1. L07
Slutsky Equation

2. Previous Class Demand function How the demand is affected by
p1 change, holding p2 and m constant
m change, holding p2 and m constant
p2 change, holding p1 and m constant
Geometric and analytical answer!
Classification of goods

3. Price Change p1’=1, Change p1=2, Fix p2=1 and m=10. x2 What happens to
1) a relative price?
2) a purchasing power (real income)?
Can we separate the two effects? x1

4. Today 2 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)

5. Change of Real Income p1’=1, p2=1 and m=10 and p1=2,
What m’ makes just affordable at x2 x1

6. 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

7. Real Income Changes Suppose p1, p2 changes to p1’, p2’ x2
Original budget constraint and choice
New budget constraint
Q: Real income
Increases
Decreases
Stays the same x1

8. Real Income Changes Suppose p1, p2, changes to p1’, p2’ x2
Original budget constraint and choice
New budget constraint x1

9. 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?”

10. Total Change x2
T.CH x1

11. Income Effect
Substitution effect x2 IE SE x1

12. Substitution and Income Effect
What happens to the demand
Instead of going directly, 2 steps:
Total Change SE IE

13. Cobb-Douglass example
Data , change

14. Cobb-Douglass example
Data , change

15. Perfect Complements
, change

16. Perfect Complements
, change

17. Normal, Inferior and Giffent goods
Normal Goods
Inferior goods
Effects: Reinforce or cancel out?

18. Normal Goods x2 x1

19. Slutsky’s Effects for Income-Inferior Goods
Normal good: demand increases in income.
Q: substitution and income effects
Always have the same sign
Always have opposite signs
Depends of assumed parameters

20. Inferior Goods x2 x1

21. Slutsky’s Effects for Inferior Goods
Some goods are inferior (i.e. demand is reduced by higher income).
Q: substitution and income effects
Always have the same sign
Always have opposite signs
Depends of assumed parameters

22. Giffen Goods x2 x1

23. 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.