Chapter 7, Problem 20P

(a)

To determine

The marginal and average product of labor.

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 follows:

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

Substitute the respective values in Equation (1) to calculate the marginal product of employing the first worker, which can be calculated as follows:

$\begin{array}{c}\text{Marginal product}=\frac{5-0}{1-0}\\ =\frac{5}{1}\\ =5\end{array}$

The marginal product of the first worker is 5.

The average product of labor can be calculated using Equation (2) as follows:

$\text{Average product= }\frac{\text{Total output}}{\text{Units of labor}}$ (2)

Substitute the respective values in Equation (2) to calculate the average product of employing the first worker as follows:

$\begin{array}{c}\text{Average product= }\frac{\text{5}}{\text{1}}\\ =5\end{array}$

The average product of the first worker is 5.

Table 1 given below shows the value of marginal product and average product calculated using Equations (1) and (2).

Table 1

Quantity of labor	Quantity of output	Marginal product of labor	Average product of labor
1	5	5	5
2	12	7	6
3	20	8	6.67
4	28	8	7
5	34	6	6.8
6	39	5	6.5
7	43	4	6.14
8	46	3	5.75
9	48	2	5.33

The shape of the marginal product curve and the average product curve are peak shaped. After the production of 4 units of inputs, both the curves decline.

Economics Concept Introduction

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

(b)

To determine

The total cost of production.

Explanation of Solution

Given the fixed cost is $25, and the cost per unit of labor is $5.

The total cost can be calculated using Equation (3) as follows:

$\text{Total cost}=\text{Total fixed cost}+\left(\text{Cost of labor}\times \text{Quantity of labor}\right)$ (3)

Substituting the respective values in Equation (3), the total cost of producing one unit of output can be calculated as follows:

$\begin{array}{c}\text{Total cost}=\text{25}+\left(5\times 1\right)\\ =25+5\\ =30\end{array}$

The total cost of producing one unit is $30.

Table 2 given below shows the total cost of production for different levels of output calculated using Equation (3).

Table 2

Quantity of labor	Quantity of output	Total cost
1	5	30
2	12	35
3	20	40
4	28	45
5	34	50
6	39	55
7	43	60
8	46	65
9	48	70

Economics Concept Introduction

Total cost: Total cost is defined as the sum of variable cost and fixed cost.

(c)

To determine

The average total cost, average variable cost, and the marginal cost.

Explanation of Solution

The average total cost can be calculated using Equation (4) as follows:

$\text{Average total cost}=\frac{\text{Total cost}}{\text{Quantity of output}}$ (4)

Substituting the respective values in Equation (4), the average total cost can be calculated as follows:

$\begin{array}{c}\text{Average total cost}=\frac{\text{30}}{1}\\ =30\end{array}$

The average total cost of producing one unit of output is $30.

The variable cost can be calculated using Equation (5) as follows:

$\text{Total variable cost}=\text{Total cost}-\text{Total fixed cost}$ (5)

$\begin{array}{c}\text{Total variable cost}=30-25\\ =5\end{array}$

The total variable cost of producing one unit of output is $5.

The average variable cost can be calculated using Equation (6) as follows:

$\text{Average variable cost}=\frac{\text{Total variable cost}}{\text{Quantity of output}}$ (6)

Substituting the respective values in Equation (6), the average variable cost can be calculated as follows:

$\begin{array}{c}\text{Average variable cost}=\frac{\text{5}}{1}\\ =5\end{array}$

The average variable cost of producing one unit of output is $5.

The marginal cost of producing one unit of output can be calculated using Equation (7) as follows:

$\text{Marginal cost}={\text{Total variable cost}}_{\text{Present}}-{\text{Total variable cost}}_{\text{Previous}}$ (7)

Substituting the respective values in Equation (7), the marginal cost at the output level 1 unit can be calculated as follows:

$\begin{array}{c}\text{Marginal cost}=5-0\\ =5\end{array}$

Marginal cost at the output level 1 unit is $5.

Table 3 given below shows the value of average variable cost, average total cost, and marginal cost calculated using Equations 4, 5, 6, and 7.

Table 3

Quantity of input	Quantity of output	Total Fixed Cost	Total Cost	Total Variable Cost	Average Variable Cost	Average Total Cost	Marginal Cost
1	5	25	30	5	$1.000	$6.00	$1
2	12	25	35	10	$0.833	$2.92	0.71
3	20	25	40	15	$0.750	$2.00	0.63
4	28	25	45	20	$0.714	$1.61	0.63
5	34	25	50	25	$0.735	$1.47	0.83
6	39	25	55	30	$0.769	$1.41	1
7	43	25	60	35	$0.814	$1.40	1.25
8	46	25	65	40	$0.870	$1.41	1.67
9	48	25	70	45	$0.938	$1.46	2.5

The marginal cost of labor and the average variable cost of labor increase after the fourth unit of output.

Economics Concept Introduction

Total cost: Total cost is defined as the sum of fixed cost and variable cost.

Fixed cost: Fixed cost is defined as the cost that is independent of the level of output or production of a firm.

Variable cost: Variable cost is defined as the cost that depends on the level of production or output of a firm.

Marginal cost: Marginal cost is defined as the additional cost that is incurred due to the production of an extra unit of output.

Average total cost: Average total cost is defined as the total cost divided by the quantity of output.

Average variable cost: Average variable cost is defined as the total variable cost divided by the quantity of output.

(d)

To determine

The marginal product and the marginal cost.

Explanation of Solution

From the values in Table 1 and Table 3, it is obvious that the marginal product decreases after the fourth unit of output and the marginal cost increases after the fourth unit of output. Thus, there is an inverse relationship between the marginal product and the marginal cost.

Economics Concept Introduction

Marginal cost: Marginal cost is defined as the additional cost that is incurred due to the production of an extra unit of output.

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