4. A vertically integrated automobile company has an upstream engine division and a downstream assembly division. The demand for the company's cars is given by Q = 20-P. Each car requires one engine. The downstream division's total cost of assembling cars is TCD(Q) = 4Q. The upstream division's total cost of producing engines is TCv (Q) = Q². (a) Suppose that there is no outside market for engines. What is the price and quantity of cars produced by the company? (b) Suppose that there is no outside market for engines. What should be the transfer price for engines? [Hint: the transfer price of an engine should equal the marginal cost of engine production at the optimal quantity.] (c) Suppose that there is a competitive outside market in which the price of an engine is 12. What is the price and quantity of cars produced by the company? (d) Suppose that there is a competitive outside market in which the price of an engine is 12. What is the quantity of engines that the company buys or sells on the outside market?

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
ChapterB: Differential Calculus Techniques In Management
Section: Chapter Questions
Problem 3E
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4. A vertically integrated automobile company has an upstream engine division and a downstream
assembly division. The demand for the company's cars is given by Q = 20-P. Each car requires
one engine. The downstream division's total cost of assembling cars is TCD(Q) = 4Q. The
upstream division's total cost of producing engines is TCv (Q) = Q².
(a) Suppose that there is no outside market for engines. What is the price and quantity of
cars produced by the company?
(b) Suppose that there is no outside market for engines. What should be the transfer price for
engines? [Hint: the transfer price of an engine should equal the marginal cost of engine
production at the optimal quantity.]
(c) Suppose that there is a competitive outside market in which the price of an engine is 12.
What is the price and quantity of cars produced by the company?
(d) Suppose that there is a competitive outside market in which the price of an engine is 12.
What is the quantity of engines that the company buys or sells on the outside market?
Transcribed Image Text:4. A vertically integrated automobile company has an upstream engine division and a downstream assembly division. The demand for the company's cars is given by Q = 20-P. Each car requires one engine. The downstream division's total cost of assembling cars is TCD(Q) = 4Q. The upstream division's total cost of producing engines is TCv (Q) = Q². (a) Suppose that there is no outside market for engines. What is the price and quantity of cars produced by the company? (b) Suppose that there is no outside market for engines. What should be the transfer price for engines? [Hint: the transfer price of an engine should equal the marginal cost of engine production at the optimal quantity.] (c) Suppose that there is a competitive outside market in which the price of an engine is 12. What is the price and quantity of cars produced by the company? (d) Suppose that there is a competitive outside market in which the price of an engine is 12. What is the quantity of engines that the company buys or sells on the outside market?
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