The principal objective of this essay is to bring together the theory of a firm's capacity decisions and certain facts of market structure which contribute to the uncertainty about the prices or revenues realized by the firm. The connecting link between the two is furnished by the fact that, under conditions of "competition among a few," the output decisions of an individual firm have a random effect on its own revenues. It is shown that considerations of uncertainty influence the capacity or utilization decisions in a manner which is fundamentally different from that under "pure" competition. In the latter case, a production decision of an individual firm does not change the probability distribution of market prices. This and some related considerations make it practically useful to interpret "capacity" in terms of profitable output--allowing the standards of profitability to be quite arbitrary. Defined in terms of profitable output, capacity emerges as a random variable--random because of the uncertain fulfillment of the standards of profitability. It is also seen that the usual interpretation of the present-value integral is to be abandoned in favor of another which, on a formal level, has close ties with the theory of integration over the space of random functions.

A model is presented for the derivation and implementation of optimal linear decision rule for a firm producing and dealing in a number of interacting products, and possessing partial influence on their prices. The behavior of a multi-item production-inventory complex is represented as the dynamics of suitably defined state variables under the influence of decision rules that are stable and linear in the state variables, but otherwise unspecified. The dynamical equations are stochastic owing to the presence of stochastic processes in the forcing terms. The statistical properties of these processes, together with the decision rules, determine the statistics of the outcome or the criterion functional. The optimum inventory decision is then derived as the "best" linear transformation on the past of the state variables such that the mean value of the criterion functional is optimized subject to the system constraints. [Likely published between 1961-1966.]