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 arm 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 x' p, if she buys from Hmm A; u =r (1 ' x) " p. if she buys from arm B; and 0 if she does not buy. If more than one arm is present, Arms simultaneously set prices. 1. Consider the monopoly problem in which only arm A is present and sets its prices to maximize prosts. Calculate the monopoly solution depending on f where r 2 [0; 4]