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 line is:

TC = wL + rK

TC = $60 x 500 + $40 x 500

TC = $30,000 + $ 20,000

TC = $50,000

So, Isocost line equation is:

$50,000 = 60L + 40K

Slope of isocost = - Price ratio = - w / r = - 60 / 40 = - 1.50

(b)

Input mix is optimal if,

(MPL / MPK) = (w / r)

Here,

(MPL / MPK) = 10 / 5 = 2

w / r = 60 / 40 = 1.5

Therefore this input mix is not optimal.

(c)

(MPL / w) = 10 / 60 = 0.17

(MPK / r) = 5 / 40 = 0.125

Since (MPL / w) > (MPK / r), firm would improve performance by reducing the amount of labor and/or increasing amount of capital until these ratios become the same.

(d)

If minimum wage rises to $80, firm's wage bill will increase. So the firm will try to use less labor and more capital to the extent capital can be substituted for labor.

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