Horizontal Mergers (25 points)Two firms each sell one differentiated product.

Each fifirm has cost function C(q) = cq. The fifirms compete in prices and the demand

for each product is:

q1 = a - p1 + p2

q2 = a - p2 + p1

(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 threshold in terms of a, c, , such that you would

allow the merger if E were smaller than that threshold.

(c) You learn that = 0.2, pre-merger margins are L =( p- c)/ p = 0.4 and E = 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 and L

. Use the fact that the firms are symmetric to simplify the algebra).