Chapter 8, Problem 3P

(a)

To determine

Complete the table.

Explanation of Solution

The variable cost is calculated as the sum of marginal cost up to a particular level of output using Equation (1) is as follows:

${\text{Total variable cost}}_{\text{n}}={\text{Marginal cost}}_1+{\text{Marginal cost}}_2+\mathrm{...}+{\text{Marginal cost}}_{\text{n}}$ (1)

Substitute the respective values in Equation (1) to calculate the variable cost of one unit of output.

$\begin{array}{c}{\text{Total variable cost}}_{\text{1}}={\text{Marginal cost}}_1\\ =30\end{array}$

The variable cost of one unit of output is 30.

The total cost  calculated using Equation (2) is as follows:

$\text{Total cost}=\text{Total fixed cost}+\text{Total variable cost}$ (2)

Substituting the respective values in Equation (2), the total cost of producing one unit of output can be calculated as follows:

$\begin{array}{c}\text{Total cost}=\text{15}+\text{30}\\ =45\end{array}$

The total cost of producing one unit is $45.

The total revenue calculated using Equation (3) is as follows:

$\text{Total revenue}=\text{Price}\times \text{Quantity}$ (3)

Substituting the respective values in Equation (3), the total revenue can be calculated as follows:

$\begin{array}{c}\text{Total revenue}=\text{50}\times \text{1}\\ =50\end{array}$

The total revenue of producing one unit of output is $50.

The profit is calculated as the difference between the total revenue and the total cost using Equation (4) is as follows:

$\text{Profit}=\text{Total revenue}-\text{Total cost}$ (4)

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

$\begin{array}{c}\text{Profit}=\text{50}-\text{30}\\ =20\end{array}$

The profit of producing the first unit of output is 20.

The marginal revenue of producing one unit of output calculated using Equation (5) is as follows:

$\text{Marginal revenue}={\text{Total revenue}}_{\text{Present}}-{\text{Total revenue}}_{\text{Previous}}$ (5)

Substituting the respective values in Equation (5) the marginal revenue at the output level 1 unit is calculated as follows:

$\begin{array}{c}\text{Marginal revenue}=\text{50}-\text{0}\\ =50\end{array}$

Marginal revenue at the output level 1 unit is $50.

Table 1 given below shows the value of total cost, average variable cost, average total cost and marginal cost calculated using Equation (1), (2), (3), (4) and (5).

Table 1

Level of output	Total Revenue	Total Fixed Cost	Total Variable Cost	Total Cost	Profit	Marginal Revenue	Marginal Cost
0	0	15	-	–	-15	-	–
1	50	15	30	45	5	50	30
2	100	15	65	80	20	50	35
3	150	15	107	122	28	50	42
4	200	15	157	172	28	50	50
5	250	15	217	222	28	50	60
6	300	15	289	304	-104	50	72

Economics Concept Introduction

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.

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

Total revenue: Total revenue is defined as the total income earned from the sale of output produced.

Profit: Profit is defined as the excess revenue earned over the total cost of production.

(b)

To determine

The quantity of output that maximizes revenue.

Explanation of Solution

The maximum revenue is obtained when the N produces 6 pounds of beeswax by earning $300.

Economics Concept Introduction

Total revenue: Total revenue is defined as the total income earned from the sale of output produced.

(c)

To determine

The quantity of output that maximizes profit.

Explanation of Solution

The maximum profit that can be produced is $28 and this profit is obtained when Nancy produces 4 pounds of beeswax.

Economics Concept Introduction

Profit: Profit is defined as the excess revenue earned over the total cost of production.

(d)

To determine

The profit maximization.

Explanation of Solution

When the profit is maximized, the marginal revenue of the firm is equal to the marginal cost of the product. The profit maximization occurs at the point when the additional revenue obtained from the selling of the last unit of output is equal to cover the additional cost of the last unit of product.

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 revenue: Marginal revenue is defined as the additional revenue earned by a firm due to the production of an extra unit of output.

(e)

To determine

Change in production and change in fixed cost.

Explanation of Solution

A change in the fixed cost changes the total cost and the variable cost remains unchanged. Since there is no change in the variable cost, the marginal cost also does not change. This implies that the profit maximizing quantity remains unchanged.

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 revenue: Marginal revenue is defined as the additional revenue earned by a firm due to the production of an extra unit of output.

(f)

To determine

Change in profit maximizing output.

Explanation of Solution

When the marginal cost at each unit increases by $8, the value of total revenue, fixed cost, variable cost, total cost, profit and marginal revenue can be calculated using Equation (1), (2), (3), (4) and (5) that shows in Table 2.

Table 2

Level of output	Total Revenue	Total Fixed Cost	Total Variable Cost	Total Cost	Profit	Marginal Revenue	Marginal Cost
0	0	15	0	15	-15	-	–
1	50	15	38	53	-3	50	38
2	100	15	81	96	4	50	43
3	150	15	131	146	4	50	50
4	200	15	189	204	-4	50	50
5	250	15	257	272	-22	50	68
6	300	15	337	352	-52	50	80

When the marginal cost increases by $8, the production decreases and the profit is maximized at $4 when the output produced is 3 pounds of beeswax.

Economics Concept Introduction

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.

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

Total revenue: Total revenue is defined as the total income earned from the sale of output produced.

Profit: Profit is defined as the excess revenue earned over the total cost of production.