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A firm produces output y using two factors of production (inputs), labour L and capital K. The firm's production function is f(L.K) ==In(L) +In(K). The wage rate w = 4 and the rental price of capital r = 4 are taken as parameters (fixed) by the firm. Solve the firm's long run cost minimization problem (minimize costs subject to the output constraint) to derive this firm's demand function for labour L= L(y) and for capital K = K(y), and the firm's long run total cost function C = C(y).

A firm produces output y using two factors of production (inputs), labour L and capital K. The firm's production function is f(L.K) ==In(L) +In(K). The wage rate w = 4 and the rental price of capital r = 4 are taken as parameters (fixed) by the firm. Solve the firm's long run cost minimization problem (minimize costs subject to the output constraint) to derive this firm's demand function for labour L= L(y) and for capital K = K(y), and the firm's long run total cost function C = C(y).

Microeconomic Theory
Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter10: Cost Functions
Section: Chapter Questions
Problem 10.3P
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A firm produces output y using two factors of production (inputs), labour Land capital K. The firm's production function is f(L. K) =In(L)+In(K). The wage rate w = 4 and the rental price of capital r=4 are taken as parameters (fixed) by the firm. Solve the firm's long run cost minimization problem (minimize costs subject to the output constraint) to derive this firm's demand function for labour L= L(y) and for capital K = K(y), and the firm's long run total cost function C = C(y).
Transcribed Image Text:A firm produces output y using two factors of production (inputs), labour Land capital K. The firm's production function is f(L. K) =In(L)+In(K). The wage rate w = 4 and the rental price of capital r=4 are taken as parameters (fixed) by the firm. Solve the firm's long run cost minimization problem (minimize costs subject to the output constraint) to derive this firm's demand function for labour L= L(y) and for capital K = K(y), and the firm's long run total cost function C = C(y).
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