1. Two firms are producing differentiated products. Firm I's demand curve is Q1(P1, P2) = a - 2p1 + 2 Firm 2's demand curve is Q2(P1, P2) = a- 2p2 + P1 Suppose both firm's marginal cost is equal to zero and no fixed cost. a) Each firm's objective is to maximize its profit. Suppose they compete in price and move simultaneously. Please derive the equilibrium prices and profits. b) If they collude, please calculate each firm's profit. c) Suppose firm 1's objective is to maximize it's profit but firm 2's objective is to maximize the difference of firm 2 and firm 1's profit, that is 72 - 71. Suppose firm 1 and firm 2 compete in price, please derive the equilibrium price and profits. d) Suppose each firm's objective is to maximize its profit. Suppose they compete in quantity and move simultaneously. Please derive the equilibrium prices and profits