A note on the "size" of determinacy and indeterminacy

Julio Davila

Economic Theory, 1998, vol. 12, issue 1, pages 213-223

Abstract: It is shown in this note that in an incomplete markets economy with uncountably many states of the world there may be uncountably many isolated equilibria as well as uncountably many non-isolated equilibria. Moreover, both subsets can be simultaneously of second category. Therefore, none of the subsets can be considered negligible with respect to the other, neither from a cardinality point of view nor from a topological one. Unfortunately, this fact prevents from claiming that these economies may have "typically" determinate equilibria - even though uncountably many of them - as would have been desirable for comparative statics exercises.

Date: 1998-06-16
Note: Received: May 19, 1995; revised version: March 24, 1997

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