Book contents
- Frontmatter
- Introduction
- 1 The coefficient of resource utilization
- 2 A social equilibrium existence theorem
- 3 A classical tax-subsidy problem
- 4 Existence of an equilibrium for a competitive economy
- 5 Valuation equilibrium and Pareto optimum
- 6 Representation of a preference ordering by a numerical function
- 7 Market equilibrium
- 8 Economics under uncertainty
- 9 Topological methods in cardinal utility theory
- 10 New concepts and techniques for equilibrium analysis
- 11 A limit theorem on the core of an economy
- 12 Continuity properties of Paretian utility
- 13 Neighboring economic agents
- 14 Economies with a finite set of equilibria
- 15 Smooth preferences
- 16 Excess demand functions
- 17 The rate of convergence of the core of an economy
- 18 Four aspects of the mathematical theory of economic equilibrium
- 19 The application to economics of differential topology and global analysis
- 20 Least concave utility functions
11 - A limit theorem on the core of an economy
Published online by Cambridge University Press: 05 January 2013
- Frontmatter
- Introduction
- 1 The coefficient of resource utilization
- 2 A social equilibrium existence theorem
- 3 A classical tax-subsidy problem
- 4 Existence of an equilibrium for a competitive economy
- 5 Valuation equilibrium and Pareto optimum
- 6 Representation of a preference ordering by a numerical function
- 7 Market equilibrium
- 8 Economics under uncertainty
- 9 Topological methods in cardinal utility theory
- 10 New concepts and techniques for equilibrium analysis
- 11 A limit theorem on the core of an economy
- 12 Continuity properties of Paretian utility
- 13 Neighboring economic agents
- 14 Economies with a finite set of equilibria
- 15 Smooth preferences
- 16 Excess demand functions
- 17 The rate of convergence of the core of an economy
- 18 Four aspects of the mathematical theory of economic equilibrium
- 19 The application to economics of differential topology and global analysis
- 20 Least concave utility functions
Summary
In his Mathematical Psychics [5], Edgeworth presented a remarkable study of the exchanges of two commodities that might arise in an economy with two types of consumers. The first case that he considers concerns two individuals each of whom initially possesses certain quantities of each commodity. The result of trading consists of a reallocation of the total amounts of the two commodities and may, therefore, be described geometrically by a point in the Edgeworth box corresponding to that economy.
Edgeworth confines his attention to those exchanges which are Pareto optimal, i.e., those which cannot yield greater satisfaction for one consumer without impairing that of the other by means of additional trade. He further restricts the admissible final allocations to those which are at least as desired by both consumers as the allocation prevailing before trading. Those allocations which are not ruled out by either of these considerations constitute the "contract curve."
- Type
- Chapter
- Information
- Mathematical EconomicsTwenty Papers of Gerard Debreu, pp. 151 - 162Publisher: Cambridge University PressPrint publication year: 1983