a . Suppose that both firms are choosing prices simultaneously. Wh each firm's profit? (5 pts) b . Suppose that again both firms are choosing prices simultaneously but instead of playing the game once, the game is played infinitely between Splint and Horizon. Is it possible for the two firms to collude in order to both charge a medium price? If you answered yes, write down the strategy that both firms will use in order to collude at the medium price. What is the minimum discount factor required in order to sustain such an agreement? (10 pts) C . Is it possible for the two firms to collude in order to both charge a high price? If you answered yes, write down the strategy that both firms will use in order to collude at the high price What is the minimum discount factor required in order to sustain such an agreement? (10 pts) 2. There are two firms in the market for cement which has demand given by P = 260 -2Q where Q = q1 + 92 is the total output in the market. Both of the firms have constant marginal cost c = 20 and the two firms compete in quantities (Cournot competition). Assume that this market game is being played infinitely many times by the two firms a. Suppose that the two firms colluded and agreed to each produce half of the monopoly output. Solve for the value of collusion V and the value of deviation VP. What is the minimum discount factor S required to sustain collusion? (10 pts) b. Now suppose that the government forms an antitrust authority whose job is to prevent the firms from colluding. This authority could detect collusion with probability q = 0.1 but for political reasons, the largest fine they could impose on a firm caught colluding is F = 2500. What is the highest possible discount value S of firms that they could successfully prevent from colluding. (5 pts) c. Suppose that the antitrust authority could detect collusion with probability q = 0.1. What is the minimum fine F that the authority could impose in order to fully prevent collusion? (5 pts) c. Suppose that the government's antitrust authority only cares about consumer surplus. What is the most the government would be willing to pay in order to prevent collusion? (5 pts) 3. Consider a market for an identical product with four firms. The inverse demand for this product is P = 100 - Q where P is price and Q is aggregate output. The production costs for firms 1 and 2 is given by C(qi) = 10qi where qi is the output of firm i and the production costs for firms 2 and 4 is given by C(qi) = 20qi. That is