Chapter 13, Problem 4PA

Subpart (a):

To determine

Calculate marginal product.

Explanation of Solution

Table -1 shows the data of hours spent for fishing and the quantity of fish caught.

Table -1

Workers	Output	Marginal product	Total cost	Average total cost	Marginal cost
0	0
1	20
2	50
3	90
4	120
5	140
6	150
7	155

Marginal product can be calculated by using the following formula:

$\text{Marginal product}=\left(\frac{{\text{Output}}_{\text{Present}}-{\text{Output}}_{\text{Previous}}}{{\text{Labor}}_{\text{Present}}-{\text{Labor}}_{\text{Previous}}}\right)$ (1)

Substitute the respective values in equation (1) to calculate the marginal product for 1 worker.

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

Thus, the value of marginal product for 1 hour is $20.

Table - 2 shows the value of marginal product that is obtained by using equation (1), above.

Table - 2

Workers	Output	Marginal product
0	0	-
1	20	20
2	50	30
3	90	40
4	120	30
5	140	20
6	150	10
7	155	5

Economics Concept Introduction

Concept introduction:

Marginal product: Marginal product refers to an additional product in the total product due to a change in one unit of labor.

Subpart (b):

To determine

Calculate Total cost.

Explanation of Solution

Total cost can be calculated by using the following formula:

$\text{Total cost}=\text{Fixed cost}+\left(\text{Variable cost}\times \text{Number of labor}\right)$ (2)

Substitute the respective values in equation (2) to calculate the total cost for 0 workers.

$\begin{array}{c}\text{Total cost}=\text{200}+\left(100\times 0\right)\\ =200\end{array}$

Thus, the value of total cost for 1 worker is $200

Table - 3 shows the value of total cost that can be obtained by using equation (2).

Table - 3

Workers	Output	Marginal product	Total cost
0	0	-	200
1	20	20	300
2	50	30	400
3	90	40	500
4	120	30	600
5	140	20	700
6	150	10	800
7	155	5	900

Economics Concept Introduction

Concept introduction:

Total cost: Total cost refers to the total expenses obtained in reaching a particular level of goods and services.

Subpart (c):

To determine

Calculate average total cost.

Explanation of Solution

Average total cost can be calculated by using the following formula:

$\text{Average total cost}=\left(\frac{\text{Total cost}}{\text{Quantity}}\right)$ (3)

Substitute the respective value in equation (3) to calculate the average total cost for quantity 1:

$\begin{array}{c}\text{Average total cost}=\left(\frac{300}{20}\right)\\ =15\end{array}$

Thus, the average total cost for quantity 1 is $15

Table - 4 shows the value of average total cost that is obtained by using equation (3).

Table - 4

Workers	Output	Marginal product	Total cost	Average total  cost	Marginal cost
0	0	-	200	-
1	20	20	300	15
2	50	30	400	8
3	90	40	500	5.56
4	120	30	600	5
5	140	20	700	5
6	150	10	800	5.33
7	155	5	900	5.81

Economics Concept Introduction

Concept introduction:

Average total cost: Average total cost refers to the cost per unit. Initially, average total cost will decline as fixed costs are spread over a larger number of units. However, the curve will go up when the marginal cost increases.

Subpart (d):

To determine

Calculate marginal cost.

Explanation of Solution

Marginal cost can be calculated by using the following formula:

$\text{Marginal cost}=\left(\frac{{\text{Total cost}}_{\text{Present}}-{\text{Total cost}}_{\text{Previous}}}{{\text{Output}}_{\text{Present}}-{\text{Output}}_{\text{Previous}}}\right)$ (4)

Substitute the respective values in equation (1) to calculate the marginal cost of 1 quantity.

$\begin{array}{c}\text{Marginal cost}=\left(\frac{300-200}{\text{20}-0}\right)\\ =5\end{array}$

Thus, the value of marginal cost is $5

Table - 5 shows the value of marginal cost that obtained by using equation (4).

Table -5

Workers	Output	Marginal product	Total cost	Average total  cost	Marginal cost
0	0	-	200	-	-
1	20	20	300	15	5
2	50	30	400	8	3.33
3	90	40	500	5.56	2.5
4	120	30	600	5	3.33
5	140	20	700	5	5
6	150	10	800	5.33	10
7	155	5	900	5.81	20

Economics Concept Introduction

Concept introduction:

Marginal cost: The marginal cost refers to the amount of the additional cost incurred in the process of increasing one more unit of output.

Subpart (e):

To determine

Relationship between marginal product and marginal cost.

Explanation of Solution

From Table - 5, the relationship is when the marginal product is increasing, the marginal cost is decreasing, and vice versa.

Economics Concept Introduction

Concept introduction:

Marginal cost: The marginal cost refers to the amount of the additional cost incurred in the process of increasing one more unit of output.

Marginal product: Marginal product refers to an additional product in the total product due to a change in one unit of labor.

Subpart (f):

To determine

Relationship between average cost and marginal cost.

Explanation of Solution

When the marginal cost is greater than the average total cost, then the average cost will increase and the cost of the last unit of output produced pushes the average cost up. If the marginal cost is less than the average total cost, then the average total cost is decreasing and the cost of the last unit of output produced pulls the average cost down.

Economics Concept Introduction

Concept introduction:

Marginal cost: The marginal cost refers to the amount of the additional cost incurred in the process of increasing one more unit of output.

Average total cost: Average total cost refers to the cost per unit. Initially, average total cost will decline as fixed costs are spread over a larger number of units. However, the curve will go up when the marginal cost increases.