Jain University - MA Econom

ics 2015

SLUTSKY’S THEOREM Presented by Suparna Pani

Date – 10/5/2015

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Jain University - MA Econom

ics 2015

INTRODUCTION

When price of something goes down, we buy more of it. This lead to two effect:

INCOME EFFECT : it becomes less expensive , we have more purchasing power

SUBSTITUTION EFFECT: it offers more utility per unit of money

Price effect is the sum of substitution effect and income effect for a price change which is known as slutsky’s theorem

Jain University - MA Econom

ics 2015

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Marshallian demand

orUncompensated demand curve

Hicksian demand

orCompensated

demand curve

Slutskytheorem

1.It deals with how demand changes when price changes holding money income constant

2.It maximise utlity given price and wealth

3.Marshallian demand is easier to observe

1.It deals with how demand changes when price changes holding the real income constant or utility constant

2.It minimise expenditure

3.Hicksian demand is more mathematically tractable

1.It is the total (Marshallian) price effect is equal to the sum of the substitution effect

(i.e,Hickisan price effect) plus income effect. Both function are related by slutsky eqation.

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Jain University - MA Econom

ics 2015

MATHEMATICALLYIts based on derivation of marshallian and hicksian demand∂xi⁄ ∂pj = ∂hi/ ∂pi – (xj* (∂xi/ ∂m)) TE SE IE Total effect: it shows total quantity of x that we

consume varies when we change price Substitution effect: Variation is due to finding similar

product(obtain from derivation of the Hicksian demand with regard price)

Income effect: change in our purchasing power affect the amount we consume of a certain goods(derivation of Marshallian demand with regard wealth)

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Jain University - MA Econom

ics 2015

GRAPHICALLY

Jain University - MA Econom

ics 2015ANALYSIS OF AGGREGATE EFFECT – DIFFERENT GOODS

Price Substitution Effect

Income Effect Total Effect = Substitution

Effect + Income Effect

Normal good ↓ X _ ↓ X _ ↓X+ ↓ X= ↓X( _)

Inferior good

1.[SE]>[IE]

2.[SE]<[IE]{Giffen goods}

3.[SE]=[IE]

↓ X _

↓↓ X _ ↓ X _

↓ X _

↑ X +

↑ X + ↑↑ X +

↑ X +

↓ X+ ↑ X= X ?

↓ ↓X+ ↑ X=↓ X(_)

↓ X+↑↑ X=↑X(+)

↓ X+ ↑ X=X

Independent good ↓ X _ X:constant(no income effect)

↓ X+ 0= ↓ X( _)

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Jain University - MA Econom

ics 2015

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