Chapter B, Problem 1E

a.

To determine

To evaluate the marginal revenue and Average revenue functions from the table given in the question.

Explanation of Solution

Average revenue is the revenue which is obtained by dividing total revenue by quantity.

Marginal revenue is the additional revenue which is obtained by selling an extra unit of the product.

Formula to find the Marginal revenue (MR) and Average revenue (AR)

  $\begin{array}{l}\text{MR=}\frac{\text{ΔTR}}{\text{ΔQ}}\text{=}\frac{{\text{TR}}_{\text{2}}{\text{-TR}}_{\text{1}}}{{\text{Q}}_{\text{2}}{\text{-Q}}_{\text{1}}}\\ \text{AR=}\frac{\text{TR}}{\text{Q}}\end{array}$

Output	Total Revenue (TR)	Marginal Revenue	Average Revenue
0	0	-	-
1	34	$\frac{T{R}_1-T{R}_o}{Q_1-Q_0}=\frac{34-0}{1-0}=34$	$\frac{TR}{Q}=\frac{34}{1}=34$
2	66	$\frac{T{R}_1-T{R}_o}{Q_1-Q_0}=\frac{66-34}{1-0}=32$	$\frac{TR}{Q}=\frac{66}{2}=33$
3	96	30	32
4	124	28	31
5	150	26	30
6	174	24	29
7	196	22	28
8	216	20	27
9	234	18	26
10	250	16	25
11	264	14	24
12	276	12	23
13	286	10	22
14	294	8	21
15	300	6	20
16	304	4	19
17	306	2	18
18	306	0	17
19	304	-2	16
20	300	-4	15

Economics Concept Introduction

Introduction: Average revenue is revenue produced per unit of product sold. It plays a part in deciding the income for a company. The average revenue is less than the average (total) expense per unit income. An organization typically aims to generate the amount of production that maximizes income.

b.

To determine

To evaluate the marginal cost and Average cost functions from the table given in the question.

Explanation of Solution

Formula to find the MC and AC are:

  $\begin{array}{l}\text{MC=}\frac{\text{ΔTC}}{\text{ΔQ}}\text{=}\frac{{\text{TC}}_{\text{2}}{\text{-TC}}_{\text{1}}}{{\text{Q}}_{\text{2}}{\text{-Q}}_{\text{1}}}\\ \text{AC=}\frac{\text{TC}}{\text{Q}}\end{array}$

Output	Total Cost (TC)	Marginal Cost	Average Revenue
0	20	-	-
1	26	$\frac{T{C}_1-T{C}_o}{Q_1-Q_0}=\frac{26-20}{1-0}=6$	$\frac{TC}{Q}=\frac{26}{1}=26$
2	34	$\frac{T{C}_1-T{C}_o}{Q_2-Q_1}=\frac{34-26}{2-1}=8$	$\frac{TC}{Q}=\frac{34}{2}=17$
3	44	10	14.7
4	56	12	14.0
5	70	14	14.0
6	86	16	14.3
7	104	18	14.9
8	124	20	15.5
9	146	22	16.2
10	170	24	17.0
11	196	26	17.8
12	224	28	18.7
13	254	30	19.5
14	286	32	20.4
15	320	34	21.3
16	356	36	22.3
17	394	38	23.2
18	434	40	24.1
19	476	42	25.1
20	520	44	26.0

Economics Concept Introduction

Introduction: The average cost method assigns a cost to inventory items based on the overall cost of the produced or manufactured goods over a period divided by the total number of products purchased or made. Often known as weighted-average method, is the average cost method.

c.

To determine

To evaluate the point where MR = MC and the output level in the graph that maximizes profits.

Explanation of Solution

In economics, profit maximization is the short-term or long-term mechanism by which a firm can decide the levels of price, input, and production that lead to the highest benefit.

The graph is shown below:

  

Marginal revenue equals to Marginal cost when Output (Q) = 8, where MC = MR =20

Economics Concept Introduction

Introduction: Marginal revenue is the rise in revenue arising from the selling of one extra output unit. Although marginal revenue may remain constant for a certain level of production, the law of diminishing returns follows and inevitably slows down as the level of production increases. Perfectly competitive firms continue to generate production until marginal revenue is equal to marginal costs.

d.

To determine

To evaluate the point where MR = MC and the output level in the graph that maximizes profits.s

Explanation of Solution

The average cost method assigns a cost to inventory items based on the overall cost of the produced or manufactured goods over a period divided by the total number of products purchased or made. Often known as weighted-average method, is the average cost method.

In economics, profit maximization is the short-term or long-term mechanism by which a firm can decide the levels of price, input, and production that lead to the highest benefit.

Referring from the tables in part (a) and part (b) and the solution at Q = 8, the table is given below:

Output	Marginal Cost	Marginal Revenue
8	20	20

Economics Concept Introduction

Introduction: Marginal revenue is the rise in revenue arising from the selling of one extra output unit. Although marginal revenue may remain constant for a certain level of production, the law of diminishing returns follows and inevitably slows down as the level of production increases. Perfectly competitive firms continue to generate production until marginal revenue is equal to marginal costs.