Economic

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: q1 = a - p1 + Bp2 92 = a - P2 + BP1 (a) Suppose the firms merge. What is the increase in price (measured in dollars) in terms of a, B 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, S, such that you would allow the merger if E were smaller than that threshhold. (c) You learn that S = 0.2, pre-merger margins are L = = .4 and E = 0. Suppose you would allow a merger if it would raise prices by less than 5%. Would you 2 recommend blocking the merger or not? (Hint: write the percentage price increase in terms of B and L. Use the fact that the firms are symmetric to simplify the algebra)