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Generic Existence of Completely Revealing Equilibria for Economies with Uncertainty when Prices Convey Information

Beth Allen

Abstract

Conditions which imply the existence of strict rational expectations equilibria for "most" static pure exchange economies where prices convey information about the state of the world are analyzed. Information is aggregated and transmitted by prices because agents have different initial information and maximize the conditional expectation of state-dependent utility functions. Major results state that if, with probability one, agents' characteristics do not vary too much as the state of the world varies, then, generically, there exist equilibrium price functions which reveal all initial information. More precisely, if the support of the image measure is contained in a compact C^1 manifold (satisfying some technical conditions) which is of sufficiently low dimension relative to the number of commodities, then existence of completely revealing equilibria is generic. Any economy satisfying these assumptions can be approximated by a sequence of economies which also obey these assumptions and have completely revealing equilibrium price functions. Slight perturbations do not destroy the existence property.