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
1 - The coefficient of resource utilization
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
A numerical evaluation of the “dead loss” associated with a nonoptimal situation (in the Pareto sense) of an economic system is sought. Use is made of the intrinsic price systems associated with optimal situations of whose existence a noncalculus proof is given. A coefficient of resource utilization yielding measures of the efficiency of the economy is introduced. The treatment is based on vector-set properties in the commodity space.
Introduction
The activity of the economic system we study can be viewed as the transformation by n production units and the consumption by m consumption units of / commodities (the quantities of which may or may not be perfectly divisible). Each consumption unit, say the ith one, is assumed to have a preference ordering of its possible consumptions, and therefore an index of its satisfaction, si. Each production unit has a set of possibilities (depending, for example, on technological knowledge) defined independently of the limitation of physical resources and of conditions in the consumption sector. Finally, the total net consumption of all consumption units and all production units for each commodity must be at most equal to the available quantity of this commodity.
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- Chapter
- Information
- Mathematical EconomicsTwenty Papers of Gerard Debreu, pp. 30 - 49Publisher: Cambridge University PressPrint publication year: 1983
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