Chapter 14, Problem 4PA

Subpart (a):

To determine

Profit maximization.

Explanation of Solution

Table – 1 represents the value of quantity, total cost, and total revenue.

Table – 1

Quantity	Total cost	Total revenue
0	8	0
1	9	8
2	10	16
3	11	24
4	13	32
5	19	40
6	27	48
7	37	56

The profit can be calculated by using the following formula:

$\text{Profit}=\text{Total revenue}-\text{Total cost}$ (1)

Substitute the respective value in equation (1) and calculate the profit.

$\begin{array}{c}\text{Profit}=\text{0}-\text{8}\\ =-8\end{array}$

The profit is –$8.

Table – 2 shows the value of the profit that is obtained, by using equation (1).

Table – 2

Quantity	Total cost	Total revenue	Profit
0	8	0	–8
1	9	8	–1
2	10	16	6
3	11	24	13
4	13	32	19
5	19	40	21
6	27	48	21
7	37	56	19

From the above table, the firm can maximize profit when they produce five or six units of output.

Economics Concept Introduction

Concept introduction:

Perfect competitive firm: Perfect competition refers to the market structure featuring more number of sellers and buyers in the market, where the firm can sell homogenous products.

Marginal Revenue (MR): Marginal revenue refers to the additional revenue earned due to increasing one more unit of output.

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

Profit maximization.

Explanation of Solution

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

$\text{Marginal revenue}=\frac{{\text{Revenue}}_{\text{Present}}-{\text{Revenue}}_{\text{Previous}}}{{\text{Quantity}}_{\text{Present}}-{\text{Quantity}}_{\text{Previous}}}$ (2)

Substitute the respective value in equation (2) and calculate marginal revenue.

$\begin{array}{c}\text{Marginal revenue}=\frac{\text{8}-\text{0}}{\text{1}-0}\\ =8\end{array}$

The marginal revenue is $8.

Table – 3 shows the value of the marginal revenue that obtained by using equation (2).

Table – 3

Quantity	Total cost	Total revenue	Marginal revenue	Profit
0	8	0	–	–8
1	9	8	8	–1
2	10	16	8	6
3	11	24	8	13
4	13	32	8	19
5	19	40	8	21
6	27	48	8	21
7	37	56	8	19

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

$\text{Marginal Cost}=\frac{{\text{Total cost}}_{\text{Present}}-{\text{Total cost}}_{\text{Previous}}}{{\text{Quantity}}_{\text{Present}}-{\text{Quantity}}_{\text{Previous}}}$ (3)

Substitute the respective value in equation (3) and calculate the marginal cost.

$\begin{array}{c}\text{Marginal cost}=\frac{\text{8}-\text{0}}{\text{1}-0}\\ =8\end{array}$

The marginal cost is $8.

Table – 4 shows the value of the marginal cost that is obtained by using equation (3).

Table – 4

Quantity	Total cost	Marginal cost	Total revenue	Marginal revenue	Profit
0	8	–	0	–	–8
1	9	1	8	8	–1
2	10	1	16	8	6
3	11	1	24	8	13
4	13	2	32	8	19
5	19	6	40	8	21
6	27	8	48	8	21
7	37	10	56	8	19

Figure – 1 shows the marginal revenue curve and marginal cost curve.

Figure – 1

From the above figure, the x axis shows the quantity of output and the y axis shows the price, that is, revenue and cost. From the above figure, the intersecting point shows the point the firm’s maximizing profit when they produce five or six units of output.

Economics Concept Introduction

Concept introduction:

Perfect competitive firm: Perfect competition refers to the market structure featuring more number of sellers and buyers in the market, where the firm can sell homogenous products.

Marginal Revenue (MR): Marginal revenue refers to the additional revenue earned due to increasing one more unit of output.

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

Profit in the long run.

Explanation of Solution

Since the marginal revenue is the same as each level of the quantity, the firm is in a competitive industry. The firm is earning an economic profit. Generally, firms in the long run earn a normal profit. Thus, the firm is not in the long run equilibrium.

Economics Concept Introduction

Concept introduction:

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