Spatial duopoly with discriminatory pricing

The concept and existence of an equilibrium is established for profit maximizing competitors whose decisions involve choices of both delivered price schedules and firm locations. Each firm faces a production function; each is allowed to locate in the plane and to set discriminatory prices. Any transport cost function that is continuous in the firm location variable may be used. It is shown that the locations of the two firms are in equilibrium if each firm is minimizing social cost (i.e., the total cost to the firms of supplying the market with the good it demands is minimized) with respect to the opponent's fixed location.