Optimization of Market Share in Spatial Competition

Abstract

Traditionally, models of spatial competition, for example Hotelling [13], Smithies [15], and Gannon [10], have been predicated upon profit maximization as the motivational basis for explaining the behavior of rival firms. This single-mindedness in approach to the objectives of firms has persisted,1 in spite of the favorable support given to such alternative goals of firms as maximization of sales revenue (subject perhaps to some predetermined lower bound on profits) and maximization of market share, in models of aspatial imperfect competition [1; 6]. Hotelling's seminal analysis [13] of spatial duopoly focused on a situation in which two identical, perfectly mobile firms market a homogeneous product to a set of identical, immobile consumers uniformly distributed along a line of finite length. Hotelling exposed the fact that the equilibrium locational arrangement of the firms involves both firms concentrated at the geographic center of the market when the demand by individual consumers is perfectly inelastic and each firm attempts to maximize its own profits. It is a trivial corollary of Hotelling's result that the same location outcome, namely central concentration, emerges whether the objective of each duopolist is maximization of its profits, gross revenues, aggregate quantity sales, or market share, provided that consumer demand is perfectly inelastic. What is apparently not well known is the fact that if each duopolist adopts a policy of maximizing its market share, then concentration of both firms at the center of the spatial market is the inevitable equilibrium locational outcome, regardless of the shape of the individual consumer demand function. Accordingly, the purpose of this note is to substantiate this proposition by examining a duopolistic spatial market and identifying the equilibrium locational arrangement of the firms, when each duopolist attempts to maximize its market share. It is assumed