Question

Suppose labour and capital are variable inputs. The wage rate is $20 per hour, the marginal product of labour is 30 units, the rental rate of capital is $100 per machine hour, and the marginal product of capital is 150 units. If the wage rate declines to $15 per hour, the firm employs more labour and the marginal product of labour declines to 20 units. Assuming the rental rate of capital remains the same, what is the marginal product of capital at the new optimal level of input usage?
Select one:
a. 100 units
b. 133 units
c. 150 units
d. We do not have enough information to answer this question.

Answer 1

Answer:

133 units ( B )

Explanation:

The marginal product of capital ( MPK )is the additional output caused by the additional/increment in the input capital. and it is calculated as by substituting it from this formula

= w / MPL = R / MPK therefore when you cross multiply equation 1 becomes

= w (MPK) = R ( MPL)

= MPK = R ( MPL ) / w

w = wage rate = $15 ( new wage rate )

R = rental rate of capital =$100 ( the same rental rate )

MPL = marginal product of labor = 20 ( new marginal product of labor )

MPK = marginal product of capital =  $100 ( 20 ) / $15

                                                         = $2000 / $15

                                                         = 133 units

Answer 2

Answer:

The correct answer is b. 133 units.

Explanation:

At the optimal level of input usage:

w / MPL = r / MPK where

w = wage rate

r = rental rate of capital

MPL = Marginal product of labor

MPK = Marginal product of capital

After the wage rate decline, we have the following values:

w = $15

r = $100

MPL = 20 units

MPK = ?

Substituting these values in the optimal condition:

$15 / 20 = $100 / MPK

MPK = $100 x 20 / $15

        = 133.33

Therefore, the marginal product of capital (MPK) at the new optimal level of input usage is 133 units which corresponds to option b.