A Co-Moment Criterion for the Choice of Risky Investment by Firms

This paper uses Taylor series expansions and the assumption of small risks to derive a co-moment criterion that firms should maximize so that the resulting equilibrium is Pareto optimal. This is done in two models of production under uncertainty: the state-of-nature (SN ) model in which the firms’ outputs depend on states of nature and financial markets are complete with respect to these states of nature; and the probability (P) model in which the firms’ risky outputs are modeled by their joint probabilities and financial markets span the outcome space of the firms. The theoretical criterion in the SN model is market-value maximization, while in the P model it is maximization of a firm’s contribution to social welfare. We show that both criteria can be transformed into a common co-moment criterion which a firm should maximize, taking as given the production decisions of other firms and the co-moment prices, which can be deduced from the security prices. The co-moment criterion provides a unifying framework for the two equilibrium models of production under uncertainty, has the merit of being based on information which is readily available to firms, and provides greater insight than the theoretical criterion into the risk characteristics of its profit stream which a firm should focus on when choosing its investment plan.