Convex Structures and Economic Theory - 1st Edition - ISBN: 9781483230030, 9781483266688

Convex Structures and Economic Theory

1st Edition

Authors: Hukukane Nikaido
Editors: Richard Bellman
eBook ISBN: 9781483266688
Imprint: Academic Press
Published Date: 1st January 1968
Page Count: 422
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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.

Table of Contents


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


Author Index

Subject Index


No. of pages:
© Academic Press 1968
Academic Press
eBook ISBN:

About the Author

Hukukane Nikaido

Affiliations and Expertise

Hitotsubashi University, Tokyo, Japan

About the Editor

Richard Bellman

Affiliations and Expertise

Departments of Mathematics, Electrical Engineering, and Medicine University of Southern California Los Angeles, California

Ratings and Reviews