Chapter 13, Problem 4PA

Subpart (a):

To determine

The fixed cost, average variable cost, average total cost, and marginal cost, profit or loss of the firm if they shutdown, profit or loss of the firm if they continue to produce.

Explanation of Solution

The table – 1 represents the value of the cost of the production.

Table – 1

Quantity	Total fixed cost	Total variable cost
0	100	0
1	100	50
2	100	70
3	100	90
4	100	140
5	100	200
6	100	360

The average fixed cost can be determined by using the formula.

$\text{Average fixed cost}=\frac{\text{Total fixed cost}}{\text{Quantity}}$ (1)

Substitute the respective value in equation (1) to calculate the average fixed cost for 1^st unit.

$\begin{array}{c}\text{Average fixed cost}=\frac{\text{100}}{1}\\ =100\end{array}$

The average fixed cost is $100.

The table - 2 shows the value of the average fixed cost that is obtained by using the equation (1).

Table - 2

Quantity	Total fixed cost	Total variable cost	Average fixed cost
0	100	0	–
1	100	50	100
2	100	70	50
3	100	90	33.3
4	100	140	25
5	100	200	20
6	100	360	16.7

The average variable cost can be determined by using the formula.

$\text{Average variable cost}=\frac{\text{Total variable cost}}{\text{Quantity}}$ (2)

Substitute the respective value in equation (2) to calculate the average variable cost for 1^st unit.

$\begin{array}{c}\text{Average variable cost}=\frac{50}{1}\\ =50\end{array}$

The average variable cost is $50.

The table -3 shows the value of the average variable cost that is obtained by using the equation (2).

Table – 3

Quantity	Total fixed cost	Total variable cost	Average fixed cost	Average variable cost
0	100	0	–	–
1	100	50	100	50
2	100	70	50	35
3	100	90	33.3	30
4	100	140	25	35
5	100	200	20	40
6	100	360	16.7	60

The average total cost can be determined by using the following formula.

$\text{Average total cost}=\text{Average variable cost }+\text{Average fixed cost}$ (3)

Substitute the respective value in equation (3) to calculate the average total cost for 1^st unit.

$\begin{array}{c}\text{Average total cost}=100+50\\ =150\end{array}$

The average total cost is $150.

The table -4 shows the value of the average total cost thatis obtained by using the equation (3).

Table – 4

Quantity	Total fixed cost	Total variable cost	Average fixed cost	Average variable cost	Average total cost
0	100	0	–	–	–
1	100	50	100	50	150
2	100	70	50	35	85
3	100	90	33.3	30	63.3
4	100	140	25	35	60
5	100	200	20	40	60
6	100	360	16.7	60	76.7

The marginal cost can be determined by using the formula.

$\text{Marginal cost}=\frac{{\text{Variable cost}}_{\text{Present}}-{\text{Variable cost}}_{\text{Previous}}}{{\text{Quantity}}_{\text{Present}}-{\text{Quantity}}_{\text{Previous}}}$ (4)

Substituting the respective value into equation (4) and calculate the marginal cost for 1^st unit.

$\begin{array}{c}\text{Marginal cost}=\frac{\left(\text{70}-\text{50}\right)}{\text{1}-0}\\ =\frac{20}{1}\\ =20\end{array}$

The marginal cost is $20.

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

Table – 5

Quantity	Total fixed cost	Total variable cost	Average fixed cost	Average variable cost	Average total cost	Marginal cost
0	100	0	–	–	–	–
1	100	50	100	50	150	50
2	100	70	50	35	85	20
3	100	90	33.3	30	63.3	20
4	100	140	25	35	60	50
5	100	200	20	40	60	60
6	100	360	16.7	60	76.7	160

Economics Concept Introduction

Concept Introduction:

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

Average total cost: Initially average total cost will decline as fixed cost spreads over a larger number of units but the curve will go up when the marginal cost increases.

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

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

Subpart (b):

To determine

The fixed cost, average variable cost, average total cost, and marginal cost, profit or loss of the firm if they shutdown, profit or loss of the firm if they continue to produce.

Explanation of Solution

Suppose the price of the ball bearing $50, the firm can produce 4 unit of the output because the price is equal to marginal cost that is the profit maximizing condition. Then the total cost of the production is $240 $\left(\$100+\$140\right)$ and revenue can earn by the firm is $200 $\left(\$50\times 4\right)$, which means that the firm incurs loss of $40 $\left(\$240-\$200\right)$. So in the short run, the revenue is less than the variable cost and the firm has shut down its production. By shutting down, they suffer a loss which is equal to their fixed cost $100but in the short run firm continues to produce when the operating profit is used to balance the fixed cost and minimizes the losses, so the chief executive officer decision of shutdown is not wise.

Economics Concept Introduction

Concept Introduction:

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

Average total cost: Initially average total cost will decline as fixed cost spreads over a larger number of units but the curve will go up when the marginal cost increases.

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

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

Subpart (c):

To determine

The fixed cost, average variable cost, average total cost, and marginal cost, profit or loss of the firm if they shutdown, profit or loss of the firm if they continue to produce.

Explanation of Solution

Suppose CEO decides to produce 1 unit of ball, then the total cost of the firm is $150  $\left(\$100+\$50\right)$ and total revenue of the firm is $50 $\left(\$50\times 1\right)$ which means that firm incurs loss of $100 $\left(\$150-\$50\right)$. Since, the marginal cost of the next two outputs is lower than the price level and that is a benefit for the firm by reducing losses, so if they produce only one output, the decision is not the best one.

Economics Concept Introduction

Concept Introduction:

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

Average total cost: Initially average total cost will decline as fixed cost spreads over a larger number of units but the curve will go up when the marginal cost increases.

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

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