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.

• Front Cover 2
• Convex Structures and Economic Theory 5
• Copyright Page 6
• Dedication 7
• Preface 9
• Table of Contents 11
• List of Basic Symbols 13
• Introduction 17
  • 1. Mathematical Analysis in Economic Theory 17
  • 2. Scope of Mathematical Economic Theory 18
  • 3. Appeal to Convexity 19
  • 4. Orientation for Chapters 20
• Chapter 1. Mathematical Theorems on Convexity 22
  • 1. Euclidean Spaces 22
  • 2. Convex Sets in Rn 31