Chapter 13, Problem 12PA

Subpart (a):

To determine

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

Explanation of Solution

Table -1 shows the value of the average variable cost and the fixed cost is assumed as $16.

Table -1

Quantity	Average variable cost
1	1
2	2
3	3
4	4
5	5
6	6

The variable cost can be calculated by using the following formula:

$\text{Variable cost}=\text{Average variable cost}\times \text{Quantity}$ (1)

Substitute the respective values in Equation (1) to calculate the variable cost.

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

Thus, the variable cost is $1.

Table -2 shows the value of the variable cost obtained by using Equation (1).

Table -2

Quantity	Average variable cost	Variable cost
1	1	1
2	2	4
3	3	9
4	4	16
5	5	25
6	6	36

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

$\text{Total cost}=\text{Fixed cost}+\text{Variable cost}$ (2)

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

$\begin{array}{c}\text{Total cost }=\text{16}\times \text{1}\\ =\text{17}\end{array}$

Thus, the total cost is $17.

Table -3 shows the value of the total cost obtained by using Equation (2).

Table – 3

Quantity	Average variable cost	Variable cost	Total cost
1	1	1	17
2	2	4	20
3	3	9	25
4	4	16	32
5	5	25	41
6	6	36	52

The marginal cost can be calculated by using the following formula:

$\text{Marginal cost}=\frac{\text{Change in total cost}}{\text{Change in quantity}}$ (3)

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

$\begin{array}{c}\text{Marginal cost }=\frac{20-17}{2-1}\\ =3\end{array}$

Thus, the marginal cost is $3.

Table -4 shows the value of the marginal cost obtained by using Equation (3).

Table -4

Quantity	Average variable cost	Variable cost	Total cost	Marginal cost
1	1	1	17	–
2	2	4	20	3
3	3	9	25	5
4	4	16	32	7
5	5	25	41	9
6	6	36	52	11

The average total cost can be calculated by using the following formula:

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

Substitute the respective values in Equation (4) to calculate the average total cost.

$\begin{array}{c}\text{Average total cost}=\frac{\text{17}}{1}\\ =1\end{array}$

Thus, the average total cost is $17.

Table -5 shows the value of the average total cost obtained by using Equation (4).

Table -5

Quantity	Average variable cost	Variable cost	Total cost	Marginal cost	Average total cost
1	1	1	17	–	17
2	2	4	20	3	10
3	3	9	25	5	8.33
4	4	16	32	7	8
5	5	25	41	9	8.20
6	6	36	52	11	8.67

Economics Concept Introduction

Concept introduction:

Marginal cost: Marginal cost refers to the additional cost incurred from producing one more additional unit of output.

Average total cost: The average total cost is the total cost per unit of the output produced by a firm.

Average variable cost: Average variable cost refers to the variable cost per unit.

Average total cost: Average total cost refers to the total cost per unit.

Subpart (b):

To determine

Total supply in the market.

Explanation of Solution

Suppose the equilibrium price is $10, then the firm will produce 5 units of the output because the market price exceeds the marginal cost at 5^th unit. Since, there are 100 firms entering the market, the quantity supplied in the market is 500 units $\left(100\times 5\right)$.

Economics Concept Introduction

Concept introduction:

Supply: Supply refers to the total value of the goods and services that are available for the purchase at a particular price in a given period of time.

Subpart (c):

To determine

Long run profit.

Explanation of Solution

In the long-run, a firm can enter or exit the market. In this transition, when a firm enters the market, price will still fall at the minimum average total cost. Since the market price is $10, which is higher than the minimum of the average total cost of $8. So, the new firm’s entry will result in a decrease in the price level. When the price decreases, the quantity demand will increase. Also, the quantity of the supply decreases because the newly entered firm will continue to produce only when the price equals the average total cost. So, beyond that equilibrium state the firm will produce zero profit or losses.

Economics Concept Introduction

Concept introduction:

Long run: Thelong run refers to the time, which changes the production variable to adjust to the market situation.

Subpart (d):

To determine

Long run supply.

Explanation of Solution

Figure – 1 shows the long-run supply curve for the market.

From the above figure, the x-axis represents the quantity of output and the y-axis represents the price and cost.

Economics Concept Introduction

Concept introduction:

Supply: Supply refers to the total value of the goods and services that are available for the purchase at a particular price in a given period of time.