SFB 303 Discussion Paper No. A - 184

Author: Werner, Jan
Title: Equilibrium with Incomplete Markets without Ordered Preferences
Abstract: The purpose of this note is to prove the existence of Radner equilibrium of plans, prices and price expectations (Radner (1972)) in an exchange economy with incomplete financial markets under weak conditions on consumers' preference relations. All the previous existence results in the case of markets for financial assets (i.e., assets with exogenously specified money returns) require monotonicity of consumers' preferences (see Werner (1985), Cass (1984), Duffie (1987)). Strict monotonicity was used for proving generic existence of equilibrium with markets for commodity futures (see Duffie and Shafer (1985), Magill and Shafer (1985)), since the results rely on the regular economy arguments. Evidently, monotonicity is a restrictive assumption in the context of uncertainty. The result of this note allows preferences to be non-monotonic and even non-complete and non-transitive. Assumptions are essentially the same as in the case of an economy with complete markets (see Shafer (1975) which is also the main reference for the idea of the proof). Only the non-satiation assumption is strengthened to non-satiation in every state of nature. We also prove (Remark 2) a variant of the existence result which allows for "zero-probability" states, i.e., states such that consumer's satisfaction does not depend on consumption conditional on this state.
Creation-Date: July 1988
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