9. A firm has the following production function, Q = Q(K, L) = K²+L², where Q is output, and K (capital) and L (labour) are inputs. The firm's costs are given by: C = wL + rK , where w is the price of labour and r is the price of capital. The price of the output is P. (a) Maximise the firm's profits and thus find the input demand functions. These will be expressed in terms of P, w, and r. (b) Ensure that the optimal point found in (a) is a maximum. (c) Express the optimal output in terms of P, w, and r. (d) Express the optimal profit in terms of P w, and r. (e) Take the derivative of the function found in (d) with respect to w. Comment on what you have found.
9. A firm has the following production function, Q = Q(K, L) = K²+L², where Q is output, and K (capital) and L (labour) are inputs. The firm's costs are given by: C = wL + rK , where w is the price of labour and r is the price of capital. The price of the output is P. (a) Maximise the firm's profits and thus find the input demand functions. These will be expressed in terms of P, w, and r. (b) Ensure that the optimal point found in (a) is a maximum. (c) Express the optimal output in terms of P, w, and r. (d) Express the optimal profit in terms of P w, and r. (e) Take the derivative of the function found in (d) with respect to w. Comment on what you have found.
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 5E
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Can you please help solve question 9 d and e please show full working so I can compare it to my own work
Thank you
Transcribed Image Text:9.
A firm has the following production function, Q = Q(K, L) = K²+L², where Q is
output, and K (capital) and L (labour) are inputs.
The firm's costs are given by: C = wL + rK , where w is the price of labour and r
is the price of capital. The price of the output is P.
(a)
Maximise the firm's profits and thus find the input demand functions. These will be
expressed in terms of P, w, and r.
(b)
Ensure that the optimal point found in (a) is a maximum.
(c)
Express the optimal output in terms of P, w, and r.
(d)
Express the optimal profit in terms of P w, and r.
(e)
Take the derivative of the function found in (d) with respect to w. Comment on what
you have found.
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