Differentiation on Main Street: Two topics in location theory

Abstract

Two topics are examined in the convex cost specification introduced by d'Aspremont et al. (1979) into the model of Hotelling (1929). The first topic introduces a finite reservation constraint and demonstrates that the maximal differentiation result of d'Aspremont et al. (1979) is a special case which holds only if the constraint is sufficiently high. The second topic demonstrates that the use of a convex cost function creates the existence of a unique subgame-perfect Nash equilibrium in pure-strategies with three firms in a finite linear interval, and so reconciles an outstanding theoretical anomaly. The welfare consequences of this equilibrium are considered. In a limited analysis the second topic also examines possible locational pre-emption strategies as a finite reservation constraint is introduced, suggesting that the reservation value of a product is perhaps relevant in a firm's ideal location commitment.