Chapter 16, Problem 3P

To determine

The marginal revenue product per unit of labor.

Explanation of Solution

Option (a):

First person can produce 5 units. The price of the first unit is $50 which is decreased by $1 for each successive unit sold in the market. The marginal revenue product of the first worker can be calculated by using the equation as follows:

$\begin{array}{c}{\text{Marginal revenue product}}_{\text{First labor}}=\left(\begin{array}{l}{\text{Marginal revenue}}_{\text{1st unit}}+\\ {\text{Marginal revenue}}_{\text{2nd unit}}+\\ {\text{Marginal revenue}}_{\text{3rd unit}}+\\ {\text{Marginal revenue}}_{\text{4th unit}}+\\ {\text{Marginal revenue}}_{\text{5th unit}}\end{array}\right)\\ =50+49+48+47+46\\ =240\end{array}$

The marginal revenue of the first labor is $240.

The marginal revenue product of the second worker can be calculated by using the equation as follows:

$\begin{array}{c}{\text{Marginal revenue product}}_{\text{Second labor}}=\left(\begin{array}{l}{\text{Marginal revenue}}_{\text{6th unit}}+\\ {\text{Marginal revenue}}_{\text{7th unit}}+\\ {\text{Marginal revenue}}_{\text{8th unit}}+\\ {\text{Marginal revenue}}_{\text{9th unit}}\end{array}\right)\\ =45+44+43+42\\ =174\end{array}$

The marginal revenue of the second labor is $174 .

The marginal revenue product of the third worker can be calculated by using the equation as follows:

$\begin{array}{c}{\text{Marginal revenue product}}_{\text{Third labor}}=\left(\begin{array}{l}{\text{Marginal revenue}}_{\text{10th unit}}+\\ {\text{Marginal revenue}}_{\text{11th unit}}+\\ {\text{Marginal revenue}}_{\text{12th unit}}+\end{array}\right)\\ =41+40+39\\ =120\end{array}$

The marginal revenue of the third labor is $120.

The marginal revenue product of the fourth worker can be calculated by using the equation as follows:

$\begin{array}{c}{\text{Marginal revenue product}}_{\text{Forth labor}}=\left(\begin{array}{l}{\text{Marginal revenue}}_{\text{13th unit}}+\\ {\text{Marginal revenue}}_{\text{14th unit}}\end{array}\right)\\ =38+37\\ =75\end{array}$

The Marginal revenue product of the fourth labor is $75.

The marginal revenue product of the fifth worker can be calculated by using the equation as follows:

$\begin{array}{c}{\text{Marginal revenue product}}_{\text{Fifth labor}}=\left({\text{Marginal revenue}}_{\text{15th unit}}\right)\\ =36\end{array}$

Therefore, the marginal revenue of the fifth worker is $36.

Option (b):

The marginal revenue product of the regulated monopoly market:

The marginal product of the first labor can be calculated by using the equation as follows:

$\begin{array}{c}{\text{Marginal revenue product}}_{\text{1st labor}}=\text{Marginal product of labor }\times \text{Price}\\ =5\times 40\\ =200\end{array}$

Therefore, the marginal revenue product of the first labor is $200.

The marginal product of the 2nd labor can be calculated by using the equation as follows:

$\begin{array}{c}{\text{Marginal revenue product}}_{\text{2nd labor}}=\text{Marginal product of labor }\times \text{Price}\\ =4\times 40\\ =160\end{array}$

Therefore, the marginal revenue product of the second labor is $160.

The marginal product of the 3rd labor can be calculated by using the equation as follows:

$\begin{array}{c}{\text{Marginal revenue product}}_{\text{3rd labor}}=\text{Marginal product of labor }\times \text{Marginal revenue}\\ =3\times 40\\ =120\end{array}$

Therefore, the marginal revenue product of the 3rd labor is $120.

The marginal product of the 4th labor can be calculated by using the equation as follows:

$\begin{array}{c}{\text{Marginal revenue product}}_{\text{4th labor}}=\text{Marginal product of labor }\times \text{Price}\\ =2\times 40\\ =80\end{array}$

Therefore, the marginal revenue product of the 4th labor is $80.

The marginal product of the 5th labor can be calculated by using the equation as follows:

$\begin{array}{c}{\text{Marginal revenue product}}_{\text{5th labor}}=\text{Marginal product of labor }\times \text{Price}\\ =1\times 40\\ =40\end{array}$

Therefore, the marginal revenue product of the 5th labor is $40.

Option (c):

The profit maximizing firm would employ the labor at the point where the marginal revenue product is greater or equal to marginal resource cost.

When the wage level is $170, the unregulated firm would employ 2 units of labor; because, the marginal revenue product exceeds the marginal resource cost (wage) at 2 units of labor.

In the regulated market, the marginal revenue product exceeds 1 unit of labor. So, the firm would employ only one unit of labor. Thus, the unregulated firm would employ more than the regulated firm.

Option (d):

When the wage level is $77, the unregulated firm would employ 3 units of labor; because, the marginal revenue product exceeds the marginal resource cost (wage) at 3 units of labor.

In the regulated market, the marginal revenue product exceeds 4 unit of labor. So, the firm would employ 4 units of labor. Thus, the regulated firm would employ more than the unregulated firm.

Option (e):

The change in the demand for labor in the regulated and unregulated market changes due to the change in the resource price (Wage). Thus, the regulating monopoly output price does not increase its demand for resource.

Economics Concept Introduction

Concept introduction:

Marginal revenue product: The marginal revenue product is the additional revenue earned by the firm by using one more input to produce an additional output.