# 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.

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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 and m constant c) p 2 change, holding p 1 and m constant Geometric and analytical answer! Classification of goods

Price Change x1x1 x2x2 Fix p 2 =1 and m=10. Change p 1 =2, p 1 =1, What happens to 1) a relative price? 2) a purchasing power (real income)? Can we separate the two effects?

Today 2 questions u How to measure Real Income (PP) u 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 x1x1 x2x2 p 1 =2, p 1 =1, What m makes just affordable at p 2 =1 and m=10 and Geometrically:

Real Income Change u 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

Real Income Changes x1x1 x2x2 Original budget constraint and choice New budget constraint Suppose p 1, p 2 changes to p 1, p 2 Real income?

Real Income Changes x1x1 x2x2 Original budget constraint and choice New budget constraint Suppose p 1, p 2, changes to p 1, p 2 Real income?

Real Income Changes x1x1 x2x2 Original budget constraint and choice New budget constraint Suppose P 1, P 2 changes to p 1, p 2 Real income?

Substitution and Income Effect u If P 1 changes, both relative price and real income are affected u Slutsky isolates the change in demand due only to the change in relative prices KEY IDEA: u What is the change in demand when the consumers income is adjusted (to m) so that, at the new prices, her real income is the same?

Total Change x2x2 x1x1 T.CH

Substitution effect x2x2 x1x1 SEIE Income Effect

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

Cobb-Douglass example Data, change

Perfect Complements, change

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

x2x2 x1x1 Normal Goods

Slutskys Effects for Income-Inferior Goods u Normal good: demand increases in income. u The substitution and income effects change demand in the same direction after own price changes.

x2x2 x1x1 Inferior Goods

Slutskys Effects for Inferior Goods u Some goods are inferior (i.e. demand is reduced by higher income). u The substitution and income effects oppose each other when an income- inferior goods own price changes.

x2x2 x1x1 Giffen Goods

Slutskys Effects for Giffen Goods u Slutskys 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.

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