#4 430 PART 3. Market Structure and Competitive strate b. Does prohibiting the u
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430 PART 3. Market Structure and Competitive strate b. Does prohibiting the use of coupons make German producers better off or worse off? 4. 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 - 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 mar- ket? 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 com- pany's profit? 5. 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 P = 15 - MR, = 15 – 20, DP, = 25 - 20, MR, = 25 - 40, The monopolist's total cost is C = 5 + 3(Q, + Q,). What are price, output, profits, marginal revenues, and deadweight loss (i) if the monopolist can price dis- criminate? (ii) if the law prohibits charging different igor in the two regions?Explanation / Answer
Find the two inverse demand functions
PE = 40,000 - 0.01QE
and PU = 50,000 - 0.05QU
Find the two marginal revenues
MRE = 40,000 - 0.02QE
MRU = 50,000 - 0.1QU
Since MC is same in both nations, we have MC = 20,000
a) MRE = MC
40,000 - 0.02QE = 20,000
20,000 = 0.02QE
QE* = 1,000,000
PE* = 40000-0.01*1000000 = $30,000
And
MRU = MC
50,000 - 0.1QU = 20,000
QU* = 300,000
PU* = 50,000 - 0.05*300,000 = $35,000
Total profit = total revenue - total cost
= ($30,000*1,000,000 + $35,000*300,000 - $20,000*1,300,000 - 10,000,000,000)
= 4.5 billion
b) Market demand Q = 5,000,000 - 120P
Inverse demand function is P = 5,000,000/120 - (1/120)Q
MR = 5,000,000/120 - (2/120)Q
Profit maximizing quatity has
MR = MC
5000000/120 - (2/120)Q = 20,000
Q* = 1,300,000
P* = $30833.33
Profit = (1,300,000*30833.33 - 20000*1,300,000 - 10000000000) = 4.08 billion
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