Hotelling Models: A General Equilibrium Approach

Abstract

Economic models wherein consumers are spatially separated from production and distribution outlets have captivated the attention of economists at least since the seminal work of Harold [8]. Under standard assumptions of uniformity, there exist apparent tradeoffs between such variables as firm size, number of firms, and distance between firms, which must be resolved if the economy is to perform efficiently. That is, as the number of firms increase, the average transport distance decreases and transport costs must be balanced with scale effects in production. When analyzed in the context of standard models of market structure, allocative problems associated with monopolistic competition and conjectural variation seem to preclude an efficient equilibrium. This general conclusion may be drawn from models developed by Smithies [11], Losch [9], Greenhut and Ohta [4], Benson [1], and Ohta [10]. The specific features and conclusions of these works have been well summarized by Capozza and Van Order [2] and by Villegas [12]. Although these models differ with regard to behavioral assumptions attributed to individual firms, the imperfectly equilibria are invariably characterized by prices in excess of marginal cost, welfare losses, and excess capacity. For reasons discussed below, partial equilibrium analysis cannot adequately address this problem because land markets are fundamental to the functioning of a spatial economy. Therefore, the purpose of this paper is to reexamine the functioning of a Hotelling type spatial economy in the context of a general equilibrium model which addresses the interactive effects of a product market, a land market, and a factor market. The model includes a more general form of the firm's production function, as well as a general representation of transport costs. The major conclusions of the paper are: (1) the optimality conditions reveal that a two-part pricing structure must prevail if a decentralized economy is to allocate its resources efficiently; (2) a market equilibrium, that appears to be monopolistically competitive but is actually purely competitive, is consistent with Pareto optimality, even though firms have some control over prices and operate under increasing returns to scale in production.