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