Chapter 10, Problem 1.3P

(a)

To determine

Complete the table.

Explanation of Solution

The marginal product is the additional output produced due to the employment of an additional unit of labor. The marginal product can be obtained using Equation 1 as given below:

$\text{Marginal product= }\frac{{\text{Total output}}_{\text{Present}}-{\text{Total output}}_{\text{Previous}}}{{\text{Units of labor}}_{\text{Present}}-{\text{Units of labor}}_{\text{Previous}}}$ (1)

Substitute the respective values in Equation (1) to calculate the marginal product.

$\begin{array}{c}\text{Marginal product}=\frac{20-0}{1-0}\\ =\frac{20}{1}\\ =20\end{array}$

The marginal product of first worker is 20.

Total revenue can be calculated using Equation (2) as follows:

$\text{Total revenue}=\text{Total output}\times \text{Price}$ (2)

Substitute the respective values in Equation (2) to calculate the total revenue.

$\begin{array}{c}\text{Total revenue}=\text{20}\times \text{12}\\ =240\end{array}$

The total revenue from one worker is $240.

When the price of the soccer ball is $12 per ball, the marginal revenue product can be calculated using Equation (3) as follows:

$\text{Marginal revenue product}=\text{Marginal product}\times \text{Price}$ (3)

Substitute the respective values in Equation (3) to calculate the marginal revenue product.

$\begin{array}{c}\text{Marginal revenue product}=20\times 12\\ =240\end{array}$

The marginal revenue product of first labor is $240.

Table 1 shows the values of marginal product, total revenue, and marginal revenue product, which are obtained using Equations (1), (2), and (3).

Table 1

Number of Workers	Number of Soccer Balls Produced Per Day	Marginal Product	Total Revenue	Marginal Revenue Product
0	0	—	$0	—
1	20	20	240	$240
2	50	30	600	360
3	90	40	1,080	480
4	140	50	1,680	600
5	180	40	2,160	480
6	210	30	2,520	360
7	238	28	2,856	336
8	256	18	3,072	216
9	270	14	3,240	168
10	280	10	3,360	120

Economics Concept Introduction

Marginal product: Marginal product is defined as the additional output produced by increasing the input factor by one unit.

Marginal revenue product: Marginal revenue product is defined as the additional revenue earned by a firm using one additional unit of an input.

Total revenue: Total revenue is defined as the total income earned from the sale of output produced.

(b)

To determine

Marginal revenue product.

Explanation of Solution

Substitute the respective values in Equation (2) to calculate the total revenue.

$\begin{array}{c}{\text{Total revenue}}_4=14\text{0}\times \text{12}\\ =1,680\end{array}$

The total revenue from four workers is $1,680.

Substitute the respective values in Equation (2) to calculate the total revenue.

$\begin{array}{c}{\text{Total revenue}}_5=18\text{0}\times \text{12}\\ =2,160\end{array}$

The total revenue from four workers is $2,160.

The marginal revenue product can be calculated using Equation (4) as follows:

$\text{Marginal revenue product}=\frac{{\text{Total revenue}}_{\text{Present}}-{\text{Total revenue}}_{\text{Previous}}}{{\text{Labor}}_{\text{Present}}-{\text{Labor}}_{\text{Previous}}}$ (4)

Substitute the respective values in Equation (4) to calculate the marginal revenue product.

$\begin{array}{c}\text{Marginal revenue product}=\frac{2,160-1,680}{5-4}\\ =480\end{array}$

The marginal revenue product of fifth worker is $480.

Calculation of marginal revenue product using marginal product.

Substitute the respective values in Equation (4) to calculate the marginal revenue product.

$\begin{array}{c}\text{Marginal revenue product}=40\times 12\\ =480\end{array}$

The marginal revenue product of fifth worker is $480.

Thus, it is verified that marginal revenue product can be calculated using both methods.

Economics Concept Introduction

Marginal product: Marginal product is defined as the additional output produced by increasing the input factor by one unit.

Marginal revenue product: Marginal revenue product is defined as the additional revenue earned by a firm using one additional unit of an input.

(c)

To determine

The numbers of workers to be hired.

Explanation of Solution

The firm should hire workers as long as the marginal revenue product of labor is greater than the wage rate. If the firm continues operation, at wage rate equal to $320, the firm should employ 7 workers. This is because the marginal revenue product of the 7th worker is $336, and when the 8th laborer is employed, the marginal revenue product of labor falls to $216.

Economics Concept Introduction

Marginal revenue product: Marginal revenue product is defined as the additional revenue earned by a firm using one additional unit of an input.

(d)

To determine

The numbers of workers to be hired.

Explanation of Solution

When the wage rate increases to $400, the number of workers to be hired reduces to 5. The marginal revenue product of the 5th laborer is $480, which is greater than the wage rate. When the 6th worker is employed, the marginal revenue product falls to $360, which is less than wage rate.

Economics Concept Introduction

Marginal revenue product: Marginal revenue product is defined as the additional revenue earned by a firm using one additional unit of an input.

(e)

To determine

The marginal product and marginal revenue product.

Explanation of Solution

When the firm uses new production technology, the marginal product of labor and the marginal revenue product of labor by 50 percent at each worker. When the wage rate is $400, the firm should hire seven workers. The marginal revenue product of the 7th worker is $504, which is higher than the wage rate.

Economics Concept Introduction

Marginal product: Marginal product is defined as the additional output produced by increasing the input factor by one unit.

Marginal revenue product: Marginal revenue product is defined as the additional revenue earned by a firm using one additional unit of an input.