PROBLEM SET 2
Problems for Chapter 5
1.
Complete the following table:
The elasticity
coefficient is (give
range):
If price rises, total
revenue will
(increase/decrease/
remain the same):
If price falls, total
revenue will
(increase/decrease/
remain the same):
If demand is:
Elastic
Inelastic
Unitarily Elastic
2.
The table below contains the points (combinations of price and quantity demanded) on a
demand curve. Complete the table by computing the total revenue at each point and the price
elasticity coefficients. Indicate under “Character of Demand” whether demand is elastic,
inelastic, or of unitarily elasticity between each price.
POINT
A
B
C
D
E
F
G
PRICE
$1.00
.90
.80
.70
.60
.50
.40
QUANTITY
DEMANDED
300
400
500
600
700
800
900
TOTAL
REVENUE
ELASTICITY
COEFFICIENT
---(Between A and B)
(Between B and C)
(Between C and D)
(Between D and E)
(Between E and F)
(Between F and G)
CHARACTER OF
DEMAND
----
2
3.
For the demand curve in each table below, calculate the total revenue at each point.
Under “Character of Demand,” indicate whether demand is elastic, inelastic, or of unitary
elasticity.
a.
QUANTITY
TOTAL
CHARACTER OF
POINT
PRICE DEMANDED
REVENUE
DEMAND
A
$10
4
---(Between A and B)
B
8
5
(Between B and C)
C
6
6 2/3
(Between C and D)
D
4
10
(Between D and E)
E
2
20
b.
POINT
A
B
C
D
E
PRICE
$10
8
6
4
2
QUANTITY
DEMANDED
10
15
20
25
30
TOTAL
REVENUE
CHARACTER OF
DEMAND
---(Between A and B)
(Between B and C)
(Between C and D)
(Between D and E)
4.
As a means of increasing sales of a slow-moving product line, “Walt’s Sport Shop”
offered a coupon worth $2 toward the purchase of Zebko fishing reels during the month of June.
During May, Walt’s sold 50 reels at an average price of $40. Due to the success of the coupon
promotion, June sales totaled 60 reels. Calculate the price elasticity coefficient for the Zebko
reels. Was demand elastic or inelastic? Explain.
5.
6.
a.
In March, the marketing department at Company X, a producer of hammers,
reported to management that the appeal of its brand name was so strong that it
could raise the price of a hammer and sales would not fall much. What kind of
elasticity of demand did the marketing department believe the hammers had?
b.
In April, management raised the price of a hammer by 20%. Revenues from
hammer sales fell during April and May. What kind of elasticity did the hammers
actually have?
a.
Suppose that the price elasticity of demand coefficient for good A is 2. If
producers raise the price of good A by 10%, by what percentage will the quantity
of good A sold fall?
Suppose that the price elasticity of demand coefficient for good B is 1. If
producers of good B lower the price by 30%, by what percentage will the quantity
of good B sold rise?
b.
3
7.
Suppose a consumer has the following utility functions for coffee and tea.
Coffee
Units
0
1
2
3
4
5
6
7
8
9
10
Total Utility
0
50
90
120
138
150
160
169
177
184
190
a.
b.
Tea
Marginal
Utility
--
Units
0
1
2
3
4
5
6
7
8
9
10
Total Utility
0
66
123
174
216
246
273
291
306
315
321
Marginal
Utility
--
Calculate the marginal utility for each successive unit of output for both goods.
Explain what utility theory tells us about the demand curve.
TEXTBOOK, p. 121 (colored page at end of chapter 5): #2, 3, 4, 6
Selected Answers
1.
YOU figure this out using the textbook and class notes!
2.
POINT
A
B
C
D
E
F
G
PRICE
$1.00
.90
.80
.70
.60
.50
.40
QUANTITY
DEMANDED
300
400
500
600
700
800
900
TOTAL
REVENUE
$300
360
400
420
420
400
360
ELASTICITY
COEFFICIENT
---(Between A and B) 2.7
(Between B and C) 1.9
(Between C and D) 1.4
(Between D and E) 1.0
(Between E and F) 0.7
(Between F and G) 0.5
CHARACTER OF
DEMAND
---Elastic
Elastic
Elastic
Unitary
Inelastic
Inelastic
4
3.
a.
POINT
A
B
C
D
E
3.
PRICE
$10
8
6
4
2
QUANTITY
DEMANDED
4
5
6 2/3
10
20
TOTAL
REVENUE
$40
40
40
40
40
CHARACTER OF
DEMAND
---Unitary
PRICE
$10
8
6
4
2
QUANTITY
DEMANDED
10
15
20
25
30
TOTAL
REVENUE
$100
120
120
100
60
CHARACTER OF
DEMAND
---Elastic
Unitary
Inelastic
Inelastic
b.
POINT
A
B
C
D
E
4.
E = 3.545, which implies a relatively elastic demand.
5.
a.
6.
a. Quantity will fall by 20% (or by .20).
7.
a.
inelastic.
Coffee
b.
elastic.
b. Quantity will rise by 30% (or by .30).
Tea
Marginal
Marginal
Total Utility
Utility
Units
Total Utility
Utility
0
-0
0
-50
1
66
50
66
90
2
123
40
57
120
3
174
30
51
138
4
216
18
42
150
5
246
12
30
160
6
273
10
27
169
7
291
9
18
177
8
306
8
15
184
9
315
7
9
190
10
321
6
6
b.
Diminishing marginal utility theoretically explains why the demand curve is
downward-sloping.
Units
0
1
2
3
4
5
6
7
8
9
10
5
Textbook, p. 121: #2
Using elasticity formula:
1.8/1 = (% chg. Q) / [(499-399)/(399+499)/2)]
Ignore absolute value.
% chg. P
1.8/1 = (% chg. Q) / .20
% chg. Q = 1.8 x .20 = .36 [x 100 = 36%]
Textbook, p. 121: #3
a.
Short-run (1-year) E = .4
.4/1 = 20%/(% chg. P)  % chg. P = 20%/.4 = 50%
Ignore absolute value.
b.
Long-run (3-year) E = .8  % chg. P = 25%
Textbook, p. 121: #4
a.
b.
c.
Assuming the price increases by $1 (price after tax is $5), % change P
= (5-4)/((4+5)/2) = 0.2222 (or 22.22%).
NOTE: price elasticity of demand (E) = % change Q/% change P (ignore absolute
value). For cigarettes, E = 0.4 (from table 5.1). Substitute % change P = 0.2222
in formula: (% change Q)/0.2222 = 0.4/1. Solve for % change Q = 0.0889 (or
8.89%).
In the long-run, the price elasticity for cigarettes may be 0.8  % change Q =
0.1778 (or 17.78%).
Textbook, p. 121: #6
a.
b.
c.
Price of cigarettes after 62 cent tax increase was $4.62
% increase in price = $.62/[($4.00 + $4.62)/2)] = .1439 [x 100 = 14.39%]
Assuming % chg. Q = .06 (see News, p. 99), E = .06/.1439 = 4.17%