Suppose a firm can use either Capital (K) or Labor (L) in a production process. The firm’s production function is given...

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Question

Suppose a firm can use either Capital (K) or Labor (L) in a production process. The firm’s production function is given...

Suppose a firm can use either Capital (K) or Labor (L) in a production process. The

firm’s production function is given by Q = 5L + 15K. The price of Capital is $20 per unit and the price of

Labor is $8 per unit.

What is the Total cost function?

business economics

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Answer 1

Answer #1

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the production function is the form of perfect substitutes so the firm only uses the input with the higher marginal product per dollar

MP per dollar =marginal product /price of input

MPL=dQ/dL=5

MP per dollar of labor =5/8=0.625

MPK=dQ/dK=15

MPK per dollar =15/20=0.75

the firm hires only labor

so production funtion is

Q=5L+15*0=Q=5L

Q=5L

then

L=Q/5

TC=wL

=8L

=8*(Q/5)

=1.6Q

so the total cost function is

TC(Q)=1.6Q

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Answer 2

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