Suppose that BMW can produce any quantity of cars at a constant marginal cost equal to $20,000 and a fixed cost of $10billion. 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=4,000,000100PE

and

QU=1,400,00020PU

where the subscript E denotesEurope, the subscript U denotes the United States. Assume that BMW can restrict U.S. sales to authorized BMW dealers only.

a.What quantity of BMWs should the firm sell in eachmarket, and what should the price be in eachmarket? What should the total profitbe? (round dollar amounts to the nearest penny and quantities to the nearestinteger)

InEurope, the equilibrium quantity is

1000000

1000000 cars at an equilibrium price of $

30000

30000.

While in the UnitedStates, the equilibrium quantity is

500,000

500,000 cars at an equilibrium price of $

45000

45000.

BMW makes a total profit of $

12,500,000,000

12,500,000,000.

b.If BMW were forced to charge the same price in eachmarket, what would be the quantity sold in eachmarket, the equilibriumprice, and thecompany's profit? (round dollar amounts to the nearest penny and quantities to the nearestinteger)

To solve thisproblem, first find the combined market demand by horizontally summing the European and US demandcurves:

Q=QE+QU=4,000,000100PE+1,400,00020PU=5,400,000120P

Thus, inverse demandis:

P=5,400,0001201120Q(To avoid roundingproblems, do not convert the fractions todecimals)

The equilibrium price would be $

, and BMW would sell

cars in Europe and

cars in the United States.

BMW makes a profit of $

.