Download Chapter 5

Chapter 5
Applying
Consumer
theory
Topics
• Deriving Demand Curves.
• How Changes in Income Shift Demand
Curves.
• Effects of a Price Change.
• Cost-of-Living Adjustments.
• Deriving Labor Supply Curves.
5-2
Copyright © 2012 Pearson Education. All rights reserved.
Budget Line, L
W=
Y PW
Wine, (W), Gallons per year
Figure 5.1 Deriving
an Individual’s
Demand Curve
(a) Indifference Curves and Budget Constraints
Pb
b
PW
12.0
e1
2.8
0
5-3
26.7
(b) Demand Curve
Copyright © 2012 Pearson Education. All rights reserved.
Beer (b), Gallons per year
Initial optimal bundle of
beer and wine
pb, $ per unit
Initial Values
Pb = price of beer = $12
PW = price of wine = $35
Y = Income = $419.
I1
L1 (pb = $12)
12.0
E1
0
26.7
Beer (b), Gallons per year
Budget Line, L
Wine, (W), Gallons per year
Figure 5.1 Deriving
an Individual’s
Demand Curve
(a) Indifference Curves and Budget Constraints
12.0
e2
4.3
W=
Y PW
Pb
b
PW
e1
2.8
I2
0
26.7
44.5
L2 (pb = $6)
Beer (b), Gallons per year
(b) Demand Curve
pb, $ per unit
New Values
Pb = price of beer = $6
PW = price of wine = $35
Y = Income = $419.
I1
L1 (p b = $12)
12.0
E1
E2
6.0
Price of beer goes down!
0
5-4
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26.7
44.5
Beer (b), Gallons per year
Budget Line, L
Wine, (W), Gallons per year
Figure 5.1 Deriving
an Individual’s
Demand Curve
(a) Indifference Curves and Budget Constraints
12.0
e3
5.2
e2
4.3
W=
Y PW
Pb
b
PW
2.8
I2
I1
L1 (pb = $12)
26.7
44.5
L2 (pb = $6)
58.9
L3 (pb = $4)
Beer (b), Gallons per year
pb, $ per unit
(b) Demand Curve
12.0
E1
E2
6.0
Price of beer goes down
again!
Copyright © 2012 Pearson Education. All rights reserved.
E3
4.0
0
5-5
I3
e1
0
New Values
Pb = price of beer = $4
PW = price of wine = $35
Y = Income = $419.
Price-consumption curve
26.7
44.5
58.9
D1, Demand for Beer
Beer (b), Gallons per year
Price-Consumption Curve
• A line through optimal bundles at each
price of one good (beer) when the price of
the other good (wine) and the budget are
held constant.
• The demand curve corresponds to the
price-consumption curve.
5-6
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Solved Problem 5.1
• In Figure 5.1, how does Mimi’s utility at E1
on D1 compare to that at E2?
• Answer:
 Use the relationship between the points in
panels a and b of Figure 5.1 to determine
how Mimi’s utility varies across these points
on the demand curve.
5-7
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Solved Problem 5.2
• Mahdu views Coke, q, and Pepsi as
perfect substitutes: He is indifferent as to
which one he drinks. The price of a 12ounce can of Coke is p, the price of a 12ounce can of Pepsi is p* and his weekly
cola budget is Y. Derive Mahdu’s demand
curve for Coke using the method
illustrated in Figure 5.1.
5-8
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Solved Problem 5.2
(cont.)
5-9
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Effects of a Rise in Income
• Engel curve - the relationship between
the quantity demanded of a single good
and income, holding prices constant.
• Income-consumption curve shows how
consumption of both goods changes when
income changes, while prices are held
constant.
5 - 10
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Wine, Gallons per year
Figure 5.2 Effect of a
Budget Increase on an
Individual’s Demand Curve
L1
2.8
Budget Line, L
Initial Values
Pb = price of beer = $12
PW = price of wine = $35
$628
Y = Income = $419.
Income goes up!
Price of beer, $ per unit
Pb
b
PW
12
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Beer, Gallons per year
E1
D1
0
Y1 = $419
0
5 - 11
26.7
I1
26.7
Beer, Gallons per year
Y, Budget
W=
Y PW
0
e1
E1*
26.7
Beer, Gallons per year
Wine, Gallons per year
Figure 5.2 Effect of a
Budget Increase on an
Individual’s Demand Curve
L2
L1
4.8
2.8
Budget Line, L
Initial Values
Pb = price of beer = $12
PW = price of wine = $35
$628
Y = Income = $419.
Income goes up!
Price of beer, $ per unit
Pb
b
PW
12
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26.7 38.2
E1
I2
Beer, Gallons per year
E2
D2
D1
0
26.7 38.2
Y2 = $628
Y1 = $419
0
5 - 12
I1
Beer, Gallons per year
Y, Budget
W=
Y PW
0
e2
e1
E2*
E1*
26.7 38.2
Beer, Gallons per year
Wine, Gallons per year
Figure 5.2 Effect of a
Budget Increase on an
Individual’s Demand Curve
L3
L2
L1
7.1
4.8
2.8
Budget Line, L
Pb
b
PW
Initial Values
Pb = price of beer = $12
PW = price of wine = $35
Y = Income = $837.
Price of beer, $ per unit
0
12
e2
e1
I1
26.7 38.2 49.1
E1
E2
0
26.7 38.2 49.1
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Beer, Gallons per year
Y1 = $419
Beer, Gallons per year
Engel curve for beer
E3*
Y2 = $628
0
5 - 13
I3
D3
D2
D1
Y3 = $837
Income goes up again!
I2
E3
Y, Budget
W=
Y PW
Income-consumption curve
e3
E2*
E1*
26.7 38.2 49.1
Beer, Gallons per year
Solved Problem 5.3
• Mahdu views Coke and Pepsi as perfect
substitutes. The price of a 12-ounce can
of Coke, p, is less than the price of a 12ounce can of Pepsi, p*. What does
Mahdu’s Engel curve for Coke look like?
How much does his weekly cola budget
have to rise for Mahdu to buy one more
can of Coke per week?
5 - 14
Copyright © 2012 Pearson Education. All rights reserved.
Solved
Problem 5.3
5 - 15
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Consumer Theory and Income Elasticities
• Formally,
Q
%Q
Q Y
Q
x


%Y Y Y Q
Y
 where Y stands for income.
• Example
 If a 1% increase in income results in a 3% decrease in
quantity demanded, the income elasticity of demand is
x = -3%/1% = -3.
5 - 16
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Consumer Theory and Income Elasticities
(cont.)
• Normal good - a commodity of which as
much or more is demanded as income
rises.
 Positive income elasticity.
• Inferior good - a commodity of which less
is demanded as income rises.
 Negative income elasticity.
5 - 17
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Housing, Squarefeet per year
Figure 5.3 Income-Consumption
Curves and Income Elasticities
• As income rises
the budget
constraint shifts to
the right.
Food inferior,
housing normal
L2
ICC 1
a
Food normal,
housing normal
ICC 2
• …where on the new
budget constraint
the new optimal
consumption bundle
will be
b
L1
 The income
elasticities depend
on….
e
c
ICC 3
Food normal,
housing inferior
I
Food, Pounds peryear
5 - 18
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 …she bought more
hamburger
• But as she became
wealthier and her
income rose…
 ….she bought less
hamburger and more
steak.
5 - 19
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All other goods per year
• When Gail was poor
and her income
increased..
(a) Indifference Curves and Budget Constraints
Y3 L3
Y2
Income-consumption curve
L2
e3
1
Y1 L
I3
e2
e1
I2
I1
Hamburger peryear
(b) Engel Curve
Y, Income
Figure 5.4 A Good
That Is Both Inferior
and Normal
Y3
E3
Y2
E2
Engel curve
Y1
E1
Hamburger peryear
Effects of a Price Change
• Substitution effect - the change in the
quantity of a good that a consumer
demands when the good’s price changes,
holding other prices and the consumer’s
utility constant.
• Income effect - the change in the
quantity of a good a consumer demands
because of a change in income, holding
prices constant.
5 - 20
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Figure 5.5 Substitution and Income
Effects with Normal Goods
Budget Line, L1
C=
Y1
PC
-
1
PF
1
PC
1
F
Budget Line, L2 (increase in salary)
C=
Y2
PC
2
-
PF
2
PC
2
 PC  PF
1
5 - 21
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F
1
Basketball, Tickets per year
Figure 5.6
Giffen Good
When the price of movie tickets
decreases the budget constraint
rotates out…
L2
e2
L1
I2
e1
Total effect
Nevertheless, the total effect is negative. WHY?
5 - 22
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allowing the consumer to
increase her utility.
I1
Movies, Tickets per year
Basketball, Tickets per year
Figure 5.6
Giffen Good
• Even though the substitution
effect is positive….
L2
 …the income effect is larger
and negative (since this is an
inferior good).
e2
L1
I2
L*
e1
e*
Total effect
Substitution effect
Income effect
5 - 23
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I1
Movies, Tickets per year
Inflation Indexes
• Inflation - the increase in the overall price
level over time.
 nominal price - the actual price of a good.
 real price - the price adjusted for inflation.
• How do we adjust for inflation to calculate
the real price?
5 - 24
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Inflation Indexes (cont.)
• Consumer Price Index (CPI) – measure the cost of a
standard bundle of goods for use in comparing prices
over time.
 We can use the CPI to calculate the real price of a
hamburger over time.
 In terms of 2008 dollars, the real price of a hamburger in
1955 was:
CPI for 2008
211.1
 price of a burger 
15  1.18
CPI for 2005
26.8
5 - 25
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Effects of Inflation Adjustments
• Scenario: Klaas signed a long-term contract when he
was hired. According to the COLA clause in his
contract, his employer increases his salary each year
by the same percentage as that by which the CPI
increases. If the CPI this year is 5% higher than the
CPI last year, Klaas’s salary rises automatically by
5% over last year’s.
• Question: what is the difference between using the
CPI to adjust the long-term contract and using a true
cost-of-living adjustment, which holds utility constant?
5 - 26
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C, Units of clothing pe year
Figure 5.7 The Consumer Price
Index
Budget Line, L1
Y1/pC1
Y2 /pC2
C1
e1
But
is
Thesince
firm Klaas
ensures
better
off, the
that Klaas
canCPI
buy
adjustment
the same bundle of
overcompensates
goods in the second
for
thethat
change
in
year
he chose
inflation
in the first year…
C=
Y1
PC
-
1
F
1
1
Pc
Budget Line, L2 (increase in salary)
C=
Y2
PC
-
2
PF
2
Pc
2
 PC  PF
e2
C2
PF
1
I2
I1
L1
F1
F2
Y1/pF1
L2
Y2/pF2
F, Units offood peryear
5 - 27
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F
1
True Cost-of-Living Adjustment
• True cost-of-living index - an inflation
index that holds utility constant over time.
• Question: how big an increase in Klaas’s
salary would leave him exactly as well off
in the second year as in the first?
5 - 28
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C, Units of clothing per year
True Cost-of-Living Adjustment
Budget Line, L1
C=
Y1/pC1
Y1
PC
C1
1
F
1
1
Pc
Budget Line, L2 (increase in salary)
Y2 /pC2
Y*/pC2
-
PF
Y2
C=
e1
PC
-
2
Pc
2
 PC  PF
1
e2
C2
2
PF
F
1
e*
I2
I1
L1
F1
F2
Y1/pF1
L*
L2
Y2* /pF2 Y2/pF2
F, Units of food per year
5 - 29
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Table 5.1 Cost-of-Living
Adjustments
5 - 30
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CPI Substitution Bias
• Income adjustments based on CPI suffer
from an upward bias.
• The CPI-based adjustment suffers from
substitution bias – it ignores that
consumers may substitute toward the
relatively inexpensive good when prices
change disproportionately.
5 - 31
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Labor-Leisure Choice
• Leisure - all time spent not working.
• The number of hours worked per day, H,
equals 24 minus the hours of leisure or
nonwork, N, in a day:
H = 24 − N.
 The price of leisure is forgone earnings.
• The higher your wage, the more an hour of leisure
costs you.
5 - 32
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Labor-Leisure Choice: Example
• Jackie spends her total income, Y, on various goods.
 The price of these goods is $1 per unit.
•
Her utility, U, depends on how many goods and how much leisure
she consumes:
U = U(Y, N).
• Jackie’s earned income equal:
wH.
• And her total income, Y, is her earned income plus her unearned
income, Y*:
Y = wH + Y*.
5 - 33
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(a) Indifference Curves and Constraints
Y , Goods per day
Figure 5.8 Demand
for Leisure
Time constraint
I1
Budget Line, L1
L1
–w1
Y = w1H
0
24
w, Wage per hour
Y = w1(24 − N).
Each extra hour of leisure
she consumes costs her w1
goods.
e1
N1 = 16
H1 = 8
24
0
N, Leisure hours per day
H,Work hours per day
(b) Demand Curve
E1
w1
0
5 - 34
1
Y1
Copyright © 2012 Pearson Education. All rights reserved.
N1 = 16
H1 = 8
N, Leisure hours per day
H, Work hours per day
Figure 5.8 Demand
for Leisure
Y, Goods per day
(a) Indifference Curves and Constraints
Time constraint
I2
L2
–w2
1
I1
e2
Y2
Budget Line, L1
L1
–w1
Y = w1H
0
24
Y = w2H
Y = w2(24 − N).
w, Wage per hour
Y = w1(24 − N).
Budget Line, L2
1
e1
Y1
N2 = 12
H2 = 12
N1 = 16
H1 = 8
24
0
N, Leisure hours per day
H,Work hours per day
(b) Demand Curve
E2
w2
E1
w1
Demand for leisure
w2 > w1
5 - 35
0
Copyright © 2012 Pearson Education. All rights reserved.
N2 = 12
H2 = 12
N1 = 16
H1 = 8
N, Leisure hours per day
H, Work hours per day
Figure 5.9 Supply Curve of Labor
5 - 36
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Y, Goods per d ay
Figure 5.10 Income and Substitution
Effects of a Wage Change
Time const raint
I2
L2
Since income effect is
positive, leisure is a normal
good.
I1
L*
e2
e*
L1
e1
0
N*
24
H*
N1 N 2
H1 H2
Substitution effect Total effect
Income effect
5 - 37
Copyright © 2012 Pearson Education. All rights reserved.
24
N, Leisure hours per d ay
0
H, Work hours per d ay
Solved Problem 5.5
• Enrico receives a no-strings-attached
scholarship that pays him an extra Y* per
day. How does this scholarship affect the
number of hours he wants to work? Does
his utility increase?
5 - 38
Copyright © 2012 Pearson Education. All rights reserved.
Solved Problem 5.5 (cont.)
5 - 39
Copyright © 2012 Pearson Education. All rights reserved.
Figure 5.11 Labor Supply Curve That
Slopes Upward and Then Bends Backward
L3
(b) Supply Curve of Labor
Time const raint
I3
I2
I1
L2
E3
E2
e3
e2
E1
L1
24
Supply curve of labor
w, Wage per hour
Y, Goods per d ay
(a) Labor-Leisure Choice
e1
H2
H
3
H1
0
0
H1 H3
H, Work hours per d ay
butlow
At
at high
wages,
wages,
an increase
an increase
in the
in the
wage causes the worker to work
more….
less….
5 - 40
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H2
24
H, Work hours per d ay
Figure 5.12 The Relationship of U.S. Tax
Revenue and the Marginal Tax Rate
5 - 41
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Figure 5.13 Per-Unit Versus LumpSum Child Care Subsidies
5 - 42
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