Question

Suppose that BMW can produce any quantity of cars at a constant marginal cost equal to ​$20,000 and a fixed cost of ​$10billion. You are asked to advise the CEO as to what prices and quantities BMW should set for sales in Europe and in the United States. The demand for BMWs in each market is given by Qe=4,500,000-100Pe and Qu=1,300,000-20Pu where the subscript E denotes​ Europe, the subscript U denotes the United States. Assume that BMW can restrict U.S. sales to authorized BMW dealers only.   a.  What quantity of BMWs should the firm sell in each​ market, and what should the price be in each​ market? What should the total profit​ be? ​ (round dollar amounts to the nearest penny and quantities to the nearest​ integer) In​ Europe, the equilibrium quantity is nothing cars at an equilibrium price of ​$ nothing. While in the United​ States, the equilibrium quantity is nothing cars at an equilibrium price of ​$ nothing. BMW make a total profit of?

Answer 1

(a)

Profit is maximized when MRe = MC and MRu = MC.

In Europe,

Pe = (4,500,000 - Qe) / 100 = 45,000 - 0.01Qe

TRe = Pe x Qe = 45,000Qe - 0.01Qe²

MRe = dTRe/dQe = 45,000 - 0.02Qe

45,000 - 0.02Qe = 20,000

0.02Qe = 25,000

Qe = 1,250,000

Pe = 45,000 - 0.01 x 1,250,000 = 45,000 - 12,500 = 32,500

In US,

Pu = (1,300,000 - Qu) / 20 = 65,000 - 0.05Qu

TRu = Pu x Qu = 65,000Qu - 0.05Qu²

MRu = dTRu/dQu = 65,000 - 0.1Qu

65,000 - 0.1Qu = 20,000

0.1Qu = 45,000

Qu = 450,000

Pu = 65,000 - 0.05 x 450,000 = 65,000 - 22,500 = 42,500

Total profit = (Pe x Qe) + (Pu x Qu) - MC x (Qe + Qu) - Fixed cost

= (32,500 x 1,250,000) + (42,500 x 450,000) - 20,000 x (1,250,000 + 450,000) - 10 billion

= 40.625 billion + 19.125 billion - 34 billion - 10 billion

= 15.75 billion