2. Consider a market containing three firms, each of which makes an identical product. The inverse demand for this product is P = 80 - Q. The production costs for firms 1 and 2 are identical and given by C(q i) = 20qi where qi is the output of firm i. The cost function of firm 3 is C(q 3) = 32q3. Assume that the firms each choose their outputs to maximize profits given they each act as a Cournot competitor. a) Derive the Cournot equilibrium output for each firm, the product price, and the profits of all four firms. b) Assume that firms 1 and 2 merge and that all firms continue to act as Cournot competitors after the merger. Confirm that this merger is unprofitable. c) Now assume that instead of merging with firm 2, firm 1 merges with firm 3. Is this merger profitable? What has happened to price as a result of this merger?