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CHAPTER 5 Applying Consumer Theory
2.3 Hugo views donuts and coffee as perfect comple-
ments: He always eats one donut with a cup of coffee and will not eat a donut without coffee or drink
coffee without a donut. Derive and plot Hugo’s
Engel curve for donuts. How much does his weekly
budget have to rise for Hugo to buy one more
donut per week? (Hint: See Solved Problem 5.2.) A
*2.4 Don spends his money on food and on operas.
Food is an inferior good for Don. Does he view
an opera performance as an inferior or a normal
good? Why? In a diagram, show a possible incomeconsumption curve for Don.
her just as “happy” as she was before the price
change, what happens to her consumption of eggs?
Draw a graph and explain your diagram. Does the
change in her consumption reflect a substitution or
an income effect? A
3.4 Under what conditions does the income effect rein-
force the substitution effect? Under what conditions does it have an offsetting effect? If the income
effect more than offsets the substitution effect for a
good, what do we call that good?
3.5 Using a figure similar to Figure 5.4 or that in Solved
*2.5 Using calculus, show that not all goods can
be inferior. (Hint: Start with the identity that
y = p1q1 + p2q2 + c + pnqn.) C
Problem 5.3, discuss the substitution, income, and
total effects of a price change for Coke for Mahdu
who views Coke and Pepsi as perfect substitutes.
(Hint: See Solved Problem 5.1.)
2.6 Could an individual’s Engel curve be the mirror
3.6 Relatively more high-quality navel oranges are sold
image of the one in the Application “Fast-Food
Engel Curve” (quantity is first decreasing and then
increasing with income)? Show in a figure. Can you
think of a good where such a figure would apply?
in California than in New York. Why? (Hint: See
Solved Problem 5.4.)
3. Effects of a Price Change
3.1 Michelle spends all her money on food and cloth-
ing. When the price of clothing decreases, she buys
more clothing.
a. Does the substitution effect cause her to buy
more or less clothing? Explain. (If the direction
of the effect is ambiguous, say so.)
b. Does the income effect cause her to buy more
or less clothing? Explain. (If the direction of the
effect is ambiguous, say so.)
3.2 Steve’s utility function is U = BC, where
B = veggie burgers per week and C = packs of cigarettes per week. Here, MUB = C and MUC = B.
What is his marginal rate of substitution if veggie
burgers are on the vertical axis and cigarettes are
on the horizontal axis? Steve’s income is $120, the
price of a veggie burger is $2, and that of a pack of
cigarettes is $1. How many burgers and how many
packs of cigarettes does Steve consume to maximize
his utility? When a new tax raises the price of a
burger to $3, what is his new optimal bundle? Illustrate your answers in a graph. In a related graph,
show his demand curve for burgers with after-tax
price on the vertical axis and show the points on
the demand curve corresponding to the before- and
after-tax equilibria. (Hint: See Appendix 4B.) C
*3.7 Draw a figure to illustrate the answer given in
Solved Problem 5.4. Use math and a figure to show
how adding an ad valorem tax changes the analysis. (See the Application “Shipping the Good Stuff
Away.”)
3.8 Remy views ice cream and fudge sauce as perfect
complements. Is it possible that either of these
goods or both of them are Giffen goods? (Hint:
See Solved Problem 5.5.)
3.9 Redraw Figure 5.4 using an equivalent variation
rather than a compensating variation approach.
4. Cost-of-Living Adjustments
4.1 The Economist magazine publishes the Big Mac
Index for various countries, based on the price of
a Big Mac at McDonald’s over time. Under what
circumstances would people find this index to be as
useful as or more useful than the Consumer Price
Index in measuring how their true cost of living
changes over time?
4.2 During his first year at school, Ximing buys eight
new college textbooks at a cost of $50 each.
Used books cost $30 each. When the bookstore
announces a 20% price increase in new texts and a
10% increase in used texts for the next year, Ximing’s father offers him $80 extra. Is Ximing better
off, the same, or worse off after the price change?
Why?
3.3 Cori eats eggs and toast for breakfast and insists
4.3 Ann’s only income is her annual college scholar-
on having three pieces of toast for every two eggs
she eats. What is her utility function? If the price
of eggs increases but we compensate Cori to make
ship, which she spends exclusively on gallons of
ice cream and books. Last year when ice cream
cost $10 and used books cost $20, Ann spent her
Questions
$250 scholarship on five gallons of ice cream and
ten books. This year, the price of ice cream rose to
$15 and the price of books increased to $25. So that
Ann can afford the same bundle of ice cream and
books that she bought last year, her college raised
her scholarship to $325. Ann has the usual-shaped
indifference curves. Will Ann change the amount
of ice cream and books that she buys this year? If
so, explain how and why. Will Ann be better off, as
well off, or worse off this year than last year? Why?
*4.4 Alix views coffee and cream as perfect complements. In the first period, Alix picks an optimal
bundle of coffee and cream, e1. In the second
period, inflation occurs, the prices of coffee and
cream change by different amounts, and Alix
receives a cost-of-living adjustment (COLA) based
on the Consumer Price Index (CPI) for these two
goods. After the price changes and she receives the
COLA, her new optimal bundle is e2. Show the two
equilibria in a figure. Is she better off, worse off, or
equally well off at e2 compared to e1? Explain why.
By how much will a CPI for these two goods differ
from the true cost-of-living index?
4.5 Change Figure 5.5 so that L2 is steeper than L1
(but still goes through e1); that is, food increases
by more than clothing in the second year. Show the
conclusion that Klaas is still better off after receiving a CPI adjustment. Explain the logic behind
the following statement: “The analysis holds as
long as the relative prices differ in the two years.
Whether both prices, one price, or neither price is
higher than in the second year is irrelevant to the
analysis.”
5. Deriving Labor Supply Curves
5.1 Using calculus, show the effect of a change in the
wage on the amount of leisure an individual wants
to consume. (Hint: See Appendix 5B.) C
5.2 If an individual’s labor supply curve slopes upward
at low wages and bends backward at high wages,
is leisure a Giffen good? If so, at high or low wage
rates? (Hint: See Solved Problems 5.5 and 5.6.)
5.3 Bessie, who can currently work as many hours as
she wants at a wage of w, chooses to work ten
hours a day. Her boss decides to limit the number of hours that she can work to eight hours per
day. Show how her budget constraint and choice
of hours change. Is she unambiguously worse off
as a result of this change? Why? (Hint: See Solved
Problem 5.6.)
5.4 Suppose that Roy could choose how many hours
to work at a wage of w and chose to work seven
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hours a day. The employer now offers him timeand-a-half wages (1.5w) for every hour he works
beyond a minimum of eight hours per day. Show
how his budget constraint changes. Will he choose
to work more than seven hours a day? (Hint: See
Solved Problem 5.6.)
5.5 Jerome moonlights: He holds down two jobs.
The higher-paying job pays w, but he can work
at most eight hours. The other job pays w*, but
he can work as many hours as he wants. Show
how Jerome determines how many hours to work.
(Hint: See Solved Problem 5.6.)
5.6 Suppose that the job in Question 5.5 that had no
restriction on hours was the higher-paying job.
How do Jerome’s budget constraint and behavior
change? (Hint: See Solved Problem 5.6.)
5.7 Suppose that Bill’s wage varies with the hours he
works: w(H) = αH, α 7 0. Show how the number
of hours he chooses to work depends on his tastes.
5.8 Joe won $365,000 a year for life in the state lottery.
Use a labor-leisure choice analysis to answer the
following questions:
a. Show how Joe’s lottery winnings affect the position of his budget line.
b. After winning the lottery, Joe continues to
work the same number of hours each day (see
the Application “Working After Winning the
Lottery”). What is the income effect from Joe’s
lottery gains?
c. Suppose Joe’s employer the same week increases
Joe’s hourly wage rate. Use the income effect
you derived in part b as well as the substitution
effect to analyze whether Joe chooses to work
more hours per week. (Hint: See Solved Problem 5.6.)
5.9 Taxes during the fourteenth century were very pro-
gressive. The 1377 poll tax on the Duke of Lancaster was 520 times the tax on a peasant. A poll
tax is a lump-sum (fixed amount) tax per person,
which does not vary with the number of hours a
person works or how much that person earns. Use
a graph to show the effect of a poll tax on the
labor-leisure decision. Does knowing that the tax
was progressive tell us whether a nobleman or a
peasant—assuming they have identical tastes—
worked more hours?
5.10 Today most developed countries have progres-
sive income taxes where rich people pay a higher
marginal tax rate than poor people. Under such a
taxation program, is the marginal tax higher than,
equal to, or lower than the average tax? A