Please show all work with the prescribed letters Consider a firm using labor and

Question

Please show all work with the prescribed letters

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: Total cost (TC) ($) = wL + rK

TC ($) = 60L + 40K

Slope of isocost = - w/r = - $60/$40 = - 1.5

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

Currently,

MPL / w = 10 / 60 = 0.17

MPK / r = 5 / 40 = 0.125

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

(c) Firm will improve performance by employing less labor and more capital until the ratio of MP to factor prices equalize.

(d) When w = $80,

MPL / w = 10 / 80 = 0.125 = MPK / r

Therefore, the input mix is now optimal.

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