CHAPTER FIVE
Answers to Self Test Questions
1.
See Table AK 9
Table AK 9
Quantity
1
2
3
4
5
6
7
8
2.
MU/Price
Total Utility (TU)
20
35
45
53
58
60
60
55
Apple
Beer
80
75
Marginal Utility (MU)
20
15
10
8
5
2
0
-5
Ice Cream
70
Hot Dog
50
A rational consumer would therefore buy an apple first.
3.
The order of purchasing would be (with MU per $ in brackets): 1st purchase, apple (18); 2nd, apple
(14); 3rd, apple (10); 4th, pear (9); 5th, pear (8); 6th, pear (7); 7th, apple or pear (6); 8th, pear or apple
(6); 9th pear (5). Total of 4 apples and 5 pears.
4.
To maximise total utility we allocate each dollar to the child who derives the greatest marginal utility
from it. The marginal utilities are:
Jan:
200, 180, 160, 140, 120, 100, 80, 60, 40, 20
Dean:
400, 100, 95, 90, 85, 80, 75, 70, 65, 60
Each dollar would be allocated to: 1st, Dean (400); 2nd, Jan (200); 3rd, Jan (180); 4th, Jan (160); 5th,
Jan (140); 6th, Jan (120); 7th, Jan or Dean (100); 8th, Dean or Jan (100); 9th, Dean (95); 10th, Dean
(90). The parents should allocate $6 to Jan and $4 to Dean. Combined total utility is 1 585.
5.
He would purchase 5 drinks and would receive a total of $12 consumer surplus, i.e. $6 (8 - 2) on the 1st
drink; $3 (5 - 2) on the 2nd drink; $2 (4 - 2) on the 3rd drink; $1 (3 - 2)) on the 4th drink; and 0 (2 - 2)
on the 5th drink. Alternatively, the total consumer surplus can be calculated as the total utility from 5
drinks (8 + 5 + 4 + 3 + 2) = $22 less the total costs of those 5 drinks (5 x $2) = $10.
6.
First you need to find the total sales revenue for each price level, as follows:
Table AK 10
Price
$20
18
16
14
12
10
8
6
4
2
Quantity
1
4
7
10
13
16
19
22
25
28
Seniors
TR
$20
72
112
140
156
160
152
132
100
56
Quantity
9
10
11
12
13
14
15
16
17
18
21
Others
TR
$180
180
176
168
156
140
120
96
68
36
Combined
TR
$200
252
288
308
312
300
282
228
168
92
A) Initially, as the price of a haircut drops, the total revenue from seniors increases, which means that the
demand is elastic over the price range of $20 down to $8. Over the whole range of prices for the other
customers, total revenue declines with price and, therefore, the demand is inelastic.
B) The price which maximises total sales revenue is $12, which generates a revenue of $312.
C) You would charge a price of $10 to seniors, giving a total sales revenue from this group of $160. You
would charge $18 (or $20) to you other customers for a total revenue of $180. In total, then, the sales
revenue would be $340.
Answers to Study Guide Questions
Are you Sure?
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
False: it means the difference between totals.
True.
True.
False: it is the increase in total utility which declines.
False: should purchase more of product A.
True.
False: it is the amount that they would be willing to pay.
True.
False: it is charging different prices for the same product.
True.
Choose the Best:
11. b
12. a
13. b
14. b
15. a
16. c
17. b
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
a
c
a
d
c
a
a
b
a
d
c
c
b
Simple Calculations
31.
Table AK 11
Quantity
1
2
3
4
5
MU
60
50
30
15
12
Quantity
6
7
8
9
10
22
MU
10
9
6
3
1
32.
Table AK 12
Quantity
1
2
3
4
5
33. a)
TU
38
64
86
104
118
Quantity
6
7
8
9
10
TU
128
136
141
144
146
40; 45; 35
b) cheesewhirls
34.
Table AK 13
Quantity
1
2
3
4
5
Marginal Consumer Surplus
$1.80
1.30
0.60
0.30
0.05
Total consumer surplus = $4.05
Problems
35. a)
11 slices.
b) 7 slices; consumer surplus = $10.50.
36. a)
4 ice creams and 2 cookies.
b) 5 ice creams and 5 cookies.
37. a)
7 hours working and 9 hours leisure.
b) 5 hours working and 5 hours leisure.
38. a)
P = $6, TR = $1170
b) $6 for teenagers (TR = $1080) and $3 for parents (TR = $240) for a total revenue of $1320.
Translations
The equation says that the marginal utility per dollar spent by this particular consumer on product A is greater
than the marginal utility per dollar spent on product B. This will lead to the consumer buying more A and less
B which will cause the marginal utility of A to fall, and the marginal utility of B to rise until the two terms are
in equality.
23
Key Problem
a)
Since marginal utility is the utility derived from the consumption of each additional unit, the total utility
is the accumulation of each unit’s marginal utility, i.e., it is a running total. This gives the figures shown
in Table AK 10.
Table AK 14
Number of
Hours
1
2
3
4
5
6
7
8
Windsurfing
Marginal
Total
Utility
Utility
85
85
80
165
65
230
60
290
55
345
40
385
30
415
5
420
Snorkelling
Marginal
Total
Utility
Utility
100
100
90
190
75
265
70
335
50
385
25
410
20
430
10
440
b) To find the best allocation, look at the marginal utility of each activity in turn. For instance, the 1st hour
of snorkelling gives greater utility than the 1st hour of windsurfing (100 compared to 85), so you would
choose snorkelling. Having spent an hour snorkelling, your choice is between a 2nd hour of snorkelling
or a 1st hour of windsurfing. Again, snorkelling is preferable giving 90 utils compared to 85 for
windsurfing. After two hours of snorkelling, you need to choose between a 3rd hour of snorkelling or,
again, your 1st hour of windsurfing. Now, windsurfing is preferable since it is worth 85 utils compared
to the 75 for the third hour of snorkelling. Continuing in a similar fashion will produce the following
results:
1st hour:
3rd hour:
5th hour:
snorkelling
windsurfing
snorkelling
2nd hour:
4th hour:
6th hour:
snorkelling
windsurfing
snorkelling
Therefore, you would spend 2 hours and $20 on windsurfing and 4 hours and $40 on snorkelling.
Glancing at the table shows that 2 hours of windsurfing produces 165 utils and 4 hours of windsurfing
gives 335 utils. The total therefore is 500 utils.
c)
The secret here is to not go back to the beginning. Since you have already worked out the first six hours
of activities, continue from that point and work out the 7th and 8th hours. You have already spent 2 hours
on windsurfing and 4 hours on snorkelling. The 7th hour’s purchase is therefore either a 3rd hour of
windsurfing or a 5th hour of snorkelling. The former is preferable since the marginal utility is 65
compared to the 50 for the 5th hour of snorkelling. Similarly, the 4th hour of windsurfing at 60 is better
than the 5th hour of snorkelling of 50. The full eight hours is therefore summarized as:
1st hour:
3rd hour:
5th hour:
7th hour:
snorkelling
windsurfing
snorkelling
windsurfing
2nd hour:
4th hour:
6th hour:
8th hour:
snorkelling
windsurfing
snorkelling
windsurfing
Therefore, you would spend 4 hours and $40 on windsurfing, and 4 hours and $40 on snorkelling.
Glancing at the table shows that 4 hours of windsurfing produces 290 utils and 4 hours of snorkelling
gives 335 utils. The total therefore is 625 utils.
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d) We are now dealing with two different prices for the activities, so in order to make them comparable we
must calculate the MU per dollar spent on each. To do this we divide the column of MUs by the price of
$10 for windsurfing and the column of MUs by the price of $15 for snorkelling. The result is as shown in
Table AK11.
Table AK 15
Windsurfing
Number Marginal Total
of Hours Utility
Utility
1
85
85
2
80
165
3
65
230
4
60
290
5
55
345
6
40
385
7
30
415
8
5
420
Snorkelling
MU per Marginal
Dollar Spent Utility
100
8.5
90
8.0
75
6.5
70
6.0
50
5.5
25
4.0
20
3.0
10
0.5
Total
Utility
100
190
265
335
385
410
430
440
MU per
Dollar Spent
6.67
6.0
5.0
4.67
3.33
1.67
1.33
0.67
We use the same method as we did before: compare utilities (this time MU per dollar), purchase by
purchase. Each of the first two hours of windsurfing gives greater MU per dollar than does the first hour
of snorkelling, but the first hour of snorkelling is better than the third hour of windsurfing, and so on. This
gives the following results.
1st hour:
3rd hour:
5th hour:
7th hour:
windsurfing
snorkelling
snorkelling or windsurfing
windsurfing
2nd hour:
4th hour:
6th hour:
windsurfing
windsurfing
windsurfing or snorkelling
Therefore, you would spend $50 (5 hours) on windsurfing and $30 (2 hours) on snorkelling. You could
not afford an 8th hour since you have now exhausted your budget of $80. Glancing at the table shows that
5 hours of snorkelling produces 345 utils and 2 hours of windsurfing gives 190 utils. The total therefore is
535 utils.
e)
The important point to remember is that a change in the price of a product (in this case, snorkelling)
causes a movement along its demand curve and a shift in the demand curve of a substitute product
(windsurfing). This is illustrated in Figure AK 16.
Figure AK 16
25
f)
Although money is no longer a constraint, you still have a scarce resource: time. Therefore, you must
allocate your time so as to maximize your total utility. The answer and the method are the same as in c).
This time the prices of each activity are the same and equal to zero. Since we ignore prices, we need only
compare MUs as we did in c). The answer then is that you would spend 4 hours on windsurfing, and 4
hours on snorkelling, and the total utility is therefore 625 utils.
More of the Same
a)
See Table AK 16
Table AK 16
# of
Hours
1
2
3
4
5
6
7
8
Fishing
Total
Utility
31
60
87
111
131
149
161
167
Marginal
Utility
31
29
27
24
20
18
12
6
# of
Hours
1
2
3
4
5
6
7
8
Tennis
Total
Utility
38
72
102
130
152
170
184
194
Marginal
Utility
38
34
30
28
22
18
14
10
b) 1 hour fishing (31 utils) and 3 hours tennis (102 utils). Total utility = 133 utils.
c)
2 hours fishing (60 utils) and 4 hours tennis (130 utils). Total utility = 190 utils.
d) 6 hours fishing (149 utils) and 3 hours tennis (102 utils). Total utility = 251 utils.
e)
See Figure AK 17.
Figure AK 17
26
APPENDIX TO CHAPTER FIVE
Answers to Study Guide Questions
Are You Sure
1.
2.
3.
4.
5.
False: it is a straight line.
True.
True.
False: lower levels of utility.
False: it is where total utility is maximum.
Choose the Best
6.
7.
8.
b
b
a
9.
10.
d
e
Problems
11. a)
See Figure AK 18
Figure AK 18
b) 6 apples and 6 bananas
c)
See Figure AK 18
d) 6 apples and 3 bananas
27
12. a)
See Figure AK 19
Figure AK 19 (Text Figure A 6 completed)
b) 4 A’s and 9 B’s
c)
See Figure AK 19
d) 4 A’s and 6 B’s
e)
See Figure AK 19
f)
Substitution effect: 2; income effect : 1.
28