THE APPROXIMATION OF PERFECT COMPETITION BY A LARGE, BUT FINITE, NUMBER OF TRADERS.
PRINCETON UNIV N J ECONOMETRIC RESEARCH PROGRAM
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The paper uses the techniques developed by Debreu and Hildenbrand for representing sequences of economies by sequences of measures on a certain topological space to prove a property similar to upper semi-continuity of the correspondence Epsilon which maps each economy into the set of allocations in the core of that economy. This result is then used to extend Scarfs proof of the nonemptiness of the core of certain finite economies to infinite economies with a finite number of different types of agent. It is also possible to use Scarfs result to prove the existence of a competitive equilibrium for a finite economy. Finally, the upper semi-continuity of Epsilon is used to prove Hildenbrands result that, loosely speaking, an allocation in the core of an approximately perfectly competitive economy is close to being a competitive allocation. It is shown how the Debreu-Scarf limit theorem on the core of an economy is a special case of this result. Author
- Economics and Cost Analysis
- Operations Research