On Equilibrium Allocations as Distributions on the Commodity Space

Sergiu Hart, Werner Hildenbrand and Elon Kohlberg

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It is shown that the distribution of agents' characteristics is a concise and accurate description of an economy as far as Walrasian equilibrium analysis for large economies is concerned: Let E be an exchange economy; W(E), the set of Walrasian allocations for E; and DW(E), the set of distributions on the commodity space of the allocations in W(E). It is shown that for two atomless economies E1 and E2 which have the same distribution of agents' characteristics, the sets DW(E1) and DW(E2) have the same closure. For every distribution μ of agents characteristics is defined a standard representation Eμ, and it is shown that DW(Eμ) is closed. Further, the correspondence μ ® DW(Eμ) is shown to be upper hemicontinuous.