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. 9. 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.
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. 9. 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.
Microeconomics A Contemporary Intro
10th Edition
ISBN:9781285635101
Author:MCEACHERN
Publisher:MCEACHERN
Chapter7: Production And Cost In The Firm
Section: Chapter Questions
Problem 19PAE
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Can you please help solve question 9 a,b and c 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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