Unanimity and the theory of the firm under multiplicative uncertainty

Abstract

The purpose of this paper is to explore several interesting implications of the unanimity model in the theory of the firm under uncertainty. After the two-period, state-preference model constructed by Ekern and Wilson [10] and reformulated by Radner [17], is reviewed and interpreted in Section II, the theory of the firm confronted solely with multiplicative uncertainty is examined. If it is assumed that the return function of the firm in each possible state of the world is simply the profit of the firm in that state, then multiplicative uncertainty is tantamount to assuming price uncertainty. Indeed, even if there is multiplicative technological uncertainty, as in the case examined by Diamond [7], the behavioral implications coincide with the price uncertainty case. If, in the spirit of perfect competition, it is assumed that there is free entry into the capital market, then firms will continue to enter until unanimity results. Since, unanimity results for all proposed changes in a firm's state-distribution of returns if the asset market is complete, there need never be more firms than possible states of the world. In this specific example, however, unanimity is ensured whenever there are as many firms as random prices. A mutual fund interpretation of this result is offered in Section IV.

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