Location and the Theory of the Imperfectly Competitive Firm under Demand Uncertainty

Abstract

There is a large and growing literature on location and the theory of the firm in a heterogeneous space, i.e., in the space where markets are given at discrete points, such as Weber [22], Isard [7], Moses [15], Sakashita [18, 19], Bradfield [3], Emerson [5], Woodward [23], Khalili, Mathur and Bodenhorn [8], Miller and Jensen [14], Mathur [13], Eswaran, Kanemoto and Ryan [6], and Mai and Shieh [11]. What is, perhaps, surprising is that within this large body of literature nothing has been said about how the firm would and should locate theoretically under conditions of uncertainty. It only with Webber [21] and Mai [10] that any real indication is given that uncertainty due to imperfect market information may exert an influence on locational choice.' In particular, Mai [10] presented a formal mathematical model to show that the results and implications of the optimum location of the firm under demand uncertainty is different from that applicable to the state of certainty. However, Mai's analytical framework is restricted to the case of pure competition, where price is given, all buyers are assumed to be concentrated at given market point, and each firm seeks to minimize expected cost and is thus risk neutral. The purpose of this paper is to extend the location theory of the competitive firm under demand uncertainty to the case where the imperfectly competitive quantity-setting firms are not risk neutral and are interested in maximizing expected utility from profit, including cost and demand factors.2 This expected utility approach will provide a more general formulation of the firm's attitude toward risk for analyzing its location decisions. The basic model evaluating the firm's location and input choices is presented in section II. Section III examines the overall impacts of demand uncertainty on the optimum location and input demands. The effect of a marginal increase in demand uncertainty on the optimum location is investigated in Section IV. Section V analyzes the effect on the optimum location of a change in the expected output price. Section VI then evaluates the