Suppose that BMW can produce any quantity of cars at a constant marginal cost equal to $20,000 and a fixed cost of $10 billion. You are asked to advise the CEO as to what prices and quantities BMW should set for sales in Europe and in the United States. The demand for BMWs in each market is given by:
QE = 4,000,000 – 100 PE and QU = 1,000,000 – 20PU
where the subscript E denotes Europe, the subscript U denotes the United States. Assume that BMW can restrict U.S. sales to authorized BMW dealers only.
Correction: Prices and costs are in dollars, not thousands of dollars as your book may indicate.
a. What quantity of BMWs should the firm sell in each market, and what should the price be in each market? What should the total profit be?
b. If BMW were forced to charge the same price in each market, what would be the quantity sold in each market, the equilibrium price, and the company’s profit?
2. A monopolist is deciding how to allocate output between two geographically separated markets (East Coast and Midwest). Demand and marginal revenue for the two markets are:
P1 = 15 – Q1 MR1 = 15 – 2Q1
P2 = 25 – 2Q2 MR2 = 25 – 4Q2
The monopolist’s total cost is C = 5 + 3(Q1 + Q2 ). What are price, output, profits, marginal revenues, and deadweight loss (i) if the monopolist can price discriminate? (ii) if the law prohibits charging different prices in the two regions?
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