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Problems for the second seminar: Product differentiation ECON4820 Strategic competition — Spring semester 2010 Solutions to the problems will be presented Wed 17 February 2010. Please direct any questions to Geir B. Asheim (Room ES1152, Tel: 228 55498, e-mail: [email protected]) Problem 1 (Linear city model with price discrimination) Consider the linear city model where firm 1 is located at the one end point (x = 0) of the line segment and firm 2 is located at the other end point (x = 1). Assume linear transportation costs, being equal to t per unit distance, independently of whether firms or consumers do the transporting. Each consumer buys one (and only one) unit from the firm offering the lowest sum of price and transportation costs. (a) Assume first that the firms sell at their respective locations and let the consumers transport the good. Show that firm i’s demand is (pj − pi + t)/2t, where pi is price excluding transport costs. Assume that firms set prices simultaneously and seek to maximize their own profit taking the price of the other as given. Show that both firms set price equal to c + t. (b) Assume then that the firms transport the good to the consumers and sell the good at the consumers’ location at a price that includes transport costs. Retain the assumption that firms set prices simultaneously and seek to maximize their own profit taking the prices of the other as given. Show that price at the end points equal c + t, while price at the middle of the line segment equals c + 2t . What kind of price discrimination is this? Is this kind of price discrimination desirable in this case? Problem 2 (Linear city model with endogenous costs) Tirole Exercises 7.2 Problem 3 (Circular city model with quadratic transportation costs) Tirole Exercise 7.3 1