Chapter 15, Problem 3PA

Subpart (a):

To determine

Calculate total revenue and marginal revenue.

Explanation of Solution

Table – 1 shows the schedule of market demand for the CD.

Table – 1

Price	Quantity
24	10,000
22	20,000
20	30,000
18	40,000
16	50,000
14	60,000

Total revenue is calculated 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 quantity of 10,000 units.

$\begin{array}{c}\text{Total Revenue}=\text{Price}\times \text{Quantity}\\ \text{=24}\times \text{10,000}\\ \text{=240,000}\end{array}$

Thus, total revenue is $240,000.

Marginal Revenue is calculated using the following formula:

$\text{Marginal Revenue}=\frac{{\text{Total Revenue}}_{\text{current}}-{\text{Total Revenue}}_{\text{Previous}}}{{\text{Quantity}}_{\text{current}}-{\text{Quantity}}_{\text{previous}}}$ (2)

Substitute the respective values in Equation (2) to calculate the marginal revenue at the output level of 20,000 units.

$\begin{array}{c}\text{Marginal Revenue}=\frac{{\text{Total Revenue}}_{22}-{\text{Total Revenue}}_{24}}{{\text{Quantity}}_{22}-{\text{Quantity}}_{24}}\\ =\frac{440000-240000}{\begin{array}{l}20000\hfill \end{array}-10000}\\ =20\end{array}$

Thus, the marginal revenue is $20.

Table – 2 shows the calculation of Total Revenue and Marginal Revenue obtained by using Equations (1) and (2).

Table – 2

Price	Quantity	Total Revenue	Marginal Revenue
24	10,000	240,000	-
22	20,000	440,000	20
20	30,000	600,000	16
18	40,000	720,000	12
16	50,000	800,000	8
14	60,000	840,000	4

Economics Concept Introduction

Concept introduction:

Monopoly: Monopoly is a market situation where a single firm exists with a large number of buyers without any available substitute.

Total revenue: Total revenue is derived by multiplying the price with total quantity sold.

Marginal revenue: Marginal revenue is the additional revenue generated due to sale of one unit of output.

Subpart (b):

To determine

Total cost and marginal cost.

Explanation of Solution

Total cost is calculated using the following formula:

$\text{Total Cost}={\text{Cost}}_{\text{Per unit}}\times \text{Quantity}$ (3)

Substitute the respective values in Equation (3) to calculate the total cost at 10,000 units of output. Since, the firm has only variable cost, the cost is $5.

$\begin{array}{c}\text{Total Cost}={\text{Cost}}_{\text{Per unit}}\times \text{Quantity}\\ =\text{5}\times 10,000\\ =50,000\end{array}$

Total cost is $50,000.

Thus, the total cost is $50,000.

Marginal Cost is calculated using the following formula:

$\text{Marginal Cost}=\frac{{\text{Total Cost}}_{\text{current}}-{\text{Total Cost}}_{\text{Previous}}}{{\text{Quantity}}_{\text{current}}-{\text{Quantity}}_{\text{previous}}}$ (4)

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

$\begin{array}{c}\text{Marginal Cost}=\frac{{\text{Total Cost}}_{22}-{\text{Total Cost}}_{24}}{{\text{Quantity}}_{22}-{\text{Quantity}}_{24}}\\ =\frac{100000-50000}{\begin{array}{l}20000\hfill \end{array}-10000}\\ =20\end{array}$

Thus, the marginal cost is $20.

Profit is calculated using the following formula:

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

Substitute the respective values in Equation (4) to calculate the profit at 10,000 units.

$\begin{array}{c}\text{Profit}=\text{Total Revenue}-\text{Total cost}\\ =\text{240,000}-50,000\\ =190,000\end{array}$

Thus, the profit is $190,000.

Table -3 shows the Total Cost and Profit obtained by using Equations (3) and (4).

Table -3

Price	Quantity	Total Revenue	Marginal Revenue	Total Cost	Marginal Cost	Profit
24	10,000	240,000	-	50,000	-	190,000
22	20,000	440,000	20	100,000	5	340,000
20	30,000	600,000	16	150,000	5	450,000
18	40,000	720,000	12	200,000	5	520,000
16	50,000	800,000	8	250,000	5	550,000
14	60,000	840,000	4	300,000	5	540,000

A firm can achieve profit maximizing condition at the point where the marginal revenue equal to the marginal cost. Thus, from Table – 3, the quantity at which MC is closest to MR without exceeding it is 50,000 CDs at a price of $16, where the profit is $550,000.

Economics Concept Introduction

Concept introduction:

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.

Marginal cost: Marginal cost is the additional cost incurred due to sale of one unit of output.

Subpart (c):

To determine

Recommended quantity.

Explanation of Solution

As Johnny's agent, the fee recommends that he demand $550,000 because all the profit generated by the firm will be received by the agents. The firm would not change the output to produce 50,000 CDs because the payment of agent’s fees does not change the marginal cost.