Spatial price discrimination in a symmetric barbell model: Bertrand vs. Cournot

This paper investigates the theory of spatial discrimination for general demands and general transportation costs in a barbell model, where markets' locations are assumed to be at opposite endpoints of a line. Duopoly firms in the Bertrand model always differentiate maximally, whereas in the Cournot model the market demand structure is not so critical, but the functional form of the transportation cost plays a crucial role in determining equilibrium location. Non†maximal distance appears in the Cournot equilibrium when a convex transportation cost is allowed, bringing about the findings that the equilibrium consumer surplus may be higher and the equilibrium profits may be lower under Cournot competition than under Bertrand competition.