2. Suppose that a car dealer has a local monopoly in Selling Volvos. It pays the
ID: 1214906 • Letter: 2
Question
2. Suppose that a car dealer has a local monopoly in Selling Volvos. It pays the wholesale price w to Volvo for each car that it sells, and charges each consumer the retail price p. The demand curve for the dealer in the retail market is p=60-q, where price is in units of thousands of dollars. The marginal cost of Volvo is 20.
A. Suppose that the car dealer and Volvo work separately. What would be the Nash equilibrium?
B. Find the equilibrium wholesale price and retail price: w and p. Find the equilibrium profits for the dealer and Volvo.
C. Now suppose that Volvo bought the ownership of the car dealer. For the integrated firm, what will be the optimal retail price p? Find the equilibrium total profit for the integrated firm.
D. In terms of total profit, is the separation scenario in (A) better than the integration scenario (C)? How about consumer surplus?
E. Now suppose that integration is not feasible. Design a franchise contract to achieve the same production, retail price and total profit as achieved in part (C) and (D). Moreover, please specify the shares of Volvo and the dealer, so that Volvo’s profit is twice that of the dealer, M=2R.
Explanation / Answer
A. Suppose that the car dealer and Volvo work separately. What would be the Nash equilibrium?
Answer:
Using the backward induction, we start with the retailer (dealer)'s problem in the retail market. Given the retailer's marginal cost, is., the wholesale price w, we have MCR=w=60-2q=MRR-. q=30-03w -)p=60-q=30+0.5w. Now we go back to solve for the manufacturer (Volvo)'s problem in the wholesale market. From the retailer's optimal condition MCR=MRR, we know the manufacturer's demand is: w=60-2q. Given the manufacturer's marginal cost 20, we have MC m=20= 60-4q=MR f-) q=10-. w=60-2q=40. So the N.E. is (w=40, p=30+0.5w)
B. Find the actual equilibrium wholesale price and retail price: w and p. Find the equilibrium profits for the dealer and Volvo.
Answer:
q=10; w=40; p=30+0.5w=50.
Volvo's profit Ilf=(w-MC)q=(40-20)10 =200;
Dealer's profit 14=(p-w)q=(50-40)10=100
The consumer surplus is: CS=1/2(60-p)q=1/2(60-50)10=50.
C. Now suppose that Volvo bought the ownership of the car dealer. For the integrated firm, what will be the optimal retail price p? Find the equilibrium total profit for the integrated firm.
Answer:
The integrated firm works as a joint monopolist for the consumers.
MR=60-2q=20=MC-. q=20 -)p=60-q=40.
D. Find the equilibrium total profit for the integrated firm. Calculate the consumer surplus.
Answer:
The total profit 111,f+R= (p-MC)q=(40-20)20=400.
The consumer surplus is: CS=1/2(60-p)q=1/2(60-40)20=200.
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