Microeconomics 7th Edition By R. Glenn Hubbard

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Sample Questions

It should be made clear, however, that food stamps may not increase expenditures
on food by low income families. The families could shift the income spent on food to
other goods or sell the food stamps. At point Oʹʹ, the familiesʹ MRS and price ratio are
not equal. We would expect families to take steps to reach equilibrium.
Diff: 2
Section: 3.3

106

114) Suppose that the price of gasoline has risen by 50%. What happens to a consumerʹs level of
well-being given he spends some of his income on gasoline? Diagram the impact of the
increase in gas prices in a commodity space diagram, and show the relevant indifference
curves.
Now, if the individualʹs income rises just enough so that his original consumption bundle
exactly exhausts his income, will the individual purchase more or less gasoline (this level of
income implies the consumer can afford his original consumption bundle)? Is the individual
better-off at the higher price level of gasoline with the higher income level or the original price
of gas and income?
Answer:

Initially, the consumer is on budget constraint BC 1 , consuming g1 units of gasoline on
indifference curve I1 , where M is the individualʹs income level and P 1 is the price of
gasoline. If only the price of gasoline changes to P 2 , the horizontal axis intercept of the
budget constraint moves towards the origin. This is illustrated above by a movement to
the budget constraint BC 2 . On indifference I 2 , his level of satisfaction is lower than
before.
Now, if the individualʹs income increases just enough so that his original consumption
bundle exactly exhausts his new budget. However, the slope of the budget constraint
(BC 3 ) that runs through his original consumption bundle is steeper due to the higher
price of gas. This also implies that his MRS is less than the ratio of prices. Thus, the
individual can attain a higher level of utility by purchasing less gasoline than g 1 . The
individual is better-off at higher prices and income than at original levels.
Diff: 2
Section: 3.3

107

115) Bobby is a college student who has $500 of income to spend each semester on books and
pizzas. The price of a pizza is $10 and the price of a book is $50. Diagram Bobbyʹs budget
constraint. Now, suppose Bobbyʹs parents buy him a $300 gift certificate each semester that
can only be used to buy books. Diagram Bobbyʹs budget constraint when he has the gift
certificate in addition to his $500 income. Is Bobby better-off with the gift certificates?
Answer:

Without the gift certificate, Bobbyʹs budget constraint is indicated by the line segment
from 10 books and 0 pizza to 0 books and 50 pizzas (labeled BC 1 ). With the gift
certificate that can only be used for book purchases, Bobby still cannot afford anymore
than 50 pizzas. However, he is guaranteed 6 books even if he spends all his money on
pizza. Since the price of books and pizza hasnʹt changed, the slope of his new budget
constraint is the same as the slope of the old budget constraint. The new budget
constraint is drawn above as BC 2 . Note that with the gift certificate, Bobby has an
expanded opportunity set and is guaranteed more of both goods no matter what his
original consumption choice on BC1 was. This implies that Bobby is strictly better-off
with the gift certificate.
Diff: 2
Section: 3.3

108

116) Larry lives with his parents and enjoys listening to jazz. Because of his living arrangements,
his only expense is on jazz music. To earn money to buy new albums, Larry must work. Larry
has 16 hours per day he could spend listening to jazz or working. Each hour he works he
earns $6. Each album costs him $12. Diagram Larryʹs budget constraint for new jazz albums
and time spent listening to jazz. If Larryʹs parents require him to spend two hours per day
doing chores around the house, what happens to his budget constraint? Does the requirement
to do chores make Larry worse off?
Answer: Larryʹs budget constraints are indicated on the following diagram. Before his parents
require him to do chores, his budget constraint is BC 1 . After the requirement to do
chores, his budget constraint becomes BC 2 . Since the requirement to do chores
contracts his opportunity set and we see he no longer may choose an optimal bundle on
BC1 , we know Larry is strictly worse off.

Diff: 2
Section: 3.3

109

117) Roberta lives alone on a deserted island. She can spend her time gathering coconuts or
bananas. She has 16 hours available each day and can gather 4 coconuts in an hour or 8
bananas in an hour. Diagram Robertaʹs budget constraint. Given that Robertaʹs Marginal
Utility of bananas is always 25 and her Marginal utility of coconuts is always 100, what is her
optimal consumption? One day an individual from a neighboring island arrives by boat and
offers to exchange any number of fruits at a rate of 1 coconut for 1 banana. Diagram Robertaʹs
budget constraint at this exchange rate assuming she will now spend all her time gathering
bananas. Is Roberta better off? What does she consume?
Answer: Robertaʹs initial budget constraint is BC 1 on the diagram below. Since Robertaʹs
indifference curves are always flatter than her budget constraint, Roberta will consume
all coconuts. Thus, she gathers and consumes 64 coconuts. When her neighbor arrives
and offers the exchange, her budget constraint becomes BC 2 . It is now optimal for her
to gather all bananas and exchange them 1 for 1 with her neighbor for coconuts. This
gives her 128 coconuts to consume. This brings her to the higher indifference curve I 2 .
Roberta is better off.

Diff: 2
Section: 3.3

110

118) Tammy and Tadʹs father has given each of them a debit card and allows each of them to use
the card to spend $500 each month. Tammy and Tad use their $500 to buy only CDs and
gasoline. In February, the price of a CD was $10 and the price of gasoline was $1 per gallon.
At these prices, Tammy purchased 45 CDs and 50 gallons of gas. Ted consumed 20 CDs and
300 gallons of gas. For the month of March, Tammy and Tadʹs father lost the records
indicating who had which debit card. From the bank statement in March, their father learned
that the price of a CD was $12 and a gallon of gas cost $0.80. The first debit card was used to
purchase 235 gallons of gas and 26 CDs. The second debit card was used to purchase 265
gallons of gas and 24 CDs. Using revealed preference theory, identify which card Tammy
must possess.
Answer:

From the diagram, we see that point D is revealed preferred to point B. This implies
that Tad would not choose to consume at point B. Thus, we know that Tad must have
consumed at point C and has the second debit card. This means Tammy has the first
debit card.
Diff: 2
Section: 3.4

111

119) Jane lives in a dormitory that offers soft drinks and chips for sale in vending machines. Her
utility function is U = 3SC (where S is the number of soft drinks per week and C the number of
bags of chips per week), so her marginal utility of S is 3C and her marginal utility of C is 3S.
Soft drinks are priced at $0.50 each, chips $0.25 per bag.
a. Write an expression for Janeʹs marginal rate of substitution between soft drinks and chips.
b. Use the expression generated in part (a) to determine Janeʹs optimal mix of soft drinks and
chips.
c. If Jane has $5.00 per week to spend on chips and soft drinks, how many of each should
she purchase per week?
Answer: a.
MRS =

MUS
MUC

MRS =

3C C
=
3S
S

b.
The optimal market basket is where
PS
MRS =
PC
Requires =

C
.5
=
S .25

C
= 2, C = 2S
S
Jane should buy twice as many chips as soft drinks.
c.
Jane must satisfy her budget constraint as well as optimal mix.
Her budget constraint is:
I = PSS + PCC
where I = income
5.00 = .5S + .25C
But she must also satisfy C = 2S, the optimal mix. Substitute 2S for C into budget
constraint
5.00 = .5S + .25(2S)
5 = .5S + .5S
5=S
Buy 5 soft drinks.
Substitute into either expression to obtain C
C = 2S
C = 2(5)
C = 10
Jane should spend her $5.00 to buy 5 soft drinks and 10 bags of chips.
Diff: 2
Section: 3.5

112

120) An individual consumes products X and Y and spends $25 per time period. The prices of the
two goods are $3 per unit for X and $2 per unit for Y. The consumer in this case has a utility
function expressed as:
U(X,Y) = .5XY
MUX = .5Y
MUY = .5X.
a.
b.
c.

Express the budget equation mathematically.
Determine the values of X and Y that will maximize utility in the consumption of X and Y.
Determine the total utility that will be generated per unit of time for this individual.

Answer: a.
The budget line can be expressed as:
I = PXX + PYY
25 = 3X + 2Y
b.
In equilibrium, maximizing utility, the following relationship must hold:
MUX MUY
=
PY
PX
In equilibrium
(0.5 Y)/3 = (0.5 X)/2
2Y = 3X, Y = (3/2)X
Thus the amount of Y to consume is 3/2 of the amount of X that is consumed. On the
budget line
3
25 = 3X + 2( X)
2
25 = 3X + 3X = 6X
X = 4.17 units per time period.
3
Y = (4.17) = 6.25 units per time period.
2
c.
The total utility is
U(x,y) = 0.5(4.17)(6.25)
= 13.03 units of utility per time period.
Diff: 2
Section: 3.5

113

121) Janice Doe consumes two goods, X and Y. Janice has a utility function given by the expression:
U = 4X 0.5Y0.5.
2Y0.5
2X0.5
So, MUX =
and MUY =
. The current prices of X and Y are 25 and 50, respectively.
X0.5
Y0.5
Janice currently has an income of 750 per time period.
a. Write an expression for Janiceʹs budget constraint.
b. Calculate the optimal quantities of X and Y that Janice should choose, given her budget
constraint. Graph your answer.
c. Suppose that the government rations purchases of good X such that Janice is limited to 10
units of X per time period. Assuming that Janice chooses to spend her entire income, how
much Y will Janice consume? Construct a diagram that shows the impact of the limited
availability of X. Is Janice satisfying the usual conditions of consumer equilibrium while the
restriction is in effect?
d. Calculate the impact of the ration restriction on Janiceʹs utility.
Answer: a.
I = PxX + PyY
750 = 25X + 50Y
b.
Optimal Combination:
PX
MRS =
PY

MRS =

MUX 2
=
MUY 2

MRS =

Y
X

PX
PY

Y.5
X.5
X.5
Y.5

25 1
=
50 2

Equating MRS to

PX
PY

Y 1
1
= ,Y= X
X 2
2
Janice should buy 1/2 as much Y as X.
Recall
750 = 25X + 50Y
Substitute (1/2)X for Y
750 = 25 X + 50(1/2)X
750 = 25X + 25X
750 = 50X
X = 15
Y = (1/2)X
Y = (1/2)(15)
Y = 7.5
Janice should consume 7.5 units of Y and 15 units of X.
114

c.
750 = 25X + 50Y
X = 10
750 = 25(10) + 50Y
500 = 50Y
Y = 10
As indicated in the graph below, at Janiceʹs optimal bundle with the restriction,
MUX MUY
. This implies Janice should consume more X to increase utility.
>
PY
PX
However, the ration restriction prevents her from doing so. Given the restriction, this is
the best Janice can do.

d.
Janiceʹs utility without the restriction is: U(x = 15, y = 7.5) = 4(15)0.5(7.5)0.5 = 42.43.
Janiceʹs utility with the restriction is: U(x = 10, y = 10) = 4(10)0.5(10)0.5 = 40. The ration
115

restriction results in a utility loss of 2.43 utils for Janice.
Diff: 3
Section: 3.5

122) Define the marginal rate of substitution. Using this concept, explain why market basket A is
not utility maximizing while market basket B is utility maximizing.

Answer: The marginal rate of substitution is the magnitude of the slope of an indifference curve.
It is the maximum amount of one good (clothing) that a consumer is willing to give up to
get another unit of another good (food). In an indifference curve diagram, MRS
measures the subjective value of the good on the horizontal axis in terms of the good on
the vertical axis. In this example, if the slope of the indifference curve through A were,
say, 5, the consumer would be willing to exchange 1 unit of food for 5 units of clothing.

The slope of the budget line, on the other hand, measures the market value of the good
on the horizontal axis in terms of the good on the vertical axis. In this example, the
indifference curve through A is steeper than the budget line, so the consumerʹs value of
good is greater than the market price. He would be better off if he bought more food.
Diff: 2
Section: 3.5

116

123) The local mall has a make-your-own sundae shop. They charge customers 35 cents for each
fresh fruit topping and 25 cents for each processed topping. Barbara is going to make herself a
sundae. The total utility that she receives from each quantity of topping is given by the
following table:
Fresh Fruit Topping
# of Units Total Utility
1
10
2
18
3
24
4
28
5
30
6
28
7
24
8
18
9
10
10
-6

Processed Topping
# of Units
Total Utility
1
10
2
20
3
10
4
0
5
-10
6
-20
7
-30
8
-40
9
-50
10
-60

a. What is the marginal utility of the 6th fresh fruit topping?
b. Of the two toppings, which would Barbara purchase first? Explain.
c. If Barbara has $1.55 to spend on her sundae, how many fresh fruit toppings and processed
toppings will she purchase to maximize utility?
d. If money is no object, how many fresh fruit toppings and processed toppings will Barbara
purchase to maximize utility?
e. Which of the basic assumptions of preferences are violated by preferences shown in the
table above?
Answer: a.
The marginal utility of the 6th fresh fruit topping is -2 utils (28 utils – 30 utils).
b.
Barbara will purchase the topping that provides the largest marginal utility per dollar
spent. The marginal utility divided by price for the first unit of fresh fruit topping is
10/.35. The marginal utility divided by price for the first unit of processed topping is
10/.25. Thus the first topping purchased will be processed (because 10/.25 > 10/.35).
c.
Barbara will continue to purchase toppings, one at a time, until she spends $1.55, by
always selecting the topping that provides the largest marginal utility per dollar spent.
Barbara will purchase 2 processed toppings first, followed by 3 fresh fruit toppings.
d.
If money is no object, Barbara will purchase an additional unit of each topping as long
as the topping provides a positive marginal utility. In this case, 2 processed toppings
and 5 fresh fruit toppings.
e.
The preferences used in this problem violate the assumption that consumers always
prefer more of a good to less.
Diff: 2
Section: 3.5

117

124) If MUa/Pa is greater than MUb/Pb, and the consumer is consuming both goods, the consumer
is not maximizing utility. True or false. Explain.
Answer: True, when the consumer has maximized utility, the marginal utility per dollar spent on
each good purchased will be equal, and the consumer will be on her budget line. In this
case, the consumer should consume more a and less b.
Diff: 2
Section: 3.5

125) John consumes two goods, X and Y. The marginal utility of X and the marginal utility of Y
satisfy the following equations:
MUX = Y
MUY = X.
The price of X is $9, and the price of Y is $12.
a.
b.
c.

Write an expression for Johnʹs MRS.
What is the optimal mix between X and Y in Johnʹs market basket?
John is currently consuming 15 X and 10 Y per time period.
Is he consuming an optimal mix of X and Y?

Answer: a.
MRS =

MUX Y
=
MUY X

b.
Optimal mix of X and Y:
Px
MRS =
Py
9
Y
=
= .75
X 12
John should consume 0.75 times as much Y as X
c.
Johnʹs current mix is not optimal. He should consume 0.75 times as much Y as X,
rather than his current 0.67 Y for each X.
Diff: 2
Section: 3.5

118

126) Natasha derives utility from attending rock concerts (r) and from drinking colas (c) as follows:
U(c,r) = c.9r.1
The marginal utility of cola (MUc) and the marginal utility of rock concerts (MUr) are given as
follows:
MUc = .9c-.1r.1
MUr = .1c.9r-.9
a. If the price of cola (Pc) is $1 and the price of concert tickets (Pr) is $30 and Natashaʹs
income is $300, how many colas and tickets should Natasha buy to maximize utility?
b. Suppose that the promoters of rock concerts require each fan to buy 4 tickets or none at all.
Under this constraint and given the prices and income in (a), how many colas and tickets
should Natasha buy to maximize utility?
c. Is Natasha better off under the conditions in (a) or (b)? Explain your answer.
Answer: a.
To maximize utility, Natasha (1) must be on her budget line, and (2) the marginal rate of
substitution must equal the ratio of the prices of the goods. The marginal rate of
substitution is equal to the ratio of the marginal utilities of the goods. Thus:
c + 30r = 300
(1)
(2)
MUc/MUr = (.9c-.1r.1)/(.1c.9r-.9) = Pc/Pr = 1/30
Solving these equations simultaneously for c and r yields c = 270 and r = 1.
b.
Without the 4 ticket constraint, Natasha would prefer to buy just 1 ticket. If required to
buy 4 tickets, Natasha would maximize utility by either buying 4 tickets and consuming
180 colas, or by buying zero tickets and consuming 300 colas. The utility function may
be used to determine which is preferred. In this case, Natasha will buy zero tickets and
300 colas.
c.
Natasha prefers (a) because constraining the choice set never leaves one better off. At
best it has no effect. Otherwise, the addition of a constraint leaves one worse off.
Diff: 2
Section: 3.5

119

127) The following table presents Alfredʹs marginal utility for each good while exhausting his
income. Fill in the remaining column in the table. If the price of tuna is twice the price of
peanut butter, at what consumption bundle in the table is Alfred maximizing his level of
satisfaction? Which commodity bundle entails the largest level of tuna fish consumption?

Bundle

MU of peanut
butter

MU of tuna

A
B
C
D

0.25
0.31
0.42
0.66

2.41
1.50
0.84
0.33

Answer:
Bundle
A
B
C
D

MRS =

MUpb
MUt

Marginal Rate
of
Substitution

MRS =

0.10
0.21
0.5
2

MUt
MUpb

9.64
4.84
2
0.5

The optimal bundle occurs where MRS =

MUt
Pt
=
= 2. This implies that
MUpb Ppb

commodity bundle C is the optimal bundle. The bundle that has the highest level of
tuna fish consumption is bundle D as the marginal utility of tuna is the lowest.
(Alternatively, the student could have defined MRS with the two goods reversed. In
that case the optimal bundle occurs where
MRS = MUpb/MUt = Ppb/Pt = 1/2. In either case, the answer is the same.)
Diff: 2
Section: 3.5

120

128) The following table presents Maryʹs marginal utility for each of the four goods she consumes
to exhaust her income. The price of Good 1 is $1, the price of Good 2 is $2, the price of Good 3
is $3 and the price of Good 4 is $4. Indicate the consumption bundle in the table that
maximizes Maryʹs level of utility.

Answer: In equilibrium, we know that

MU1 MU2 MU3 MU4
. Since P2 = 2P1 , we know
=
=
=
P1
P2
P3
P4

we need a bundle such that MU2 = 2MU1 . This only occurs at bundle C. In fact, the
marginal utility per dollar across all goods are equivalent for bundle C. Bundle C is the
optimal choice.
Diff: 2
Section: 3.5

129) At commodity bundle A, which consists of only apples and oranges, Annetteʹs marginal utility
per dollar spent on apples is 10 and her marginal utility per dollar spent on oranges is 8.
Diagram a representative budget constraint and indifference curve that that passes through
bundle A given Annetteʹs budget is exhausted at bundle A. Is Annette maximizing utility?
Why or why not? If she is not, what could she do to increase her level of satisfaction?
Answer:

Annette should buy more apples and fewer oranges to increase her level of satisfaction.
Diff: 2
Section: 3.5

121

130) May enjoys spending her free time with her friends at the mall and solving problems from her
microeconomics text. She has 16 hours per week of free time. Diagram Mayʹs time constraint.
1 F 3/4
3 P 1/4
and MUP =
where F is her time spent with friends at the mall and
If MUF =
4 P
4 F
P is her time spent working problems, how much time should May spend at each activity?
Answer: The time constraint is 16 = F + P.
Since the price of each activity is equivalent, Mayʹs optimal choice will be to set
the marginal utilities of each activity to be equal. Doing so will allow us to solve
for time spent with friends as a function of time spent working problems.
1 F 3/4
3 P 1/4
MUF =
=
= MUP ⇒ F = 3P. From Mayʹs time constraint, we know
4 P
4 F
that 16 = F + P. Substituting the optimal choice of F as a function of P into the time
P=4
constraint gives us 16 = 4P ⇔
.
F = 12
Diff: 2
Section: 3.5

131) Suppose the table below lists the price and consumption levels of food and clothing during
1990 and 2000. Calculate a Laspeyres and Paasche index using 1990 as the base year.

Answer: The Laspeyres Index is calculated as follows:

LI =

F
C
P 2000 F1990 + P 2000 C1990
F
C
P 1990 F1990 + P 1990 C1990

(6.25)100 + (3.35)75
876.25
=
= 1.209.
(5)100 + (3)75
725

The Paasche Index is calculated as follows:

PI =

F
C
P 2000 F2000 + P 2000 C2000
F
C
P 1990 F2000 + P 1990 C2000

Diff: 2
Section: 3.6

122

(6.25)110 + (3.35)87
978.95
=
= 1.207.
(5)110 + (3)87
811

132) Suppose that a consumerʹs increase in nominal income from the base year exceeds the inflation
level given by a Laspeyres cost of living index for their level of purchases
F
C
P t Fb + P t Cb
F
C
P b Fb + P b Cb