[30 MARKS] Two profit-maximising firms produce differentiated products at no cost and compete in prices. Letting i, j = 1, 2 with i # j, the inverse demand function and the corresponding demand function faced by each firm i are Pi = 1200 - qi 2 and qi = = (1200 - 3pi + 2p;) (a) [5 MARKS] Find the equilibrium prices and quantities. (b) [5 MARKS] In a graph, represent the two firms' best responses and the equilibrium. (c) [5 MARKS] Suppose that the two firms merge to create a monopoly. What are the equilibrium prices and quantities? (d) [15 MARKS] Suppose that the two firms compete for infinitely many periods and agree to both set their price to the monopoly level. Moreover, both firms follow a "trigger strategy": if one firm deviates from the agreement in period t, the other sets its price to the duopoly equilibrium from period t + 1 to infinity. Let o, and 62 2 of 3 ECON31002 (with 61, 62 E [0, 1]) be the discount rates of firms 1 and 2, respectively. For what values of 61 and 62 is the collusive agreement sustainable? 6 130 MARKS1 There is a continuum of consumers distributed uniformly with dencity 1 over - rw 1 1