Q1 Consider a market in which consumer type a: 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 0 = 1/2. There is mass 1 of consumers. A consumer located at m E [0, 1] obtains utility um = 'r' m pA if she buys from rm A; use = 7' (1 3:) 113 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 E [0, 4]. (2) Consider the duopoly problem in which rms compete in prices. Solve for Nash equilibrium depending on 7" (make sure that you characterize the equilib- rium for any parameter 7' E [0, 4]). (3) Compare the price level in duopoly to the price level under monopoly. Are duopoly pricing necessarily lower than monopoly prices? Explain your ndings. (4) Suppose that rm A is the incumbent and, thus, has already entered the market. Suppose at a stage prior to the price-setting stage, rm B decides whether to enter. To enter the rm has to pay an entry cost K which is sunk. Depending on r calculate the critical sunk cost ff above which rm B would not be willing to enter the market