CHAPTER 7
Utility Maximization
A. Short-Answer, Essays, and Problems
1. Describe the law of diminishing marginal utility. On what assumptions is this law based?
4. What is the difference between total utility and marginal utility?
5. Can marginal utility be negative? Briefly explain with an example.
6. Fill in the following table on the total and marginal utilities of a product A. Also answer the questions.
7. Fill in the following table on the total and marginal utilities of product A. Also answer the questions.
Units of
product A
Total utility
Marginal
utility
0
0
1
50
_____
2
80
_____
3
_____
20
4
_____
15
5
_____
10
6
130
_____
7
125
_____
8
_____
−15
Units of
product A
Total utility
Marginal
utility
0
0
1
20
_____
2
35
_____
3
_____
10
4
_____
5
5
_____
0
6
45
_____
7
35
_____
8
_____
−15
8. (Consider This) In 2015 the federal government began requiring restaurants print the number of calories for
9.Describe how marginal utility and demand are related.
10. Give a brief description of the law of diminishing marginal utility and use it to explain the downward slope
11. What are the four dimensions of the typical consumer’s situation?
13. What is consumer equilibrium? How is it achieved?
14. Explain the utility maximizing rule in terms of hot dogs and hamburgers purchased at a ballgame.
15. Why is it not sufficient to just compare the marginal utility of two goods when maximizing utility?
16. Assume that a consumer purchases a combination of products A and B. The MUa is 5 and the Pa is $5.
17. Assume that a consumer purchases a combination of products Y and Z. The MUy is 50 and the Py is $25.
18. Columns 1 through 3 in the table below show the marginal utility which a particular consumer would get
by purchasing various quantities of products A, B, and C.
Unit of
product
(1)
Marginal
utility, A
(2)
Marginal
utility, B
(3)
Marginal
utility, C
First
18
39
12
Second
16
36
10
Third
14
33
9
Fourth
12
30
8
Fifth
10
27
7
Sixth
8
24
5
Seventh
6
21
3
If the prices of A, B, and C are $2, $3, and $1, respectively, and the consumer has $26 to spend on these
three products, what combination of the three products should be purchased in order to maximize utility?
19. The table below shows the marginal utility a costumer would get by purchasing various quantities of A, B,
and C. The product prices for A, B, and C are $3, $2, and $1 respectively. The consumer has $20 to spend
on the three products.
Unit of
product
(1)
Marginal
utility, A
(2)
Marginal
utility, B
(3)
Marginal
utility, C
First
30
22
12
Second
27
20
10
Third
24
18
8
Fourth
21
16
6
Fifth
18
14
4
Sixth
15
12
2
20. A consumer finds only three products, X, Y, and Z, are for sale. The amount of utility which their
consumption will yield is shown in the table below. Assume that the prices of X, Y, and Z are $10, $2, and
$8, respectively, and that the consumer has an income of $74 to spend.
Product X
Product Z
Quantity
Utility
Marginal
Utility
per $
Quantity
Utility
Marginal
Utility
per $
Quantity
Utility
Marginal
Utility
per $
1
42
_____
1
14
_____
1
32
_____
2
82
_____
2
26
_____
2
60
_____
3
118
_____
3
36
_____
3
84
_____
4
148
_____
4
44
_____
4
100
_____
5
170
_____
5
50
_____
5
110
_____
6
182
_____
6
54
_____
6
116
_____
7
182
_____
7
56.4
_____
7
120
_____
21. A consumer has an income of $24 to spend each day. The only two goods the consumer is interested in
purchasing are goods A and B. The marginal-utility schedules for these two goods are shown in the table
below. The price of B does not change and is $2. The marginal utility per dollar from B is also shown in
the table. But the price of A varies as shown in the table. The marginal utility per dollar from A when the
price of A is $8 and $4 is shown in the following table.
Good A
Good B
Quantity
MU
MU/$8
MU/$4
MU
MU/$2
1
48
6
12
24
12
2
32
4
8
15
8
3
24
3
6
12
6
4
16
2
4
8
4
5
8
1
2
6
3
6
4
0.5
1
4
2
Complete the table below to show how much of A the consumer will buy each week at each of the two
possible prices of A. Also, show how much B will be demanded when the price of A changes.
Price of A
Quantity of A
demanded
Price of B
Quantity of B
demanded
$8.00
_____
$2.00
_____
4.00
_____
2.00
_____
22. Discuss the basic determinants for an individual’s demand for a specific good or service.
24. What are two related effects that combine to make a consumer able and willing to buy more of a specific
25. A student asserts in class that the income and substitution effects lead to a decrease in the consumption of a
26. Assume that a person only purchases two goods, food and clothing, and has a fixed budget constraint. Both
goods are normal goods. If the price of food decreases, what will happen to the consumption of clothing
based on the income effect?
27. In a typical month, a family buys six bags of candy bars as snacks when the price of a bag costs $4.00.
When the price of the candy bars falls to $3.00 a bag, the family buys seven bags of candy bars a month.
When the price of a bag of candy bars rises to $6.00, the family buys three bags a month. Answer these
28. How can the utility-maximizing rule be used to explain the substitution and income effect?
29. Discuss the cost of leisure time in industrially advanced countries relative to those in developing countries.
30. A vice president of a company argues that the president of the company should raise workers’ wages if the
president wants less absenteeism. The president says that wages probably should be cut so that the workers
31. Use marginal-utility analysis to explain why the growing popularity of iPad over laptop and desktop
32. Why would an ounce of gold be priced higher than an ounce of coffee beans, even though coffee is
33. Is the following quotation consistent with the theory of consumer behavior? “The yield on time spent
34. A person has a basic choice between eating meals at home and eating meals in a restaurant. The cost of the
food that is eaten at home is $10 per meal. The cost of a restaurant meal is $20. It takes two hours to eat a
meal at home (including preparation time and cleanup time). It takes one hour of time to eat a meal in a
restaurant. The marginal utilities of the home meal and the restaurant meal are the same. The person
values time at $12 per hour. What does the theory of consumer behavior suggest the rational consumer will
decide to do: eat at home or in a restaurant? Answer by first excluding the value of time from the decision.
35. How does the pricing of medical care in the United States affect the quantity consumed?
36. Explain why, in most cases, you would rather receive a gift of $25 cash over receiving a $25 sweater
37. Meaning well, your grandmother gives you a new wool sweater for your birthday that she knitted herself.
You, however, hate wearing wool. What is the utility problem that you face? What can you do to remedy
the problem?
38. (Last Word) Describe the relationship between raising the marginal cost of crime and the quantity of crime
39. (Last Word) Suppose Billy is determining whether he should steal a movie from Walmart. The cost of the
movie is $25 and the direct cost and the opportunity cost of stealing the movie is zero. There is a 15 percent
chance of getting caught, and caught, a fine of $250 will be charged.
(a) Will Billy steal the movie?
(b) Suppose Billy has a guilt cost of $10. Will Billy steal the movie?
40. (Last Word) Discuss the decision a criminal must make before deciding whether or not to steal.
B. Answers to Short-Answer, Essays, and Problems
1. Describe the law of diminishing marginal utility. On what assumptions is this law based?
The law of diminishing marginal utility means that as the consumer obtains more units of a given good or
service, the consumer receives increasing amounts of total utility or satisfaction. However, the more units
2. Use diminishing marginal utility to explain why millionaires often do not have many homes, even if they
can afford it.
3. Explain the three characteristics of utility.
4. What is the difference between total utility and marginal utility?
5. Can marginal utility be negative? Briefly explain with an example.
Yes. The consumption of an additional unit of a product may be unpleasant. Consider a person who likes
6. Fill in the following table on the total and marginal utilities of a certain product A. Use your results to
answer the following questions.
Units of
product A
Total utility
Marginal
utility
0
0
1
20
_____
2
35
_____
3
_____
10
4
_____
5
5
_____
0
6
45
_____
7
35
_____
8
_____
−15
(a) Graph both the total utility and marginal utility curves together on the same graph.
(b) Explain the shape of both of the curves.
(c) Identify the point where utility is maximized on both curves. Discuss the reasoning behind each value.
Units of
product A
Total
utility
Marginal
utility
0
0
1
20
20
2
35
15
3
45
10
4
50
5
5
50
0
6
45
−5
7
35
−10
8
20
−15
-20
-10
0
10
20
30
40
50
60
0 2 4 6 8 10
Units of Product A
Total Utility/ Marginal Utility
7. Fill in the following table on the total and marginal utilities of a certain product A. Use your results to
answer the following questions.
Units of
product A
Total utility
Marginal
utility
0
0
1
50
_____
2
80
_____
3
_____
20
4
_____
15
5
_____
10
6
130
_____
7
125
_____
8
_____
−15
(a) Graph both the total utility and marginal utility curves together on the same graph.
(b) Explain the shape of their curves.
(c) Identify the point where utility is maximized on both curves. Discuss the reasoning behind each value.
Units of
product A
Total utility
Marginal
utility
0
0
1
50
50
2
80
30
3
100
20
4
115
15
5
125
10
6
130
5
7
125
-5
8
110
−15
(a) See graph.
8. (Consider This) In 2015 the federal government began requiring restaurants print the number of calories for
each menu item. Discuss the desired outcome and the actual outcome that occurred.
9. Describe how marginal utility and demand are related.
10. Give a brief description of the law of diminishing marginal utility and use it to explain the downward slope
of the demand curve.
11. What are the four dimensions of the typical consumer’s situation?
12. Explain the utility maximizing rule for two products in words and using algebra.
Utility maximizing rule explains how a consumer decides to allocate his or her money income so that the
13. What is consumer equilibrium? How is it achieved?
14. Explain the utility maximizing rule in terms of hot dogs and hamburgers purchased at a ballgame.
15. Why is it not sufficient to just compare the marginal utility of two goods when maximizing utility?
16. Assume that a consumer purchases a combination of products A and B. The MUa is 5 and the Pa is $5.
The MUb is 6 and the Pb is $6. What should this consumer do to maximize utility?
17. Assume that a consumer purchases a combination of products Y and Z. The MUy is 50 and the Py is $25.
The MUz is 20 and the Pz is $5. What should this consumer do to maximize utility?
18. Columns 1 through 3 in the table below show the marginal utility which a particular consumer would get
by purchasing various quantities of products A, B, and C.
Unit of
product
(1)
Marginal
utility, A
(2)
Marginal
utility, B
(3)
Marginal
utility, C
First
18
39
12
Second
16
36
10
Third
14
33
9
Fourth
12
30
8
Fifth
10
27
7
Sixth
8
24
5
Seventh
6
21
3
If the prices of A, B, and C are $2, $3, and $1, respectively, and the consumer has $26 to spend on these
three products, what combination of the three products should be purchased in order to maximize utility?
19. The table below shows the marginal utility a costumer would get by purchasing various quantities of A, B,
and C. The product prices for A, B, and C are $3, $2, and $1 respectively. The consumer has $20 to spend
on the three products.
Unit of
product
(1)
Marginal
utility, A
(2)
Marginal
utility, B
(3)
Marginal
utility, C
First
30
22
12
Second
27
20
10
Third
24
18
8
Fourth
21
16
6
Fifth
18
14
4
Sixth
15
12
2
(a) 5 units of A, 6 units of B, and 4 units of C.
(b) 2 units of A, 5 units of B, and 4 units of C.
(c) 3 units of A, 4 units of B, and 3 units of C.
(d) 4 units of A, 3 units of B, and 2 units of C.
20. A consumer finds only three products, X, Y, and Z, are for sale. The amount of utility which their
consumption will yield is shown in the table below. Assume that the prices of X, Y, and Z are $10, $2, and
$8, respectively, and that the consumer has an income of $74 to spend.
Product X
Product Z
Quantity
Utility
Marginal
Utility
per $
Quantity
Utility
Marginal
Utility
per $
Quantity
Utility
Marginal
Utility
per $
1
42
_____
1
14
_____
1
32
_____
2
82
_____
2
26
_____
2
60
_____
3
118
_____
3
36
_____
3
84
_____
4
148
_____
4
44
_____
4
100
_____
5
170
_____
5
50
_____
5
110
_____
6
182
_____
6
54
_____
6
116
_____
7
182
_____
7
56.4
_____
7
120
_____
(a) Complete the table by computing the marginal utility per dollar for successive units of X, Y, and Z to
one or two decimal places.
(b) How many units of X, Y, and Z will the consumer buy when maximizing utility and spending all
income? Show this result using the utility maximization formula.
(c) Why would the consumer not be maximizing utility by purchasing 2 units of X, 4 units of Y, and 1 unit
of Z?
(a) See table.
Product X
Product Z
Quantity
Utility
Marginal
Utility
per $
Quantity
Utility
Marginal
Utility
per $
Quantity
Utility
Marginal
Utility
per $
1
42
4.2
1
14
7.0
1
32
4.00
2
82
4.0
2
26
6.0
2
60
3.50
3
118
3.6
3
36
5.0
3
84
3.00
4
148
3.0
4
44
4.0
4
100
2.00
5
170
2.2
5
50
3.0
5
110
1.25
6
182
1.2
6
54
2.0
6
116
.75
7
182
0.0
7
56.4
1.2
7
120
.50
(b) The consumer will purchase 4 units of X, 5 units of Y, and 3 units of Z to maximize utility. The
marginal utility per dollar for each of the products is equal to 3.0. Also, all income ($74) is spent on
the products ($40 for X, $10 for Y, and $24 for Z equals $74).
(c) Although the marginal utility per dollar spent is equal to 4.0 for X, Y, and Z, the consumer does not
spend all available income. There is $74 available but the consumer only spends $36. More goods
could be obtained by spending the income to maximize utility as shown in the answer to (b).
21. A consumer has an income of $24 to spend each day. The only two goods the consumer is interested in
purchasing are goods A and B. The marginal-utility schedules for these two goods are shown in the table
below. The price of B does not change and is $2. The marginal utility per dollar from B is also shown in
the table. But the price of A varies as shown in the table. The marginal utility per dollar from A when the
price of A is $8 and $4 is shown in the following table.
Good A
Good B
Quantity
MU
MU/$8
MU/$4
MU
MU/$2
1
48
6
12
24
12
2
32
4
8
15
8
3
24
3
6
12
6
4
16
2
4
8
4
5
8
1
2
6
3
6
4
0.5
1
4
2
Complete the table below to show how much of A the consumer will buy each week at each of the two
possible prices of A. Also, show how much B will be demanded when the price of A changes.
Price of A
Quantity of A
demanded
Price of B
Quantity of B
demanded
$8.00
_____
$2.00
_____
4.00
_____
2.00
_____
Price of A
Quantity of A
demanded
Price of B
Quantity of B
demanded
$8.00
2
$2.00
4
4.00
4
2.00
4
22. Discuss the basic determinants for an individual’s demand for a specific good or service.
23. Explain the income and substitution effects and use the concepts to describe what happens when the price
of a product decreases.