Consider a firm using labor and capital as its only inputs. The price of capital

Question

Consider a firm using labor and capital as its only inputs. The price of capital is $40 where the price of labor (wage) is $60. Using 500 units of labor and 500 units of capital the firm is producing 1200 units of output. At this mix of input, the firm's MPL is 10 while its MPK is 5.

a. Write the firm's isocost equation. What is the slope of the isocost?
b. Determine if the firm's mix of inputs is optimal. Explain.
c. If your answer to "b" is no, what should the firm do to improve its performance? Explain.
d. Now suppose as a result of a mandated increase in the minimum wage the wage increases to $80. What would be the implication of this change for this firm?

Explanation / Answer

(a) Isocost equation is:

Total cost (C) ($) = wL + rK

C = 60L + 40K

(b) Input mix is optimal when (MPL / w) = (MPK / r)

MPL / w = 10 / 60 = 0.17

MPK / r = 5 / 40 = 0.125

Since (MPL / w) > (MPK / r), input mix is not optimal.

(c) To achieve optimal input mix, firm will decrease the quantity of labor and increase the quantity of capital until the ratios are equalized.

(d) When w = $80,

MPL / w = 10 / 80 = 0.125

MPK / r = 5 / 40 = 0.125

Since (MPL / w) = (MPK / r), input mix is optimal after increase in minimum wage.

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