In: Economics
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 process 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 – 100PE 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.
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?
We are given the following information:
For profit maximisation, we must have:
(b) Now, for same price in the two markets, we need the following profit maximisation condition
In order to calculate MR, we need to calculate t he total revenue, for which we know that the price charged across the markets will be same, but we have to find the total demand also.
where P = PE = PU
For the quantities sold in the individual markets, we use the original demand equations and calculate the values as shown below.
(rounded off to the nearest decimal)
(rounded off to the nearest decimal)
Also, the total profit is given by:
Due to equal pricing in the two markets, we see that the European markets suffer due to higher prices than before (old P = 30,000 and new P = 30833.33), thereby resulting in lower quantity being sold in that market. However, prices are comparatively lower in the United States market than the previous case. So, demand is also higher in the US market, implying a gain in the US market. Along with the gain and loss in the two markets, we also see that equal pricing in the two markets also reduces the profit from $4.5 billion to $4.083 billion which is a reduction of $0.417 billion in profits.