Consider two nns i and j producing goods at marginal costs Cf and C] . respectively. with C; . cj 2 0. Consumers consider the two goods to be perfect complements. That is. consumers have demand for bundles consisting of one of each good. Assume that aggregate demand for bundles is given by q =0 (Pr' +101) with a > c;- + cj Z 0. Denote the amounts demanded of the good by q: and Q} and note that qt 2 Q} 2 '1- {a) Suppose that the two rms set prices noncooperatively. Write down the rms' maximization problems and derive their reaction functions. (b) Find the equilibrium prices, quantities. and prots of the two rms. (c) Suppose the two rms merge and set prices in order to maximize joint prots. Write down the merged rm's maximization problem and derive the equilibrium price. quantity. and prots. (d) Carefully compare the prices, quantities, and prots under non-cooperative price setting with those of the merged rm. Briefly provide an intuition for the differences. Assess whether the merger increases social welfare