On Equilibrium Allocations as Distributions on the Commodity Space*

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 8 be an exchange economy; W(8), the set of Walras allocations for 8; and g?(8), the set of distributions on the commodity space of the allocations in W(8). It is shown that for two atomless economies 8, and b, which have the same distribution of agents’ characteristics, the sets SIV(&,) and 2@W(b,) have the same closure. For every distribution ,u of agents’ characteristics is defined a standard representation B”, and it is shown that S’W(@) is closed. Further, the correspondence p H gW(&‘) is shown to be upper hemicontinuous.