Competition of Firms: Discriminatory Pricing and Location

Two costlessly mobile firms are to be located in a market region, a subset of the plane. The firms compete by setting locations and delivered price schedules. To study this competitive stiuation an appropriate extensive form game is defined, along with an appropri- ate noncooperative solution concept. Existence and general properties of the equilibrium are demonstrated. Among the results are: Each firm increases its profit by locating so as to decrease total cost to both firms of serving the market. Firms will never locate coinciden- tally if they have identical production costs and transport cost rates, or if these are different and the firms are located in a circular market region having a uniform demand distribution. THIS PAPER STUDIES competition between two profit maximizing firms in space who are costlessly mobile and may discriminate in price. We will allow the firms to set locations and delivered price schedules and we will be concerned with the existence- and properties of equilibria in location and price. Starting with Hotelling (9), the spatial competition literature has focused on location on bounded linear markets by two or more firms. Hotelling assumed identical firms that produced a single good with constant cost of production and considered consumers to be uniformly distributed and to have inelastic demand. He also assumed that the consumers pay transport cost and purchase the good from the cheapest source. Hotelling claimed that a Nash equilibrium in locations for the two firm market existed and yielded back-to-back locations at the center of the market. Many authors, most recently, D'Aspremont, Gabszewicz, and Thisse (2) have noted that an equilbrium in prices and location does not exist for Hotelling's model. However, if the firms employ identical exogeneously specified prices, Hotelling's conclusions hold. Subsequent work by Smithies (14), Hartwick and Hartwick (7), and Eaton (3) claimed to show that a Nash equi- librium in f.o.b. prices and locations can exist in markets with a uniform distribu- tion of consumers each of whom have identical elastic demand functions for the two and three firm problems. The work of D'Aspremont et al. casts doubt on these conclusions without the adoption of restrictive conditions. Our work contrasts with these works and related research which has dealt with linear markets, with uniform distributions of customers and with identical firms. Our work will involve markets that are subsets of the plane having nonuniform distributions of customers. Our firms will be allowed to be different, that is, have differences in production and transport costs. However, the fundamental difference in our approach is that our firms will set discriminatory prices and not price f.o.b. In many ways our work will represent the discriminatory pricing