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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.
List of Basic Symbols
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
1. Euclidean Spaces
2. Convex Sets in Rn
3. Separation Theorems for Convex Sets
4. Fixed-Point Theorems
5. Homotopy and Extension Theorems
Chapter II. Simple Multisector Linear Systems
6. Leontief's Input-Output Systems, Matrix Multipliers
7. Frobenius-Perron's Theorem
8. Imprimitivity and Oscillatory Behavior
9. Other Linear Systems
Chapter III. Balanced Growth in Nonlinear Systems
10. The Solow-Samuelson-Type Relative Stability Theorems
11. Income Propagation Under Autonomous Spending
Chapter IV. Efficient Allocation and Growth
12. Production Technology Sets
13. Theorems on Self-Sustained Efficient Growth
14. A Consumption Turnpike Theorem
Chapter V. The Working of Walrasian Competitive Economies
15. Allocation in Decentralized Systems
16. Existence of a Competitive Equilibrium
17. Normative Implications of Competition
Chapter VI. Special Features of Competitive Economies: Gross Substitutability
18. Gross Substitutability and Extremization
19. Stability in Gross Substitutes Systems
Chapter VII. The Jacobian Matrix and Global Univalence
20. Conditions on the Jacobian Matrix for Global Univalence
21. Applications to Special Jacobian Matrices
- No. of pages:
- © Academic Press 1968
- 1st January 1968
- Academic Press
- eBook ISBN:
Hitotsubashi University, Tokyo, Japan
Departments of Mathematics, Electrical Engineering, and Medicine University of Southern California Los Angeles, California
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