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