L07 Slutsky Equation. Previous Class Demand function How the demand is affected by a) p 1 change, holding p 2 and m constant b) m change, holding p 2.

L07

Slutsky Equation

Previous Class

Demand function

How the demand is affected by

a) p1 change, holding p2 and m constant

b) m change, holding p2 and m constant

c) p2 change, holding p1 and m constant

Geometric and analytical answer!

Classification of goods

),,( 21*1 mppx

Price Change

x1

x2

Fix p2=1 and m=10. Change p1=2, p1’=1,

What happens to 1) a relative price?2) a purchasing power (real income)?

Can we separate the two effects?

Today2 questions How to measure Real Income (PP) Decomposition of the change in demand

– The effect resulting from the change of a relative price (substitution effect)

– The effect resulting from the change of real income (income effect)

Change of Real Income

x1

x2

10

p1=2, p1’=1,

5

10

)5,5.2(* x

What m’ makes just affordable at*x

p2=1 and m=10 and

'm

... then ' mmif

1,1' 21 pp

Geometrically:

Real Income Change

If, at the new prices,

– less income is needed to buy the original bundle then “real income” is increased

– more income is needed to buy the original bundle then “real income” is decreased

mm '

mm '

Real Income Changes

x1

x2

Original budget constraint and choice

New budget constraint

Suppose p1, p2 changes to p1’, p2’

Real income?

Real Income Changes

x1

x2

Original budget constraint and choice

New budget constraint

Suppose p1, p2, changes to p1’, p2’

Real income?

Real Income Changes

x1

x2

Original budget constraint and choice

New budget constraint

Suppose P1, P2 changes to p1’, p2’

Real income?

Substitution and Income Effect

If P1 changes, both relative price and real income are affected

Slutsky isolates the change in demand due only to the change in relative prices

KEY IDEA: “What is the change in demand when the

consumer’s income is adjusted (to m’) so that, at the new prices, her real income is the same?”

Total Changex2

x1

10

,1

,2

2

1

m

p

p

10

,1

,1

2

1

m

p

p

T.CH

)5,5()5,5.2('m

Substitution effectx2

x1

10

,1

,2

2

1

m

p

p

5.7'

,1

,1

2

1

m

p

p

SE

)5,5()5,5.2(

IE

5.7'

,1

,1

2

1

m

p

p

10'

,1

,1

2

1

m

p

p

Income Effect

Substitution and Income Effect

What happens to the demand

Instead of going directly, 2 steps:

10

,1

,2

2

1

m

p

p

10

,1

,1

2

1

m

p

p

10

,1

,2

2

1

m

p

p

5.7'

,1

,1

2

1

m

p

p

10

,1

,1

2

1

m

p

p

*1x

SE IE

Total Change

Cobb-Douglass example

),,( 21*1 mppx

Data , change20,1p , 222

21 mxxU

),,( 21*2 mppx

41 p 2

Perfect Complements

),,( 21*1 mppx

, change20,1p ),min( 221 mxxU

),,( 21*2 mppx

41 p 2

Normal, Inferior and Giffent goods

Normal Goods Inferior goods

Effects: Reinforce or cancel out?

x2

x1

Normal Goods

Slutsky’s Effects for Income-Inferior Goods

Normal good: demand increases in income.

The substitution and income effects change demand in the same direction after own price changes.

x2

x1

Inferior Goods

Slutsky’s Effects for Inferior Goods

Some goods are inferior (i.e. demand is reduced by higher income).

The substitution and income effects oppose each other when an income-inferior good’s own price changes.

x2

x1

Giffen Goods

Slutsky’s Effects for Giffen Goods

Slutsky’s decomposition of the effect of a price change into a pure substitution effect and an income effect thus explains why the Law of Downward-Sloping Demand is violated for extremely income-inferior goods.