In February 2005, the U.S. Federal Trade Commission (FTC) went to court to undo the January 2000 takeover of Highland Park Hospital by Evanston Northwestern Healthcare Corp. The FTC accused Evanston Northwestern of antitrust violations by using its post-merger market power in the Evanston hospital market to impose 40% to 60% price increases (Bernard Wysocki, Jr., "FTC Targets Hospital Merger in Antitrust Case," Wall Street Journal, January 17, 2005, A1). Hospitals, even within the same community, are geographically differentiated as well as possibly quality differentiated. Suppose that the demand for an appendectomy at Highland Park Hospital is a function of the price of the procedure at Highland Park and Evanston Northwestern Hospital: qH = 50 - 0.01(H + 0.005(N. The comparable demand function at Evanston Northwestern is qN = 500 - 0.01(N + 0.005(H. At each hospital, the fixed cost of the procedure is $20,000 and the marginal cost is $2,000.

a. Use the product-differentiated Bertrand model to analyze the prices the hospitals set before the merger. Find the Nash equilibrium prices of the procedure at the two hospitals.

b. After the merger, find the profit-maximizing monopoly prices of the procedure at each hospital. Include the effect of each hospital's price on the profit of the other hospital.

c. Does the merger result in increased prices? Explain.