The Nature of Equilibria under Noncollusive Product Design and Collusive Pricing

It is well known that in a two stage duopoly model of product choice with quadratic transportation cost, the firms locate at the extreme endpoints of the market. This paper examines this model in an infinite horizon setting where in the initial period the firms choose locations and in subsequent periods choose prices. The firms collude in prices and share the profits on the profit possibility frontier. It is shown that under very general conditions, both the firms locating at the center is an equilibrium. It is not necessarily unique and multiple symmetric equilibria can exist. So, the products are not minimally differentiated and the degree of differentiation can vary. Sufficient conditions for three types of equilibria are given: a unique equilibrium at the center of the market, multiple symmetric equilibria and multiple asymmetric agglomerated equilibria. The first two cases obtain if the firms share profits equally when they are located at the same point and the last case otherwise.