Hospitals, even within the same community, are geographically differentiated as well as possibly quality differentiated. The demand for an appendectomy at Highland Park Hospital is a function of the price at Evanston Northwesters Hospital q_H = 50 - 0.01p_H + 0.005p_N. The comparable demand function at Evanston Northwestern is q_N = 500 - 0.01p_N + 0.005p_N. 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.
b) After the merger, find the profit maximizing monopoly prices of the procedure at each hospital
c) Does the merger result in price increases?