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Existence of Equilibrium of Plans, Prices, and Price Expectations in a Sequence of Markets

Roy Radner

Abstract

Consider a sequence of markets for goods and securities at successive dates, with no market at any date complete in the Arrow-Debreu sense. A concept of common expectations is proposed that requires traders to associate the same future prices to the same future exogenous events, but does not require them to agree on the (subjective) probabilities associated with those events. An equilibrium is a set of prices at the first date, a set of common price expectations for the future, and a consistent set of individual plans for consumers and producers such that, given the current prices and price expectations, each individual agent's plan is optimal for him, subject to an appropriate sequence of budget constraints. The existence of such an equilibrium is demonstrated under assumptions about technology and consumer preferences similar to those used in the typical Arrow-Debreu theory of complete markets. However, an equilibrium can fail to exist if some provision is not made for the elimination of "unprofitable" enterprises. The usual assumptions of "rationality" imply, in this model, that agents learn from experience and modify their expectations as Bayesians.