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.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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