Econometrica: Jan 1975, Volume 43, Issue 1

Nonstandard Exchange Economies<41:NEE>2.0.CO;2-J
p. 41-56

Abraham Robinson, Donald J. Brown

Edgeworth's conjecture that as the number of traders in an exchange economy increases the core approaches the set of competitive equilibria has been formalized both as a theorem about a sequence of finite economies, and as a theorem about an economy having an infinite number of agents. This paper, using nonstandard analysis, provides a synthesis of these two approaches. It is shown that the core and the set of competitive equilibria are equivalent within a non-standard exchange economy. This theorem implies a asymptotic theorem concerning the core and competitive equilibria of sequences of finite economies.

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