Exercise 2 Monopoly versus Duopoly Consider a market in which consumer type x is uniformly distributed on the unit interval. Consumers demand 0 or 1 unit (they buy at most one unit overall in the market). Firm A is located at 0 and rm B at 1. Firms incur constant marginal costs of production c = 1 = 2 . There is mass 1 of consumers. A consumer located at x 2 [0 ; 1] obtains utility u x = r x p A if she buys from rm A ; u x = r (1 x ) p B if she buys from rm B ; and 0 if she does not buy. If more than one rm is present, rms simultaneously set prices. 1. Consider the monopoly problem in which only rm A is present and sets its prices to maximize prots. Calculate the monopoly solution depending on r where r 2 [0 ; 4]