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.