CHAPTER #3 EXERCISES
3. If Jane is currently willing to trade 4 movie tickets for 1 basketball ticket then she must like
basketball better than movies. True or false? Explain.
This statement is not necessarily true. If she is always willing to trade 4 movie tickets for 1
basketball ticket then yes she likes basketball better because she will always gain the same
satisfaction from 4 movie tickets as she does from 1 basketball ticket. However, it could be that she
has convex preferences (diminishing marginal rate of substitution) and is at a bundle where she has
a lot of movie tickets relative to basketball tickets. This would make her willing to give up more
movie tickets to get another basketball ticket. It would not mean though that she liked basketball
better. Her willingness to give up a good would in this case depend on the quantity of each good in
her current basket.
4. Janelle and Brian each plan to spend $20,000 on the styling and gas mileage features of a new car.
They can each choose all styling, all gas mileage, or some combination of the two. Janelle does not care
at all about styling and wants the best gas mileage possible. Brian likes both equally and wants to
spend an equal amount on the two features. Using indifference curves and budget lines, illustrate the
choice that each person will make.
Assume styling is on the vertical axis and gas mileage is on the horizontal axis. Janelle has
indifference curves that are vertical. If the styling is there she will take it, but she otherwise does
not care about it. As her indifference curves move over to the right, she gains more gas mileage and
more satisfaction. She will spend all $20,000 on gas mileage. Brian has indifference curves that are
L-shaped. He will not spend more on one feature than on the other feature. He will spend $10,000
on styling and $10,000 on gas mileage.
5. Suppose that Bridget and Erin spend their income on two goods, food (F) and clothing (C). Bridget’s
preferences are represented by the utility function U(F,C)  10FC , while Erin’s preferences are
represented by the utility function
a.
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U(F,C)  .20F C .
On a graph, with food on the horizontal axis and clothing on the vertical axis, identify the set of
points that give Bridget the same level of utility as the bundle (10,5). Do the same for Erin on a
separate graph.
Bridget receives a utility of 10*10*5=500 from this bundle. The indifference curve is represented by
the equation 10FC=500 or FC=50. Some bundles on this indifference curve are (5,10), (10,5), (25,2),
and (2,25). Erin receives a utility of .2*10*10*5*5=500 from the bundle (10,5). Her indifference
2 2
curve is represented by the equation 500  .2F C , or 50=FC. This is the same indifference curve
as Bridget. Both indifference curves have the normal, convex shape.
b.
c.
On the same two graphs, identify the set of bundles that give Bridget and Erin the same level of
utility as the bundle (15,8).
For each person, plug in F=15 and C=8 into their respective utility functions. For Bridget, this gives
her a utility of 1200, so her indifference curve is given by the equation 10FC=1200, or FC=120. Some
bundles on this indifference curve are (12,10), (10,12), (3,40), and (40,3). For Erin, this bundle gives
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her a utility of 2880, so her indifference curve is given by the equation 2880  .2F C , or FC=120.
This is the same indifference curve as Bridget.
Do you think Bridget and Erin have the same preferences or different preferences? Explain.
They have the same preferences because for any given bundle they have the same level of utility.
This means that they will rank all bundles in the same order. Note however, that it is not necessary
that they receive the same level of utility to have the same set of preferences. All that is necessary is
that they rank the bundles in the same order.
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15. Jane receives utility from days spent traveling on vacation domestically (D) and days spent
traveling on vacation in a foreign country (F), as given by the utility function U(D,F)  10DF . In
addition, the price of a day spent traveling domestically is $100, the price of a day spent traveling in a
foreign country is $400, and Jane’s annual travel budget is $4,000.
a.
Illustrate the indifference curve associated with a utility of 800 and the indifference curve
associated with a utility of 1200.
The indifference curve with a utility of 800 has the equation 10DF=800, or DF=80. Choose
combinations of D and F whose product is 80 to find a few bundles. The indifference curve with a
utility of 1200 has the equation 10DF=1200, or DF=120. Choose combinations of D and F whose
product is 120 to find a few bundles.
b.
Graph Jane’s budget line on the same graph.
If Jane spends all of her budget on domestic travel she can afford 40 days. If she spends all of her
budget on foreign travel she can afford 10 days.
c.
Can Jane afford any of the bundles that give her a utility of 800? What about a utility of 1200?
Yes she can afford some of the bundles that give her a utility of 800 as part of this indifference curve
lies below the budget line. She cannot afford any of the bundles that give her a utility of 1200 as this
whole indifference curve lies above the budget line.
d.
Find Jane’s utility maximizing choice of days spent traveling domestically and days spent in a
foreign country.
The optimal bundle is where the slope of the indifference curve is equal to the slope of the budget
line, and Jane is spending her entire income. The slope of the budget line is

PD
1
 .
PF
4
The slope of the indifference curve is
MRS  
MUD
10F
F

 .
MU F
10D
D
Setting the two equal we get:

F 1

D 4
4F  D.
We now have two equations and two unknowns:
4F  D
100D  400F  4000.
Solving the above two equations gives D=20 and F=5. Utility is 1000.
This bundle is on an indifference curve between the two you had previously drawn.
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CHAPTER #4 QUESTIONS FOR REVIEW.
3. Explain whether the following statements are true or false.
a.
The marginal rate of substitution diminishes as an individual moves downward along the demand
curve.
This is true. The consumer will maximize his utility by choosing the bundle on his budget line where
the price ratio is equal to the MRS. Suppose the consumer chooses the quantity of goods 1 and 2 such
that
P1
 MRS. As the price of good 1 falls, the price ratio becomes a smaller number and hence the
P2
MRS becomes a smaller number. This means that as the price of good 1 falls, the consumer is willing
to give up fewer units of good 2 in exchange for another unit of good 1.
b.
The level of utility increases as an individual moves downward along the demand curve.
This is true. As the price of a good falls, the budget line pivots outwards and the consumer is able to
move to a higher indifference curve.
c.
Engel curves always slope upwards.
This is false. The Engel curve identifies the relationship between the quantity demanded of a good
and income, all else the same. If the good is inferior, then as income increases, quantity demanded
will decrease, and the Engel curve will slope downwards.
8. For which of the following goods is a price increase likely to lead to a substantial income (as well as
substitution) effect?
a.
salt
Small income effect, small substitution effect: The amount of income that is spent on salt is relatively
small, but since there are few substitutes for salt, consumers will not readily substitute away from it.
As the price of salt rises, real income will fall only slightly, thus leading to a small decline in
consumption.
b.
housing
Large income effect, no substitution effect: The amount of income spent on housing is relatively large for
most consumers. If the price of housing were to rise, real income would be reduced substantially,
thereby reducing the consumption of all other goods. However, consumers would find it impossible to
substitute for housing, in general.
c.
theater tickets
Small income effect, large substitution effect: The amount of income that is spent on theater tickets is
relatively small, but consumers can substitute away from the theater tickets by choosing other forms of
entertainment (e.g., television and movies). As the price of theater tickets rises, real income will fall
only slightly, but the substitution effect can be large enough to reduce consumption by a large amount.
d.
food
Large income effect, no substitution effect: As with housing, the amount of income spent on food is
relatively large for most consumers. Price increases for food will reduce real income substantially,
thereby reducing the consumption of all other commodities. Although consumers can substitute out of
particular foods, they cannot substitute out of food in general.
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