Suppose there are two firms producing a homogeneous good, with cost functions given by C1(q1) = 3911 and C2(q2) = 2:12 + 6. Firms are playing an infinitely repeated game, facing a market demand given by P(Q) = 150 Q, where Q = q] + 172. Both firms discount profits with a common discount factor 5 E [0, 1). If firms were to collude and behave as if they were a single monopolist, then production would be done using firm 2's technology (cost function), since it is considerably more efficient than firm 1, at least for large amounts of output. a) (1 point) What is the total discounted profit for each firm, from following a collusive agreement? (obvi- ously, profits are not the same for each firm) b) (1 point) Suppose both firms are considering collusion. If firm 1 decides to collude and firm 2 decides to cheat on the agreement, what is firm 2's profit for the period in which it cheats? If firm 2 decides to collude and firm 1 decides to cheat, what is firm 1's profit for the period in which it cheats? c) (1 point) Consider now a \"trigger\" strategy like the ones we saw in class. What is the total discounted profit associated with cheating for each firm? d) (1 point) What is the value of (5 such that firm 1 is indifferent between following the collusive agreement or cheating on it? e) (1 points) What is the value of 6 such that firm 2 is indifferent between following the collusive agreement or cheating on it? f) (1 points) Based on your answers in d) and e), what is the minimum value of (5 such that both firms will choose to honor a collusive agreement