Chapter 8, Problem 19CQ

(a)

To determine

The change in total product as the marginal product changes.

Explanation of Solution

Marginal product can be calculated using the following formula:

$\text{Marginal product}=\frac{{\text{Total product}}_{\text{present}}-{\text{Total product}}_{\text{previous}}}{{\text{Units of variable}}_{\text{present}}-{\text{Units of variable}}_{\text{previous}}}$        (1)

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

$\begin{array}{c}\text{Marginal product}=\frac{6-0}{1-0}\\ =\frac{6}{1}\\ =6\end{array}$

The marginal product for variable unit 1 is 6.

Average product can be calculated using the following formula:

$\text{Average product}=\frac{\text{Total product}}{\text{Variable input}}$        (2)

Substitute the respective values in Equation (2) to calculate the average product for variable unit

1.

$\begin{array}{c}\text{Average product}=\frac{6}{1}\\ =6\end{array}$

The average product for variable unit 1 is 6.

Total variable cost can be calculated using the following formula:

$\text{Total variable cost}=\text{Price of input}\times \text{variable input}$        (3)

Substitute the respective values in Equation (3) to calculate the total variable cost for variable unit 1.

$\begin{array}{c}\text{Total variable cost}=\text{1}\times \text{1}\\ =1\end{array}$

The total variable cost for variable unit 1 is 1.

Average variable cost can be calculated using the following formula:

$\text{Average variable cost}=\frac{\text{Total variable cost}}{\text{Units of variable inputs}}$        (4)

Substitute the respective values in Equation (4) to calculate the average variable cost for variable unit 1.

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

The average variable cost for variable unit 1 is 1.

Total cost can be calculated using the following formula:

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

Substitute the respective values in Equation (5) to calculate the total cost for variable unit 1.

$\begin{array}{c}\text{Total cost}=1+\text{2}\\ =3\end{array}$

The total cost for variable unit 1 is 3.

Average total cost can be calculated using the following equation:

$\text{Average total cost}=\frac{\text{Total cost}}{\text{Units of variable input}}$        (6)

Substitute the respective values in Equation (6) to calculate the average total cost for variable unit 1.

$\begin{array}{c}\text{Average total cost}=\frac{\text{3}}{\text{1}}\\ =3\end{array}$

The average total cost for variable unit 1 is 3.

Marginal cost can be calculated using the following formula:

$\text{Marginal cost}=\frac{\text{Change in total cost}}{\text{Change in units of labor }}$        (7)

Substitute the respective values in Equation (7) to calculate the marginal cost for variable unit 1.

$\begin{array}{c}\text{Marginal cost}=\frac{\text{1}}{\text{ 1 }}\\ =1\end{array}$

The marginal cost for variable unit 1 is 1.

Table-1

Units of variable input	Total product	Marginal product	Average product	Price of input	Total variable cost	Average Variable cost	Total Fixed cost	Total Cost	Average total cost	Marginal cost
0	0	0	0	1	0	0	2	2	0	0
1	6	6	6	1	1	1	2	3	3	1
2	15	9	7.5	1	2	1	2	4	2	1
3	27	12	9	1	3	1	2	5	1.66	1
4	37	10	9.25	1	4	1	2	6	1.5	1
5	45	8	9	1	5	1	2	7	1.4	1
6	50	5	8.33	1	6	1	2	8	1.33	1
7	52	2	7.4	1	7	1	2	9	1.28	1
8	50	-2	6.25	1	8	1	2	10	1.25	1

 The total product of a firm decreases as its marginal product falls to negative. It is clear from Table-1 that the total product decreases from 52 to 50 as the marginal product falls from 2 to -2.

Economics Concept Introduction

Total product: Total product refers to the total quantity of goods that is produced by a firm with available resources in a given period of time.

Marginal product: Marginal product refers to an addition to the total product, as a result of employing an additional unit of variable factor.

(b)

To determine

The relation between average product and marginal product.

Explanation of Solution

When the marginal product is greater than the average product, the average product increases. In Table-1, the average product increases up to the point where, the marginal product is greater than the average product, after that it starts to decline.

(c)

To determine

The position of average product, when the marginal product is less than the average product.

Explanation of Solution

When the marginal product is less than the average cost, the average cost begins to fall. In Table-1, a fall in marginal product from 10 to 8 leads to a corresponding fall in the average product from 9.25 to 9.

(d)

To determine

The point at which marginal product begins to decrease.

Explanation of Solution

When the average product reaches the maximum point, the marginal product begins to fall. It can be seen from Table 1, where the marginal product falls from 12 to 10 as the average product increases from 9 to 9.25.

(e)

To determine

The point at which the marginal cost begins to increase.

Explanation of Solution

In Table 1, the marginal cost is same for all units of variable inputs. This is because the input price is same for all units of production.

Economics Concept Introduction

Marginal cost: Marginal cost refers to an addition to the total cost by employing an extra unit of worker or producing an extra unit of product.

(f)

To determine

The relationship between marginal product and marginal cost.

Explanation of Solution

Marginal product refers to an addition to the total product by employing an extra unit of input or worker. The marginal cost also refers to an addition to the total cost by producing an extra unit of output. These marginal product and marginal costs are inversely related and this relationship works on the basis of the law of diminishing returns. Marginal product initially rises and reaches at the maximum and then begins to decrease. Correspondingly, the marginal cost initially declines then reaches to a minimum point and then begins to rise. The maximum point of marginal product is corresponding to the minimum point of marginal cost.

(g)

To determine

Change in the marginal cost as the total product declines.

Explanation of Solution

Usually, the marginal cost increases when the total product begins to fall. In Table 1, the marginal cost is same for all units of inputs, where the input price is same for all units of variable factor.

(h)

To determine

The relationship between average variable cost and marginal cost.

Explanation of Solution

Marginal cost and average variable cost equals at the minimum of average variable cost. After that the average variable cost begins to rise.

Economics Concept Introduction

Average variable cost: Average variable cost refers to the total cost as per unit of variable input.

(i)

To determine

At what level of output marginal cost and average variable cost will be equal.

Explanation of Solution

Table 1 shows that the marginal cost equals the average variable cost at all levels of output.

(j)

To determine

The relationship between average total cost and marginal cost.

Explanation of Solution

When, the average total cost equals the marginal costs, then the average total cost begins to rise. This is because the marginal cost equals the average cost when the average cost reaches at its minimum point.

Economics Concept Introduction

Average total cost: Average total cost refers to the total cost as per the unit of output produced.

(k)

To determine

At what level of output the marginal cost equals the average total cost.

Explanation of Solution

Marginal product does not equal the average total cost until employing 8 units of variable inputs.