# Problems for the second seminar: Product differentiation ```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: g.b.asheim@econ.uio.no)
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
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