Chapter 15, Problem 1PA

Subpart (a):

To determine

Revenues, costs and profits.

Explanation of Solution

Table -1 shows the total quantity and respective price level.

Table -1

Price	Quantity
100	0
90	100,000
80	200,000
70	300,000
60	400,000
50	500,000
40	600,000
30	700,000
20	800,000
10	900,000
0	1,000,000

Total revenue can be calculated by using the following formula.

$\text{Total Revenue}=\text{Price }\times \text{ Quantity}$ (1)

Substitute the respective values in Equation (1) to calculate the total revenue at price $90.

$\begin{array}{c}\text{Total revenue}=\text{90}\times \text{100,000}\\ =\text{9,000,000}\end{array}$

Total revenue is $9,000,000.

Total cost can be calculated by using the following formula.

$\text{Total Cost}=\text{Cost }\times \text{ Quantity}$ (2)

Substitute the respective values in Equation (2) to calculate the total cost at quantity 100,000 units.

$\begin{array}{c}\text{Total Cost}=\text{2}\times \text{100,000}\\ =\text{2,000,000}\end{array}$

Total cost is $2,000,000.

Profit can be calculated by using the following formula.

$\text{Profit}=\text{Total revenue}-\text{Total cost}$ (3)

Substitute the respective values in Equation (3) to calculate the profit for the quantity 100,000 units.

$\begin{array}{c}\text{ Profit}=\text{9,000,000}-\text{2,000,000}\\ =\text{7,000,000}\end{array}$

Profit is 7,000,000.

Table -2 shows the total revenue, total cost and profit that are obtained by using Equations (1), (2) and (3).

Table -2

Price	Quantity	Total revenue	Total cost	Profit
100	0	0	2,000,000	-2,000,000
90	100,000	9,000,000	3,000,000	6,000,000
80	200,000	16,000,000	4,000,000	12,000,000
70	300,000	21,000,000	5,000,000	16,000,000
60	400,000	24,000,000	6,000,000	18,000,000
50	500,000	25,000,000	7,000,000	18,000,000
40	600,000	24,000,000	8,000,000	16,000,000
30	700,000	21,000,000	9,000,000	12,000,000
20	800,000	16,000,000	10,000,000	6,000,000
10	900,000	9,000,000	11,000,000	-2,000,000
0	1,000,000	0	12,000,000	-12,000,000

The maximum profit of $18 million is obtained at a quantity of 500,000 at a price of $50. Thus, the equilibrium price is $560.

Economics Concept Introduction

Concept introduction:

Profit: Profit refers to the excess revenue after subtracting the total cost from the total revenue.

Total revenue: Total revenue refers to the revenue of a firm through its total sale of goods.

Total cost: Total cost refers to the cost of all the inputs used by the firm. It includes both the fixed cost and the variable costs.

Subpart (b):

To determine

Calculate marginal revenue.

Explanation of Solution

Marginal revenue can be calculated as follows:

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

Substitute the respective values in equation (4) to calculate the marginal revenue at price level $60.

$\begin{array}{c}\text{Marginal revenue}=\frac{\text{24,000,000 - 21,000,000}}{400,000-300,000}\\ =\text{30}\end{array}$

Marginal revenue is $30.

Table -3 shows the marginal revenue that obtained by using equation (4).

Table -3

Price	Quantity	Total revenue	Marginal revenue
100	0	0	-
90	100,000	9,000,000	$90
80	200,000	16,000,000	70
70	300,000	21,000,000	50
60	400,000	24,000,000	30
50	500,000	25,000,000	10
40	600,000	24,000,000	-10
30	700,000	21,000,000	-30
20	800,000	16,000,000	-50
10	900,000	9,000,000	-70
0	1,000,000	0	-90

From table 4, it can be inferred that Marginal Revenue is less than price. Since the demand curve slopes downwards, Price declines when quantity rises. The marginal revenue declines even more than price because the firm loses revenue on all the units of the good sold when it lowers the price.

Economics Concept Introduction

Concept introduction:

Marginal revenue: Marginal revenue refers to the amount of extra revenue attained in the process of increasing one more unit of output.

Subpart (c):

To determine

Profit maximization.

Explanation of Solution

Figure 1illustrates the deadweight loss.

Figure 1 represents the marginal-revenue, marginal-cost, and demand curves. The horizontal axis represents the quantity and the vertical axis the prices, revenues and costs. The MR and MC curves cross between quantities of 400,000 and 500,000 which signify that the firm is maximizing profit in that region.

Economics Concept Introduction

Concept introduction:

Marginal product of labor (MPL): Marginal product of labor refers to the additional output produced due to employing one more unit of labor.

Marginal product of capital (MPC): Marginal product of capital refers to the additional output produced due to employing one more unit of capital.

Profit maximization: A firm can maximize its profit at the point where its marginal revenue is equal to marginal cost.

Subpart (d):

To determine

Deadweight loss.

Explanation of Solution

The deadweight loss is depicted by area DWL in figure 1. Deadweight loss is greater in monopoly as monopolist produces less than the socially efficient level of output. As a result the total surplus in the economy is less than it would be if the market were competitive.

Economics Concept Introduction

Concept introduction:

Deadweight loss: Deadweight loss refers to loss of total economic benefit that arises due to the inefficient allocation of resource.

Subpart (e):

To determine

Change in profit.

Explanation of Solution

The price would not change if the author were paid $3 million instead of $2 million, the publisher since there would be no change in marginal cost or marginal revenue. The result would be a fall in the firm’s profit.

Economics Concept Introduction

Concept introduction:

Profit: Profit refers to the excess revenue after subtracting the total cost from the total revenue.

Subpart (f):

To determine

Maximize economic efficiency.

Explanation of Solution

To maximize economic efficiency, the publisher would charge the price at $10 per book. This is because it is the marginal cost of the book. At price $10 per book, the publisher would receive negative profits equal to the amount paid to the author.

Economics Concept Introduction

Concept introduction:

Economic efficiency: Economic efficiency is the situation where the economy is efficient. Which means that the marginal benefit from the last unit produced is equal to the marginal cost of production and the economic surplus will be at maximum.