers interested in equilibrium analysis.