A Dynamic Model of the Competitive Firm

Abstract

IN THE PAST FEW YEARS a number of authors have attempted to develop a dynamic theory of monopoly, variously taking into account uncertainty of demand or lags in demand and allowing holdings of the final good, explicitly or implicitly, either by the monopolist or consumer [1, 2, 3, 4, 6]. While some progress has been made in these studies, considerable work needs to be done to bring this theory to a satisfactory state. The very different problem of the dynamic behavior of the purely competitive firm, however, has attracted little attention, and results in this area are at a still more elementary stage of development. The only recent, though fragmentary, attempt to present an explicit dynamic model of the competitive firm is contained in a study by Edwin Mills [4, chapter 4]. Apart from a number of possible uses, a dynamic theory of the competitive firm would seem to be particularly useful in the study of dynamic adjustment and stability in competitive markets. In this paper we offer a contribution in this direction by beginning an investigation of the competitive firm's behavior over a finite or infinite horizon. In the next section we specify the model, and in subsequent sections we consider the questions of existence and uniqueness and the properties of optimal behavior. We are able to show specific circumstances in which behavior in the static theory and the dynamic models coincide or differ and are able to obtain important features of optimal production and sales policies in a number of cases.