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On Equilibrium Allocations as Distributions on the Commodity Space

Sergiu Hart, Werner Hildenbrand and Elon Kohlberg

**Abstract**

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 *E*_{1} and *E*_{2}
which have the same distribution of
agents' characteristics, the sets *DW*(*E*_{1}) and
*DW*(*E*_{2}) have the same closure. For
every distribution *μ* of agents characteristics
is defined a
standard representation *E*^{μ},
and it is shown that
*DW*(*E*^{μ}) is closed.
Further, the correspondence
*μ* ® *DW*(*E*^{μ})
is shown to be upper hemicontinuous.

*Journal of Mathematical Economics* 1 (1974), 2, 159-166