1
Chapter 5
Applying Consumer Theory
Key issues
1. deriving demand curves
2. income effect
3. effects of a price change
4. CPI bias
5. labor supply curve
Questions
1.What would happen if a consumer behaved
randomly?
2. Do we measure incomes in developing
countries accurately?
3. What are the effects of overtime laws?
4. What are the effects on hours of work of
tax cuts?
5. Can a flat tax be progressive?
• trace out the demand curve by holding
income and the price of wine constant, and
varying the price of beer
• example: estimated set of indifference
curves for the typical American consumer
are bowed away from origin, so beer and
wine are imperfect substitutions
Deriving Demand Curves
Figure 5.1 Deriving an
Individual’s Demand Curve
4.3
5.2
12.0

2.8
12.0
6.0
4.0
26.7
0
44.5 58.9
L
1
(
p
b
= $12)
p
b
, $ per unit
L
2
(p
b
= $6) L
3
(p
b
= $4)
26.70 44.5 58.9
e
3
e
2

e
1
E
3
E
2
E
1
I
1
I
2
I
3
Beer, Gallons per year
Beer, Gallons per year
D
1
, Demand for beer
Price-consumption curve
Wine, Gallons
per year
(a) Indifference Curves and Budget Constraints
(b) Demand Curve
Price-consumption curve
shows how the optimal pairs of beer and
wine vary as the relative price varies
2
How income changes shift
demand curves

• hold prices fixed and vary income
• increase in income causes
• shift of the demand curve
• movement along income-consumption curve
• movement along the Engel curve
Figure 5.2 Effect of a Budget
Increase on an Individual’s
Demand Curve
per year
Income-consumption
curve
Engel curve for beer
0
2.8
4.8
7.1
49.138.226.7 Beer, Gallons per year
0
12
0
49.138.226.7 Beer, Gallons per year
49.138.226.7 Beer, Gallons per year
I
2
I
3
I
1
(a) Indifference Curves and Budget Constraints
Price of beer,

$ per unit
(b) Demand Curves
Y, Budget
(c) Engel Curve
e
2
e
3
E
3
E
1
E
2
Y
1
= $419
Y
2
= $628
Y
3
= $837
L
3
L
2
L
1
e

1
D
1
D
2
D
3
E
1
*
E
2
*
E
3
*
Wine, Gallons
Income elasticities
• income elasticity:
• normal good: ξ >0
• inferior good: ξ≤0
p
ercentage change in quantity demanded
percentage change in income
/
/
QQ
YY
ξ
=

∆
=
∆
Mimi's income elasticities
• beer: ξ
b
= 0.88
•wine: ξ
w
= 1.38
• both are normal goods
Are children inferior?
• mother with relative little education:
ξ = -0.18
• mother relatively well educated:
ξ = 0.044
Income-consumption curves and
income elasticities
• shape of income-consumption curve for 2
goods tells us sign of income elasticities
• some goods must be normal: not all goods
can be inferior
3
Figure 5.3 Income-Consumption Curves and Income Elasticities
Housing, Square feet
per year
Food, Pounds per year
Food normal,
housing normal
Food inferior,

housing normal
Food normal,
housing inferior
b
c
e
a
L
1
L
2
I
ICC
2
ICC
1
ICC
3
Income elasticities may vary with
income
Gail may view hamburger as
• a normal good at a low income
• an inferior good at a high income
Figure 5.4 A Good That
Is Both Inferior and Normal
Y
2
Y
1
Y

1
Y
2
Y
3
Y
3
L
1
Y, Income
L
2
L
3
e
2
e
3
e
1
E
2
E
3
E
1
I
1
I
2

I
3
Hamburger per year
Income-consumption curve
Hamburger per year
All other goods
per year
(a) Indifference Curves and Budget Constraints
(b) Engel Curve
Engel curve
Quality and income elasticities
• when their incomes rise, some people buy
higher quality goods rather than more of
what they’re currently buying
•examples:
• fancier cars
• fancier foods
• designer clothing
Effects of a price change
as price of one good goes up (all else the
same), there are two effects:
• a substitution effect
• an income effect
Substitution effect
• consumers substitute other, now relatively
cheaper, goods for the one whose price rose
• direction of the effect is unambiguous
4
Income effect
• price increase ⇒ consumers' buying power

falls, reducing “income” (opportunity set)
• so consumer buys less of at least some
goods
• direction of income effect depends on
income elasticity of each good
Income and substitution effects
positivenegativeinferior good
negativenegativenormal good
income effectsubstitution effectprice rise
Figure 5.5 Substitution and Income Effects with Normal Goods
Wine, Gallons
per year
12.0
5.5
0 58.926.7 30.6
Substitution
effect
Total effect
Income effect
Beer, Gallons per year
I
2
I
1
L*
L
2
L
1
e

2
e
1
e *
Income and substitution effect
with an inferior good
• substitution effect: opposite of price movement
• income effect: same direction as price movement
• Giffen good: good for which a decrease in its price
causes the quantity demanded to fall
• potatoes in Ireland?
• quinine water for lab rats
Figure 5.6 Giffen Good
Basketball,
Tickets per year
Movies, Tickets per year
L
1
L*
Total effect
Income effect
Substitution effect
L
2
e
1
e
2
e*
I

1
I
2
Solved problem
• dinner plate manufacturer sells
• first-quality (perfect)
• second-quality (slight color defects) dinner plates
• manufacturer has an outlet store located next to its
manufacturing plant
• [assume tastes same everywhere; cost of shipping
each plate from factory to distant stores is s]
5
Solved problem (cont.)
compared to sales at other stores, does the
outlet store sell
A. a relatively large share of seconds
B. the same ratio of first and second quality
plates
C. a relatively small share of seconds?
Answer
• relative prices at outlet store:
• relative prices elsewhere:
•
• relative price of seconds rises—causing
substitution away from seconds
• presumably the income effect is small
/
s
f
pp

s
f
p
s
p
s
+
+
Shipping the Good Stuff Away
• expect larger share of higher-quality goods
shipped, greater per-unit shipping fee
• Hummels and Skiba (2002) examined
shipments between 6,000 country pairs for
more than 5,000 goods
Results
• doubling per unit shipping costs results in a
70 to 143% increase in average price
(excluding cost of shipping) — larger share
of top-quality products shipped
• farther apart are trading countries, greater
the cost of shipping—may explain relatively
high-quality of Japanese goods
Results (cont.)
• ad valorem tariff raises relative price of higher-
quality goods (given that there is also a per unit
shipping fee)
• doubling ad valorem tariff decreases average price
three to four fold, as average quality falls
• thus, using an ad valorem rather than a specific
(per unit) tariff reduces quality of imported goods

Inflation
• because of inflation, prices today are not
directly comparable to past prices
• inflation harms people on fixed incomes,
net lenders, and others
6
Cost-of-living adjustments
many long-term contracts include cost-of-
living adjustments (COLAs):
• general business contracts
•rental
• alimony payments
• salaries
• pensions
Consumer Price Index (CPI)
• many governments report a cost-of-living
measure: CPI
• measure of inflation: overall rise in prices
over time
• CPI overestimates how true cost-of-living
changes over time
• overestimate hurts you if your landlord
increases rent on your apartment using CPI
Real vs. nominal prices
• nominal price = “current dollars” price
• real price = “constant dollar” price (adjusted
for inflation)
•
• real price = nominal price divided by CPI
CPI for 2000 168.7

price of a burger = 15¢ 94¢
CPI for 1955 26.8
××=
Government collects prices
on 364 individual goods and services, such as:
• housing
• dental services
• watch and jewelry repairs
• college tuition fees
•taxi fares
• women's hair pieces and wigs
• hearing aids
• slip covers and decorative pillows
• bananas
• funeral expenses
Summary statistics
• if government reports all price increases
separately, information is overwhelming
• instead use a single summary statistic, CPI:
how prices rose on average
Averaging
• one way to average price increases: weight
the good equally
• but do we really want to weight price
increase of skateboards as much as that of
automobiles?
7
CPI approach
• give a larger weight to price change of a
good, the larger its budget share

• example: suppose CPI consists of only
clothing (C) and food (F)
Price of bundles
• CPI in Year 1:
• cost of buying first year’s bundle in second
year is:
• how much income would have to rise to buy
first year’s bundle in second year:
11
111CF
YpCpF
=
+
22
211CF
YpCpF
=
+
22
211
11
111
CF
CF
YpCpF
YpCpF
+
=
+
Calculate rate of inflation

Y
2
/Y
1
shows average price rise
21
21
1
21
11
11 1
2
2
11
CC
FF
CF
C
F
CF
CF
ppC
YppF
YpY pY
p
p
pp
θθ



=+






=+




CPI adjustment
• we assume price of clothing rose more
rapidly than that of food
• CPI overcompensates (upward bias)
• utility rises because consumer substitutes
toward the relatively cheaper good
Figure 5.7 The Consumer Price Index
C
2
C
1
C, Units of clothing
per year
e
2
e
1
I

1
L
1
e*
L*
L
2
I
2
F
, Units of food per year
Y
2
*/p
2
F
Y
1
/p
1
F
Y
1
/p
1
C
Y */p
2
C
F

2
F
1
Y
2
/p
2
F
Y
2
/p
2
C
Source of Bias
• CPI calculates price increase as Y
2
/Y
1
. We
can rewrite this expression as
• Y*/Y
1
= increase in true cost of living
• Y
2
/Y* = substitution bias in CPI (> 1
because Y
2
> Y*)
*

22
*
11
YY
Y
YYY
=
8
Total CPI bias
CPI Commission concluded that CPI has a total
upward bias of about 1.1 percentage points per
year:
• substitution bias: 0.4 percentage points per year
• failure to take proper account of spread of
discount stores: 0.1 percentage point
• failure to account fully for quality improvements
and new products (drugs, computers): 0.6
percentage point
USPS
• in 2002, a typical union employee earned
$59,900 (including benefits)
• Substitution bias of 0.5% a year costs USPS
$300 extra per employee
• multiplied by 860,000 employees:
substitution bias costs USPS over
$257 million per year (and benefits
its employees by same amount)
Federal Government
• CPI Commission concluded CPI is fourth
largest "federal program" after Social

Security, health care, defense
• $634 billion of national debt would be
eliminated in 5 years if CPI rose 1% less
rapidly per year
• gain to government would largely be at
expense of Social Security recipients
How rich are developing
countries?
• commonly used measure of income
understates third-world country incomes
relative to those of industrial nations
• problem: ignores substitution effects (as
with CPI)
International Monetary Fund
• IMF used to report country’s income by
converting native currency into dollars at market
exchange rate
• IMF switched to using purchasing-power parities
(PPP), which take account of international
differences in prices
• used to report how much Chinese could buy at
high US prices, now use lower Chinese prices
Result
IMF now reports that third world's share of
world's income went from
• 18% to 34% for developing countries
• 9% to 11% for Eastern Europe and the
former Soviet Union
• 7% to 18% for Asia
• 73% to 54% for industrialized countries

9
More plausible
• old system: China's total income < Canada's; its
income per person only slightly > India
• improbable
• China has a high daily food consumption
• 70% of Chinese urban households have color TVs
• 81% have washing machines
• new Chinese av. income is $1,950
• China's share of the world income rose from 2% to
6%, making it third-biggest economy behind U.S.
(22.5%) and Japan (7.6%)
0.0 0.2 0.4 0.6 0.8 1.0
012345
income
density
1999 U.S. income distribution (solid)
2001 China income distribution (dashes)
Deriving labor supply curves
• use consumer-theory model to derive supply
curve of labor by deriving demand curve for
time spent not working
• time constraint:
H = 24 - N
• H = hours of work in a day
•
N = hours of leisure or nonwork in a day
Price of leisure
foregone earnings are greater for a lawyer
who earns $250 an hour than for someone

who works for minimum wage
Utility
• Jackie's utility,
U(Y, N)
• depends on
• goods she consumes, represented by her
income,
Y
• number of hours of leisure, N
Budget constraint
• her total income is:
Y = wH + Y*
• where
• w = her wage
•
H = hours she works
•
wH = her earned income
•
Y* = unearned income (if any)
10
Time constraint
 can’t increase hours in a day
 vertical constraint at 24 hours of leisure
Figure 5.8
Demand for Leisure
Y, Goods
per day
Time constraint
H

2
= 12 H
1
= 824 0
N
2
= 12 N
1
= 16024
H, Work hours per day
N, Leisure hours per day
H
2
= 12 H
1
= 8
N
2
= 12 N
1
= 160
H, Work hours per day
N, Leisure hours per day
Demand for leisure
I
2
I
1
1
–w

2
L
1
L
2
(a) Indifference Curves and Constraints
w, Wage
per hour
(b) Demand Curve
–w
1
1
e
2
Y
2
Y
1
w
1
w
2
e
1
E
2
E
1
Supply curve of labor
• her supply curve of hours worked (labor) is

“mirror image” of demand curve for leisure:
H = 24 - N
• for every extra hour of leisure she
consumes, she works one fewer hour
Figure 5.9 Supply Curve of Labor
w, Wage
per hour
(a) Leisure Demand
Demand for leisure
w
1
w
2
16120
N, Leisure hours per day
E
1
E
2
w, Wage
per hour
(b) Labor Supply
Supply of work hours
w
1
w
2
8120
H, Work hours per day
e

2
e
1
Solved problem
• Mark’s utility function is
• his budget constraint is:
• How many hours a day does he chose to
work if the wage is w?
(, )UUYN YN==
YwH=
Answer
• substitute Mark’s budget constraint and his hours
constraint,
H = 24 – N, into his utility function:
• he maximizes his utility by differentiating
U with
respect to
N and setting the derivative equal to 0:
•or
N = 12
2
() ([24 ])
(24 ) 24
UYN wHN w NN
wwNN wN wN
=
==−
=− = −
24 2 0wwN
−

=
11
Income and substitution effects
increase in wage causes both income and
substitution effects that alter an individual's
demand for leisure and supply of hours
worked
Figure 5.10 Income and Substitution Effects of a Wage Change
Y, Goods
per day
Time constraint
H
2
H * H
1
24 0
N
2
N * N
1
024
Substitution effect
Income effect
Total effect
H, Work hours per day
N, Leisure hours per day
I
2
I
1

L
2
L*
L
1
e
2
e
1
e*
Estimated labor supply curves
• typical British male
• slightly backward-sloping supply curve
• labor supply elasticity between –0.2 and –0.05
• American male workers
• vertical supply curve
• elasticity between –0.2 and 0.15 (best estimates is 0)
• unmarried women
• upward sloping
• elasticity between 0 and 4
Married women's supply curves
• slightly backward bending in Canada and
U.S.
• slightly forward sloping in U.K. and
Germany
Do animals make rational
choices?
• animals have to make choices between
scarce resources, as do humans
• income-leisure choices of pigeons

• “job”: pecking a response key for a 3
second access to a food hopper containing
mixed pigeon grains
• (I assume they used adult pigeons - so far as
I know, no one has ever seen a baby pigeon)
Wages and income
• wages could be altered by varying number of
pecks required for a payoff from about 12 to 400
• income varied by providing free access for 3
seconds to food hopper at regular intervals
• by varying both wage rate and income,
experimenters could determined pure
(compensated) substitution effect of a wage
change and income effect
12
Researchers found
• compensated substitution effect for leisure > 0: as
price of leisure falls and pigeons compensated
with more income, consumed more leisure
•
leisure normal good: as pigeons' income increased
(food without working), pigeons consumed more
leisure by spending less time pecking
• pigeons' supply curve of labor is backward
bending
Rational pigeons
• if pigeons use arbitrary rule (such as
working constant percent of time), would
not respond to wage and income changes in
this systematic, nonconstant manner

• apparently pigeons are rational enough to
react consistently to variations in a price
and income
Income tax rates and labor supply
• why care about shape of labor supply curves?
• if supply curves are upward sloping, income tax
causes
• people to work fewer hours
• reducing goods produced
• raising fewer tax revenues
• if supply curves slope backward, a small increase
in income tax rate may increase tax revenues and
increase total production
Bush tax cut
“I want all Americans to study my tax cut
proposal.” – President George W. Bush,
February 6, 2001
Tax cuts
• Presidents John Kennedy and Ronald
Reagan argued that cutting marginal tax rate
would stimulate people to work more
• Reagan also claimed that, due to extra work,
tax receipts would increase
• because tax rates have adjusted substantially
over time, we have a natural experiment to
test this hypothesis
Tax rates
• Kennedy tax cuts: lowered top personal
marginal tax rate from 91% to 70%
• rate fell over the next couple of decades

13
Reagan Tax Reform Act of 1986
• Due to the Reagan tax cuts, the maximum
rate fell to
• 50% from 1982-1986
• 38.5% in 1987
• 28% in 1988-1990
• rate rose to
• 31% in 1991-1992
• 39.6% from 1993-2000
Bush Administration’s Tax Relief
Act of 2001
• tax cut reduces top rate to
• 38.6% for 2001-2003
• 37.6% for 2004-2005
• 35% for 2006 and thereafter
• Marginal rates
• original: 15%, 28%, 31%, 36%, 39.6%
• proposed: 10%, 15%, 25%, 33%
• after 7/2001: 15%, 27.5%, 30.5%, 35.5%, 39.1%
International Comparison (2001)
• highest marginal tax rate including both central (federal)
and sub-central government taxes (state and local):
• ranged from 35.6% in Turkey to 65.2% in Belgium
• top rates:
• United States 47.5%
• Australia 48.5%
• Canada 43.2%
• Denmark 63.3%
• Iceland 43.1%

• Japan 49.5%
• Netherlands 52.0%
• New Zealand 39.0%
• United Kingdom 40%
Effect of tax
• effect of a tax rate of τ = 0.28 is to reduce
the effective wage from w to
(1- τ)w = 0.72w
• tax reduces after-tax wage by 28%, so that a
worker's budget constraint rotates down
Figure 5.11a Labor Supply Curve That Slopes Upward and
Then Bends Backward
Y, Goods
per day
(a) Labor-Leisure Choice
Time constraint
H
2
H
3
H
1
24 0
H
, Work hours per day
L
2
I
2
I

3
I
1
L
3
L
1
e
2
e
1
e
3
Figure 5.11b Labor Supply Curve That Slopes Upward and
Then Bends Backward
E
1
E
3
E
2
w, Wage
per hour
(b) Supply Curve of Labor
Supply curve of labor
H
2
H
3
H

1
240
H, Work hours per day
14
Tax revenue and tax rate
if labor supply is first upward sloping and
then backward bending then, relationship
between total tax revenues, τwH, and tax
rate, τ, is bell shaped
Figure 5.12 Relationship of Tax Revenue to Tax Rates
600
800
400
200
Tax revenue, $
500
τ
* = 79 100
τ
, Marginal tax rate, %
Tax revenue
Effects of U.S. tax cuts
• estimates of τ* between 79% and 85%
• Kennedy era tax cut from 91% to 70% raised tax
revenue and increased work effort of top-income-
bracket workers
• Reagan tax cuts had opposite effects because
actual tax rate, τ, was only about half as big as τ*
• ⇒ U.S. was in upward-sloping section of bell-shaped
curve

• rapid growth of U.S. deficit during Reagan era partially
due to tax cuts
Effects of tax cuts in other
countries
• Sweden: 80% marginal tax rate is greater
than that country's τ*
• Netherlands: τ* is about 70% - close to
actual rate of 67.4% in 1985
California tax cut
• Gov. Wilson proposed dropping income tax
rate by 15%
• 35% of that goes to feds (for wealthiest)
• [top 2% pay 50% of CA taxes]
• so resulting cut to a Californian would be
9.75%
Tax cut on wealthy
• top CA tax bracket is 9.3%, so resulting top
tax is 9.07%: a tax rate reduction of 0.23
percentage points
• for everyone else, the tax cut is less
• if you made $200,000, drop in your total tax
is $460
• is that enough to change behavior?
15
State general fund revenues
• share of total state general fund revenues (~$40
billion):
 personal income tax: 35%
 sales tax: 35.7%
 banking and corporations: 12.3%

 tobacco: 0.4%
 horse racing and liquor are 0.7%
• Intel pays no tax
• cut welfare, lose 50% from feds
Winning the Good Life
• Would you stop working if you won a big lottery
prize or inherited a large sum?
• Imbens, Rubin, and Sacerdote (2001) compared
major-prize winners and others who played the
Massachusetts Megabucks lottery
• prizes ranged from $22,000 to $9.7 million, with
an average of $1.1 million (paid in yearly
installments over two decades)
Results
• typical person playing lottery earned $16,100
• average winner received $55,200 in prize money
per year and chose to work slightly fewer hours so
that his or her labor earnings fell by $1,877 per
year
• thus, winners increased their consumption and
savings but did not substantially decrease how
much they worked
• for every dollar of unearned income, winners
reduced their work effort and hence their labor
earnings by 11¢ on average
Demographic differences
• behavior same for:
• men and women
• big and very big prize winners
• people of all education levels

• differences by age of the winner and by income
groups:
• people 55 to 65 reduced their effort by about a third
more than younger people (retired early)
• people with no earnings in year before winning lottery
tended to increase their labor earnings after winning
Child-Care Subsidies
• increased employment of mothers outside the
home led to a steep rise in child care over past
several decades
• 6 of 10 U.S. mothers work today—twice the rate
in 1970
• 6 of 10 children under the age of 6 are in child
care (45% of children under age one)
• 8 of 10 employed mothers with children under 6
have some form of nonparental child care
arrangement
Child-Care Subsidies (cont.)
• child care is a major burden for poor; may
prevent poor mothers from working
• Child-care expenses for children under 5
absorbed 25% of the earnings for families
with annual incomes <$14,400, but only 6%
for families with incomes of $54,000 or
more
16
Question
• Congress must decide how to aid poor families
• child-care program could provide an
ad valorem

or a specific subsidy (as many states currently do
under PRWORA)
• alternatively, government could provide an
unrestricted lump-sum payment under the major
welfare program that could be spent on day care or
on all other goods such as food and housing
Question (cont.)
• for a given government expenditure, does
the price subsidy or the lump-sum subsidy
provide greater benefit to recipients?
• which increases the demand for day care
services by more?
• which inflicts less cost on other consumers
of day care?
0
L
o
I
1
I
2
e
1
e
3
Q
1
Q, Hours of day care per day
Q
2

e
2
L
LS
Y
o
Y
2
L
PS
I
3
Q
3
Solution
• on initial budget constraint is L
o,
poor family
chooses the bundle
e
1
• with a day-care price subsidy,budget line is L
PS
;
family consumes
e
2
• measure the value of the subsidy to family:
calculate how many
other goods the family could

buy before and after the subsidy
• (given price of other goods is $1 per unit, these
other goods are essentially income,
Y
o
)
Solution (cont.)
• given family consumes Q
2
hours of day care,
family could have consumed
Y
o
other goods with
the original budget constraint and
Y
2
with L
PS
• thus, value to family of day-care price subsidy is
Y
2
– Y
o
• lump-sum payment of Y
2
– Y
o
, budget constraint
L

LS
goes through e
2
,but family chooses e
3
1 Deriving demand curves
• individual demand curves derived using
consumer's indifference curve map
• consumers' tastes (indifference curves)
determine the shape of the demand curve
(elasticity of demand)
17
2 Income effect
• use indifference curve maps to show how
entire demand curve shifts as a consumer's
income rises
• relationship between income and quantity
demand is summarized in an Engel curve
3 Effects of a price change
• when price of a good rises, it causes both a
substitution and an income effect
• if good is normal (income elasticity > 0)
• income effect < 0 and reinforces substitution effect
• total effect of a price change < 0
• if good is inferior (income elasticity < 0)
• income effect is positive
• possible (not likely) income effect more than offsets
substitution effect so that total effect > 0 (Giffen good)
4 CPI bias
• Consumer Price Index, by ignoring the

substitution effect, overestimates inflation
• substitution bias is on average small, but
may be substantial for particular individuals
or firms
5 Labor supply curves
• using consumer theory, we derive the
demand curve for leisure
• daily labor supply curve:
24 - demand curve for leisure
• income elasticity of leisure determines slope
of labor supply curve
• effect of a tax cut depends on slope of labor
supply curve