1. There are four firms in a market. Demand is given by D(p) = 100 - p. Each firm has a cost function of C(q) = =q =192 + 2q. a. Suppose that the firms compete (i.e. behave like price takers). What is the competitive equilibrium price and quantity? b. Now suppose that the firms collude, with each firm producing an equal share of the output. Find the new prices and quantities. c. Calculate consumer surplus under the equilibria in parts (a) and (b). d. One firm is considering cheating on the collusive agreement. Suppose the other three firms play their collusive quantities from part (b). How much profit could the cheating firm make? Hint: first find the residual demand for the cheating firm, and then write down and maximize its profit function. 2. There are two firms in a market. Demand is given by D (p) = 400 - 2p and each firm's cost is C (q) = 2q2. a. Firm 1 enters the market first and is initially a monopolist. Find firm 1's profit- maximizing price and quantity. For parts (b)-(c), assume firm 2 enters and the firms compete a la Cournot by simultaneously choosing quantities. b. Find the best responses for the two firms and plot them in a graph. c. Find the Nash equilibrium quantities and the resulting market price. d. Calculate the profits for firm 1 under parts (a) and (c). How much is firm 1 willing to pay firm 2 not to enter the market