A firm faces the following production function, Y = AK a L¹-a (1) Here Y is output, K is capital, L is fixed labour, and A is a measure of technology. The firm uses an optimal amount of capital determined by the condition, (2) Where MPK is the marginal productivity of capital, r is the real interest rate, and 8 is the depreciation rate. MPK = r + 8 Suppose that a = 0.5, L = 25, and A = 20. Further, the real interest rate, r, is 2% and capital depreciates at a rate (8) of 18% per year. What is the optimal amount of capital this firm should install? [2 marks] Now suppose that A increases to 25, while a, Land & remain unchanged. Further, the optimal capital stock remains at the amount you found in part (c). What does this mean must have happened to the real interest rate? Find the new real interest rate and draw a clear diagram showing MPK and user cost of capital lines before and after the changes to A and r. [4 marks]

A firm faces the following production function, Y = AK a L¹-a (1) Here Y is output, K is capital, L is fixed labour, and A is a measure of technology. The firm uses an optimal amount of capital determined by the condition, (2) Where MPK is the marginal productivity of capital, r is the real interest rate, and 8 is the depreciation rate. MPK = r + 8 Suppose that a = 0.5, L = 25, and A = 20. Further, the real interest rate, r, is 2% and capital depreciates at a rate (8) of 18% per year. What is the optimal amount of capital this firm should install? [2 marks] Now suppose that A increases to 25, while a, Land & remain unchanged. Further, the optimal capital stock remains at the amount you found in part (c). What does this mean must have happened to the real interest rate? Find the new real interest rate and draw a clear diagram showing MPK and user cost of capital lines before and after the changes to A and r. [4 marks]

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

Chapter7: Production Economics

Section: Chapter Questions

Problem 7E

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