A Co-Moment Criterion for Firms for the Two Canonical Models of Production Under Uncertainty

Abstract

This paper shows that there is a common criterion for firms for the two canonical equilibrium models of production under uncertainty, the state-of-nature model and the probability model. When security markets are sufficiently rich to efficiently allocate firms' profit streams among the consumer-investors, the theoretical criterion in the state-of nature model is market-value maximization, while for the probability model it is maximization of a firm's contribution to social welfare. Both criteria however require information not readily available to firms in practice. We show that if risks are not too large then both criteria can be transformed into a common co-moment criterion which a Nash-competitive firm should maximize, taking as given the production decisions of other firms and the co-moment prices, which can be easily deduced from security prices if co-moments of high order are neglected. The co-moment criterion provides a unifying framework for the two equilibrium models of production under uncertainty, and has the merit of being based on information which is readily available.

Keywords: optimal choice of firm's investment, co-moment formula for security prices, co-moment criterion for firms

JEL Classification: D21, D51