3. Horizontal Mergers (25 points) Two firms each sell one differentiated product. Each firm has cost function C(q) = cq. The firms compete in prices and the demand for each product is: 91 api + Bp2 92a-P2+ Bp (a) Suppose the firms merge. What is the increase in price (measured in dollars) in terms of a, and c. (b) Now suppose that by merging the firms can lower their cost function from C(q) = cq to C(q) = Ecq, where E 1. You would block the merger if it would increase prices. Derive an efficiency threshhold in terms of a, c, , such that you would allow the merger if E were smaller than that threshhold. = p-c4 and E (c) You learn that 3 = 0.2, pre-merger margins are = 0. Suppose you would allow a merger if it would raise prices by less than 5%. Would you recommend blocking the merger or not? (Hint: write the percentage price increase in terms of 3 and L. Use the fact that the firms are symmetric to simplify the algebra).