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Edgeworth's Conjecture

Truman F. Bewley

Abstract

We study the properties of the core of large markets. We assume that traders' preferences have certain standard properties, that their preferences belong to a set which is compact with respect to a certain topology, and that there is a bound on their initial endowments. It is then found that if a market contains sufficiently many traders and if there are many traders similar to any one trader, then every core allocation is similar to a price equilibrium in a very strong sense. This fact implies a precise formulation of the following statement: for most large markets, the core decomposes into disjoint clusters of allocations, the allocations in each cluster being very similar. This statement may be interpreted as an explanation of why traders in large markets normally feel that they have little bargaining power.