Two firms each sell one differentiated product.Each firm has cost functionC(q) =cq. The firms compete in prices and the demandfor each product is:q1=ap1+p2 q2=ap2+p1

(a) Suppose the firms merge. What is the increase in price (measured in dollars) interms ofa,andc.

(b) Now suppose that by merging the firms can lower their cost function fromC(q) =cqtoC(q) =Ecq, whereE1. You would block the merger if it would increaseprices. Derive an efficiency threshhold in terms ofa,c,, such that you wouldallow the merger ifEwere smaller than that threshhold.

(c) You learn that= 0.2, pre-merger margins are L= pc p=0.4 andE= 0. Supposeyou would allow a merger if it would raise prices by less than 5%. Would you ecommend blocking the merger or not? (Hint: write the percentage price increasein terms of and L. Use the fact that the firms are symmetric to simplify the algebra).