Download - July23
Outline for Wednesday, July 23
� Remember
� Homework due Friday
� Midterm Monday
� Review Tuesday� Review Tuesday
� Income and substitution effects
� Production
Price-consumption curves
� What if we don’t have a Cobb-Douglas utility?
� If X is a necessity and we change PX… the PCC is vertical
� If X and Y are substitutes and we change PX… the PCC X
slopes down
� If X and Y are complements and we change PX… the PCC slopes up
� In particular, for perfect complements… the PCC does not depend on I or PY
� This is easier to see on graphs of Price and Quantity
4
Y� ICCa:
� Cars – normal
� Houses – normal
� ICCb: � Cars – normal
� Houses – inferior
(Cars)
3
4
5
ICCa
Income-consumption curves
ICCb
7/27/2008M. L. Williams, Department of Economics, PSU
X
1 2 3 4 5
� Houses – inferior
� ICCc: � Cars – inferior
� Houses – normal
(Houses)
0
1
2
BL2BL1
ICCcThere must be AT
LEAST ONE normal
good
5
Y
� ICCa� Cars – luxury
� Houses – necessity
� ICCb
(Cars)
3
4
5
ICCa
Income-consumption curves
ICCb ICCc
7/27/2008M. L. Williams, Department of Economics, PSU
X
1 2 3 4 5
� ICCb
� Cars – necessity
� Houses – luxury
� ICCc
� Both are unit elastic
� Cobb-Douglas case(Houses)
0
1
2
BL2BL1
Why income elasticity matters?
� How will taxpayers spend their rebate checks?
� The government wants to increase consumer spending as part of a “stimulus package”
� What share of the stimulus will go to consumption?
Why income elasticity matters?
� How will taxpayers spend their rebate checks?
� Marginal propensity to consume
Why income elasticity matters?
� How will taxpayers spend their rebate checks?
� Marginal propensity to consume
� Marginal propensity to save
� Marginal propensity to work less� Marginal propensity to work less
� Marginal to pay off debt
Why income elasticity matters?
� How will taxpayers spend their rebate checks?
� Marginal propensity to consume
� Marginal propensity to save
� Marginal propensity to work less� Marginal propensity to work less
� Marginal to pay off debt ���� not in our model
Why income elasticity matters?
� How will taxpayers spend their rebate checks?
� Marginal propensity to consume
� Marginal propensity to save
� Marginal propensity to work less� Marginal propensity to work less
� We could assume a utility function of the form
and estimate α, β, and γ
γβαSLCU =
Why income elasticity matters?
� How will taxpayers spend their rebate checks?
� We could assume a utility function of the form
and estimate α, β, and γ
γβαSLCU =
and estimate α, β, and γ
� What’s the effect on consumer spending?
Why income elasticity matters?
� How will taxpayers spend their rebate checks?
� We could assume a utility function of the form
and estimate α, β, and γ
γβαSLCU =
and estimate α, β, and γ
� What’s the effect on consumer spending?
rebate×++ γβα
α
Why income elasticity matters?
� How will taxpayers spend their rebate checks?
� We could assume a utility function of the form
and estimate α, β, and γ
γβαSLCU =
and estimate α, β, and γ
� What’s the effect on consumer spending?
� Cobb-Douglas is unit income elastic, so the same fraction is spent by consumers of all income levels
rebate×++ γβα
α
Outline for Wednesday, July 23
� Remember
� Homework due Friday
� Midterm Monday
� Review Tuesday� Review Tuesday
� Income and substitution effects
� Production
What happens when PX rises?
� X becomes less attractive relative to Y
� Fewer bundles of X and Y are affordable
What happens when PX rises?
� X becomes less attractive relative to Y
SUBSTITUTION EFFECT
� Fewer bundles of X and Y are affordable
INCOME EFFECT
What happens when PX rises?
� X becomes less attractive relative to Y
SUBSTITUTION EFFECT
How would the price change affect decisions on the same indifference curve?same indifference curve?
� Fewer bundles of X and Y are affordable
INCOME EFFECT
What happens when PX rises?
� X becomes less attractive relative to Y
SUBSTITUTION EFFECT
How would the price change affect decisions on the same indifference curve?same indifference curve?
� Fewer bundles of X and Y are affordable
INCOME EFFECT
What change results from the change in income alone?
Un
its o
f g
oo
d Y
f
Income and substitution effects: normal goodIncome and substitution effects: normal goodU
nits o
f g
oo
d
I1
I2
I3
I4
I5
I6B1
f
QX1Units of Good X
Un
its o
f g
oo
d Y
h
f
Rise in the priceof good X
Income and substitution effects: normal goodIncome and substitution effects: normal goodU
nits o
f g
oo
d
I1
I2
I3
I4
I5
I6
B2 B1
QX1
f
Units of Good XQX3
Un
its o
f g
oo
d Y
h
f
Substitution effectof the price rise
g
Income and substitution effects: normal goodIncome and substitution effects: normal goodU
nits o
f g
oo
d
B2
Substitutioneffect
B1
QX1
fI1
I2
I3
I4
I5
I6
QX
2
B1a
Units of Good XQX3
Un
its o
f g
oo
d Y
h
f
g
Income effect ofthe price rise
Income and substitution effects: normal goodIncome and substitution effects: normal good
Units of Good X
Un
its o
f g
oo
d
I1
I2
I3
I4
I5
I6
Substitutioneffect
Incomeeffect
QX1
f
B2 B1
QX2QX3
B1a
What happens when PX rises?
Start at (X0, Y0) and U0 � (X1, Y1) and U1
What happens when PX rises?
Start at (X0, Y0) and U0 � (X1, Y1) and U1
� SUBSTITUTION EFFECT
Change PX
Hold U constantHold U0 constant
What happens when PX rises?
Start at (X0, Y0) and U0 � (X1, Y1) and U1
� SUBSTITUTION EFFECT
Change PX
Hold U constantHold U0 constant
(X0, Y0) and U0 � (XS, YS) and US = U0
Un
its o
f g
oo
d Y
h
f
Substitution effectof the price rise
g
Income and substitution effects: normal goodIncome and substitution effects: normal goodU
nits o
f g
oo
d
B2
Substitutioneffect
B1
QX1
fI1
I2
I3
I4
I5
I6
QX
2
B1a
Units of Good XQX3
What happens when PX rises?
Start at (X0, Y0) and U0 � (X1, Y1) and U1
� SUBSTITUTION EFFECT
Change PX
Hold U constantHold U0 constant
(X0, Y0) and U0 � (XS, YS) and US = U0
� INCOME EFFECT
Hold PX, PY constant
Change income
What happens when PX rises?
Start at (X0, Y0) and U0 � (X1, Y1) and U1
� SUBSTITUTION EFFECT
Change PX
Hold U constantHold U0 constant
(X0, Y0) and U0 � (XS, YS) and US = U0
� INCOME EFFECT
Hold PX, PY constant
Change income
(XS, YS) and US = U0 � (X1, Y1) and U1
Un
its o
f g
oo
d Y
h
f
g
Income effect ofthe price rise
Income and substitution effects: normal goodIncome and substitution effects: normal good
Units of Good X
Un
its o
f g
oo
d
I1
I2
I3
I4
I5
I6
Substitutioneffect
Incomeeffect
QX1
f
B2 B1
QX2QX3
B1a
What happens when PX falls?
� SUBSTITUTION EFFECT
MRS is falling with X (Diminishing MRS), so…
What happens when PX falls?
� SUBSTITUTION EFFECT
MRS is falling with X, so…
PX falls � MRT falls � MRS falls � X rises
20
30 a
b
Un
its o
f g
oo
d Y
26
∆Y = 4
∆X = 1
MRS = 4
MRS = ∆∆∆∆Y/∆∆∆∆X
Deriving the marginal rate of substitution (MRS)Deriving the marginal rate of substitution (MRS)
Diminishing marginal
rate of substitution
0
10
0 10 20
Un
its o
f g
oo
d
Units of good X
6 7
d∆Y = 1
∆X = 1
MRS = 1
13 14
9
c
rate of substitution
What happens when PX falls?
� SUBSTITUTION EFFECT
MRS is falling with X, so X rises
We say the substitution effect is always
positive for decreases in price, and positive for decreases in price, and
negative for increases in price
It increases X after a fall in price
What happens when PX falls?
� SUBSTITUTION EFFECT
MRS is falling with X, so X rises
positive
� INCOME EFFECT
X may rise or fall with income – inferior or normal
What happens when PX falls?
� SUBSTITUTION EFFECT
MRS is falling with X, so X rises
positive
� INCOME EFFECT
X may rise or fall with income
positive - normal goods, same as substitution
or negative - inferior goods, opposite of sub.
What happens when PX falls?
Type of good Substitution Income Total effect
Normal + + +
Inferior + – ?
What happens when PX falls?
Type of good Substitution Income Total effect
Normal + + +
Inferior + –+
–
What happens when PX falls?
Type of good Substitution Income Total effect
Normal + + +
Inferior + –+
–
�The table reverses for rises in PX
Type of good Substitution Income Total effect
Normal – – –
Inferior – + –
+
What happens when PX falls?
� For inferior goods we need to know
Type of good Substitution Income Total effect
Normal + + +
Inferior + –+
–
� For inferior goods we need to know
which effect is greater
� Can we write that in an equation?
What happens when PX falls?
� For inferior goods we need to know
Type of good Substitution Income Total effect
Normal + + +
Inferior + –+
–
� For inferior goods we need to know
which effect is greater
� Can we write that in an equation?
� The total effect is the price elasticity, ε
� The income effect is from the income elasticity, ξ
� What is the substitution effect?
20
30 a
b
Un
its o
f g
oo
d Y
26
∆Y = 4
∆X = 1
MRS = 4
MRS = ∆∆∆∆Y/∆∆∆∆X
Compensated demandCompensated demand
Diminishing marginal
rate of substitution
0
10
0 10 20
Un
its o
f g
oo
d
Units of good X
6 7
d∆Y = 1
∆X = 1
MRS = 1
13 14
9
c
rate of substitution
Un
its o
f g
oo
d Y
26
For any slope, gives us a point
along the indifference curve
Compensated demandCompensated demand
Compensated Demand
Un
its o
f g
oo
d
Units of good X
6 7 13
10
What is the marginal effect of a change in PX?
� What is the equation for marginal price changes?
� The substitution effect is the elasticity of compensated demand, ε*
What is the marginal effect of a change in PX?
� What is the equation for marginal price changes?
� The substitution effect is the elasticity of compensated demand, ε*
� The income effect is the income elasticity, ξ, times the share of income spent on the good, θ, times -1
� If only a small part is spent on the good, the effect will be smaller
� If all of the consumer’s income is spent on the good
� We are reducing income, so we take -θξ
What is the marginal effect of a change in PX?
� What is the equation for marginal price changes?
� The substitution effect is the elasticity of compensated demand, ε*
� The income effect is the income elasticity, ξ, times the share of income spent on the good, θ, times -1
� The total effect is the price elasticity, ε
θξεε −= *
The Slutsky equation
� We add the income and substitution effects
� ε* = elasticity of compensated demand
θξεε −= *
X
P
P
XX
UX
⋅
∆
∆
constant
� ξ = elasticity of income
� θ = share of income spent on X
XPUX ∆
constant
X
I
I
X⋅
∆
∆
YX
XX
YPXP
XP
I
XP
+=
The Slutsky equation
� We add the income and substitution effects
� ε* = elasticity of compensated demand
θξεε −= *
0
constant
<⋅
∆
∆
X
P
P
XX
UX
� ξ = elasticity of income
� θ = share of income spent on X
constant ∆ XPUX
?0 X
I
I
X⋅
∆
∆
10 <<I
XPX
><
The Slutsky equation
� When is a good Giffen, with a positive price elasticity?
θξεε −= *
The Slutsky equation
� When is a good Giffen, with a positive price elasticity?
θξεε −= *
* & 0 εθξθξ ><� The income effect is both
� negative (inferior)
� and stronger than the substitution effect
Un
its o
f g
oo
d Y
Income and substitution effects: Giffen goodIncome and substitution effects: Giffen good
f
I
Units of Good X
Un
its o
f g
oo
d
B1
QX1
I1
I2
Un
its o
f g
oo
d Y
f
I
Rise in the priceof good X
Income and substitution effects: Giffen goodIncome and substitution effects: Giffen good
Units of Good X
Un
its o
f g
oo
d
QX1
B2
QX3
I1
I2
h
B1
Un
its o
f g
oo
d Y
f
I
g
Substitution effectof the price rise
Income and substitution effects: Giffen goodIncome and substitution effects: Giffen good
Units of Good X
Un
its o
f g
oo
d
QX1
B2
h
QX3
I1
I2
QX2
B1a
Substitution effect
B1
Un
its o
f g
oo
d Y
f
I
g
Income effect ofthe price rise
Income and substitution effects: Giffen goodIncome and substitution effects: Giffen good
A positive income
Units of Good X
Un
its o
f g
oo
d
QX1
B2
h
QX3
I1
I2
QX2
Substitution effectIncome effect
B1
B1a
A positive income
effect that is bigger
than the negative
substitution effect. A
rise in price causes a
rise in consumption.
The Slutsky equation
� When is a good Giffen, with a positive price elasticity?
θξεε −= *
* & 0 εθξθξ ><� The income effect is both
� negative (inferior)
� and stronger than the substitution effect
� What if the effect is weaker?
� Price elasticity is still negative
� The demand curve still slopes downward
Un
its o
f g
oo
d Y
Income and substitution effects: Inferior (non-Giffen) goodIncome and substitution effects: Inferior (non-Giffen) good
f
Units of Good X
Un
its o
f g
oo
d
B1
f
QX1
I1
I2
Un
its o
f g
oo
d Y
f
Rise in the priceof good X
Income and substitution effects: Inferior (non-Giffen) goodIncome and substitution effects: Inferior (non-Giffen) good
Units of Good X
Un
its o
f g
oo
d
f
QX1
B2
QX3
I1
I2
h
B1
Un
its o
f g
oo
d Y
f
Substitution effectof the price rise
Income and substitution effects: Inferior (non-Giffen) goodIncome and substitution effects: Inferior (non-Giffen) good
g
Units of Good X
Un
its o
f g
oo
d
f
QX1
B2
h
QX2
I1
I2
Substitution effect
B1aB1
Un
its o
f g
oo
d Y
f
g
Income effect ofthe price rise
Income and substitution effects: Inferior (non-Giffen) goodIncome and substitution effects: Inferior (non-Giffen) good
A positive income
effect: a rise in price
partially offsetting the
Units of Good X
Un
its o
f g
oo
d
f
QX1
B2
QX2QX3
I1
I2
Substitution effect
h
Income effect
B1aB1
partially offsetting the
fall in consumption.
The Slutsky equation
� What is it for perfect complements?
θξεε −= *
The Slutsky equation
� What is it for perfect complements?
� There is no substitution: ε* = 0
� Goods are unit income elastic: ξ = 1
θξεε −= *
The Slutsky equation
� What is it for perfect complements?
� There is no substitution: ε* = 0
� Goods are unit income elastic: ξ = 1
� So, X falls by its share: ε = -θ
θξεε −= *
� So, X falls by its share: ε = -θ
Substitution Effects for Perfect Compliments
Fig. 4.10
From a book by Robert Frank
The Slutsky equation
� What is it for perfect complements?
� There is no substitution: ε* = 0
� Goods are unit income elastic: ξ = 1
� So, X falls by its share: ε = -θ
θξεε −= *
� So, X falls by its share: ε = -θ
� What is it for perfect substitutes?
The Slutsky equation
� What is it for perfect complements?
� There is no substitution: ε* = 0
� Goods are unit income elastic: ξ = 1
� So, X falls by its share: ε = -θ
θξεε −= *
� So, X falls by its share: ε = -θ
� What is it for perfect substitutes?
� Complicated – see the demand curve on A-31
Outline for Wednesday, July 23
� Remember
� Homework due Friday
� Midterm Monday
� Review Tuesday� Review Tuesday
� Income and substitution effects
� Production