Convex Structures and Economic Theory

Mathematics in Science and Engineering, Volume 51: Convex Structures and Economic Theory consists of an account of the theory of convex sets and its application to several basic problems that originate in economic theory and adjacent subject matter.

This volume includes examples of problems pertaining to interesting static and dynamic phenomena in linear and nonlinear economic systems, as well as models initiated by Leontief, von Neumann, and Walras. The topics covered are the mathematical theorems on convexity, simple multisector linear systems, balanced growth in nonlinear systems, and efficient allocation and growth. The working of Walrasian competitive economies, special features of competitive economies, and Jacobian matrix and global univalence are also covered.

This publication is suitable for advanced students of mathematical economics and related fields, but is also beneficial for anyone who wishes to become familiar with the basic ideas, methods, and results in the mathematical treatment in economic theory through a detailed exposition of a number of typical representative problems.

Contenu

Preface
List of Basic Symbols
Introduction

1. Mathematical Analysis in Economic Theory
2. Scope of Mathematical Economic Theory
3. Appeal to Convexity
4. Orientation for Chapters
   Chapter I. Mathematical Theorems on Convexity
5. Euclidean Spaces
6. Convex Sets in Rn
7. Separation Theorems for Convex Sets
8. Fixed-Point Theorems
9. Homotopy and Extension Theorems
   Chapter II. Simple Multisector Linear Systems
10. Leontief's Input-Output Systems, Matrix Multipliers
11. Frobenius-Perron's Theorem
12. Imprimitivity and Oscillatory Behavior
13. Other Linear Systems
    Chapter III. Balanced Growth in Nonlinear Systems
14. The Solow-Samuelson-Type Relative Stability Theorems
15. Income Propagation Under Autonomous Spending
    Chapter IV. Efficient Allocation and Growth
16. Production Technology Sets
17. Theorems on Self-Sustained Efficient Growth
18. A Consumption Turnpike Theorem
    Chapter V. The Working of Walrasian Competitive Economies
19. Allocation in Decentralized Systems
20. Existence of a Competitive Equilibrium
21. Normative Implications of Competition
    Chapter VI. Special Features of Competitive Economies: Gross Substitutability
22. Gross Substitutability and Extremization
23. Stability in Gross Substitutes Systems
    Chapter VII. The Jacobian Matrix and Global Univalence
24. Conditions on the Jacobian Matrix for Global Univalence
25. Applications to Special Jacobian Matrices
    Bibliography
    Author Index
    Subject Index