Location-Price Competition with Delivered Pricing and Elastic Demand

Abstract

In the past, implementing delivered pricing has been perceived as unrealistic because of practical difficulties in distinguishing between customers, determining an individual’s willingness to pay, and setting different prices to individuals. The rise of e-commerce has introduced the possibility of doing all three. Competitive location with delivered pricing was studied by Lederer and Hurter (1986) but only with inelastic customer demand. This paper extends the literature by allowing price elastic demand. A Nash equilibrium with inelastic demand always exists but examples show that it may not with price elasticity. General sufficient conditions guaranteeing existence of a Nash equilibrium are developed despite the fact that even with these conditions a firm’s profit function is generally not concave, quasi-concave, supermodular or even continuous in location choices. Examples demonstrate how violation of sufficient conditions result in lack of existence. Given price elasticity, equilibrium locations demonstrate properties unlike the inelastic case, for example, as transportation cost rises or firms’ production costs rise, each firm locates closer to its competitor. Given our sufficient conditions for equilibrium’s existence, the interval spanning firms’ ordered equilibrium locations always contains a social welfare optimum pair and a social welfare optimum pair is always contained by an ordered equilibrium.