Two identical firms currently serve a market. Each has a cost function of C(q) = 30q. Market demand is P(Q) = 80 − 0.01Q. The firms compete by setting prices simultaneously as in Bertrand competition. Let PB represent the equilibrium Bertrand duopoly price. The firms have proposed to merge, and they announce that this merger will result in considerable cost savings. The firms’ new cost function will have the form Cm(q) = cq + 100, 000. Note that the merged firm has positive fixed costs while the unmerged firms do not. (a) What is the merged firm’s profit-maximizing price if the merger is approved? Is it possible for the cost savings (via c < PB) to be sufficiently large for the merged firms’ profit-maximizing price to be below the duopoly equilibrium price? (b) Suppose that the Department of Justice permits the merger with the requirement that the new (post-merger) price must be no greater th
Two identical firms currently serve a market. Each has a cost function of C(q) = 30q. Market
The firms have proposed to merge, and they announce that this merger will result in considerable cost savings. The firms’ new cost function will have the form Cm(q) = cq + 100, 000. Note that the merged firm has positive fixed costs while the unmerged firms do not.
(a) What is the merged firm’s profit-maximizing price if the merger is approved? Is it possible for the cost savings (via c < PB) to be sufficiently large for the merged firms’ profit-maximizing price to be below the duopoly
(b) Suppose that the Department of Justice permits the merger with the requirement that the new (post-merger) price must be no greater than the pre-merger price. Under what circumstances are the firms willing to go through with the merger?
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