Answers to Additional Problems and Applications
Use the following data to work Problems 12 to 15.
Marc has a budget of $20 a month to spend on root beer and DVDs. The price of
root beer is $5 a bottle, and the price of a DVD is $10.
12. What is the relative price of root beer in terms of DVDs and what is the
opportunity cost of a bottle of root beer?
The relative price of root beer is 1/2 DVD. The relative price of root beer is the price
of root beer divided by the price of a DVD. The price of root beer is $5 a bottle and
the price of a DVD is $10, so the relative price of root beer is $5 a bottle divided by
13. Calculate Marc’s real income in terms of root beer. Calculate his real income
in terms of DVDs.
Marc’s real income is 4 bottles of root beer. Marc’s real income in terms of bottles
of root beer is equal to his money income divided by the price of a bottle of root
beer. Marc’s money income is $20, and the price of root beer is $5 a bottle. Marc’s
14. Calculate the equation for Marc’s budget line (with the quantity of root beer
on the left side).
The equation that describes Marc’s budget line is QR = 4 – 2QDVD. Call the price of a
bottle of root beer PR and the quantity of root beer QR, the price of a DVD PDVD and
the quantity of DVDs QDVD, and income y. Marc’s budget equation is PRQR +
15. Draw a graph of Marc’s budget line
with the quantity of DVDs on the
x-axis. What is the slope of Marc’s
budget line? What determines its
value?
The budget line is illustrated in Figure
9.4. The slope of the budget line, when
DVDs are plotted on the x-axis is 2.
The magnitude of the slope is equal to
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Use the following data to work Problems 16 to 19.
Amy has $20 a week to spend on coBee and cake. The price of coBee is $4 a cup,
and the price of cake is $2 a slice.
16. Calculate Amy’s real income in terms of cake. Calculate the relative price of
cake in terms of coBee.
Amy’s real income in terms of cake is $20/($2 per slice), which is 10 slices. The
17. Calculate the equation for Amy’s budget line (with cups of coBee on the left
side).
The equation that describes Amy’s budget line is QCOFFEE = 5 – 0.5QCAKE. Call the
price of a cup of coBee PCOFFEE and the quantity of coBee QCOFFEE, the price of a
slice of cake PCAKE and the quantity of cake QCAKE, and income y. Amy’s budget
18. If Amy’s income increases to $24 a week and the prices of coBee and cake
remain unchanged, describe the change in her budget line.
19. If the price of cake doubles while the price of coBee remains at $4 a cup and
Amy’s income remains at $20, describe the change in her budget line.
Amy’s budget line rotates inward. If the quantity of cake is plotted on the
Use the following news clip to work Problems 20 and 21.
Gas Prices Straining Budgets
With gas prices rising, many people say they are staying in and scaling back
spending to try to keep within their budget. They are driving as little as possible,
cutting back on shopping and eating out, and reducing other discretionary
spending.
Source: CNN, February 29, 2008
20.a. Sketch a budget line for a household
that spends its income on only two
goods: gasoline and restaurant
meals. Identify the combinations of
gasoline and restaurant meals that
are aBordable and those that are
unaBordable.
Figure 9.5 shows a budget line. The
combinations of gasoline and
restaurant meals that lie on and inside
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21. How does a rise in the price of gasoline
change the relative price of a restaurant
meal? How does a rise in the price of
gasoline change real income in terms of
restaurant meals?
The relative price of restaurant meals equals the price of restaurant meals divided
Use the following information to work
Problems 22 and 23.
Rashid buys only books and CDs and Figure
9.7 shows his preference map.
22.a. If Rashid chooses 3 books and 2 CDs,
what is his marginal rate of
substitution?
Rashid’s marginal rate of substitution is
1 book per CD. Rashid’s marginal rate
of substitution equals the magnitude of
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b. If Rashid chooses 2 books and 6 CDs, what is his marginal rate of
substitution?
Rashid’s marginal rate of substitution is 1/2. Rashid’s marginal rate of substitution
23. Do Rashid’s indiBerence curves display diminishing marginal rate of
substitution? Explain why or why not.
Rashid’s indiBerence curves display diminishing marginal rate of substitution.
24. You May Be Paid More (or Less) Than You Think
It’s so hard to put a price on happiness, isn’t it? But if you’ve ever had to
choose between a job you like and a better-paying one that you like less, you
probably wished some economist would tell you how much job satisfaction is
worth. Trust in management is by far the biggest component to consider. Say
you get a new boss and your trust in management goes up a bit (say, up 1
point on a 10-point scale). That’s like getting a 36 percent pay raise. In other
words, that increased level of trust will boost your level of overall satisfaction
in life by about the same amount as a 36 percent raise would.
Source: CNN, March 29, 2006
a. Measure trust in management on a 10–point scale, measure pay on the
same 10–point scale, and think of them as two goods. Sketch an indiBerence
curve (with trust on the x-axis) that is consistent with the news clip.
The clip implies that a 1 point increase in
trust combined with a 3.6 point (which is
36 percent on a 10 point scale) decrease
in income leaves the person indiBerent.
b. What is the marginal rate of
substitution between trust in
management and pay according to this
news clip?
The news clip implies that the
indiBerence curves are linear (as
illustrated in Figure 9.82) which means
c. What does the news clip imply about
the principle of diminishing marginal
rate of substitution? Is that implication likely to be correct?
The news clip implies that the indiBerence curves are linear, as illustrated in Figure
9.8. Linear indiBerence curves mean that the marginal rate of substitution is
constant, that is, the principle of diminishing marginal rate of substitution does not
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from, say, 8 to 9 is probably not nearly so worthwhile because at 8 management is
Use the following information to work Problems 25 and 26.
Jim has made his best aBordable choice of muNns and coBee. He spends all of his
income on 10 muNns at $1 each and 20 cups of coBee at $2 each. Now the price
of a muNn rises to $1.50 and the price of coBee falls to $1.75 a cup.
25.a. Will Jim now be able and want to buy 10 muNns and 20 coBees?
Jim is able to buy 10 muNns and 20 coBees because this combination remains
aBordable. Jim will not want to buy this combination, however, because the relative
b. Which situation does Jim prefer: muNns at $1 and coBee at $2 a cup or
muNns at $1.50 and coBee at $1.75 a cup?
Jim prefers the $1.50 per muNn/$1.75 per coBee prices because he can attain a
higher indiBerence curve. The new budget line goes through the old budget line at
26.a. If Jim changes the quantities that he buys, will he buy more or fewer muNns
and more or less coBee? Explain your answer.
b. When the prices change, will there be an income eBect, a substitution eBect,
or both at work? Explain your answer.
Use the following data to work Problems 27 to 29.
Sara’s income is $12 a week. The price of
popcorn is $3 a bag, and the price of cola is
$1.50 a can. Figure 9.9 shows Sara’s
preference map for popcorn and cola.
27. What quantities of popcorn and cola
does Sara buy? What is Sara’s marginal
rate of substitution at the point at
which she consumes?
Sara buys 6 cans of cola and 1 bag of
popcorn. Sara’s budget line runs from 8
cans of cola on the x-axis to 4 bags of
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28. Suppose that the price of cola rises
from $1.50 to $3.00 a can while the price
of popcorn and Sara’s income remain the
same. What quantities of cola and
popcorn does Sara now buy? What are
two points on Sara’s demand curve for
cola? Draw Sara’s demand curve.
29. Suppose that the price of cola rises to $3.00 a can and the price of popcorn
and Sara’s income remain the same.
a. What is the substitution eBect of this price change and what is the income
eBect of the price change?
The substitution eBect is 1 can of cola. To divide the price eBect into a substitution
eBect and an income eBect, take enough income away from Sara and gradually
move her new budget line back toward the original indiBerence curve until it just
touches Sara’s Lrst indiBerence curve I1. The point at which this budget line just
b. Is cola a normal good or an inferior good? Explain.
Economics in the News
30. After you have studied Economics in the News on pp. 214–215, answer the
following questions.
a. How do you buy books?
b. Sketch your budget line for books and other goods.
Suppose the student has $800 to spend, the price of a print book is $25, the price
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illustrated in Figure 9.11.
If the student buys Amazon’s e-books, the student needs to buy a $200 e-book
c. Sketch your indiBerence curves for
books and other goods.
The indiBerence curves will be
conventional showing some
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d. Identify your best aBordable point.
For the student who consumes print books, the best aBordable point is point A in
Figure 9.14, with 20-books and 300 other goods. For the student who consumes
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