# Hicks and Slutsky Decomposition of Price Effect

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Hicks & Slutsky Decomposition of Price Effect

Hicks & Slutsky Decomposition of Price Effect

Compiled by

Compiled by

Nilanjan Patra

Nilanjan Patra

( (nilanjan@econdse.org) )

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Compiled by: Nilanjan Patra

Compiled by: Nilanjan Patra

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Hicks & Slutsky Decomposition of Price Effect

Hicks & Slutsky Decomposition of Price Effect

Representative rational consumer maximizes utility subject to the budget constraint.

Objective: to see the effect on the change in demand of good-1 for a fall in its price and its

decomposition.

Price of good-1 falls, price of good-2 and income remain unchanged.

When price of good-1 falls, two things happen: a) relative price of good-1 falls, and b) real

income or purchasing power rises.

Price effect: if good-1 is a normal good, its demand goes up due to fall in its price (inverse

relationship between price and quantity and hence price effect is negative). It can be

decomposed into two parts: a) Substitution effect (two concepts due to Hicks and Slutsky),

and b) Income effect.

Substitution effect (Hicks): it measures change in demand for good-1 due to change in relative

price of good-1 after compensating (here, reduce income e.g., by income tax) for the change

in income so that the consumerâ€™s utility level remains unchanged.

Substitution effect (Slutsky): it measures change in demand for good-1 due to change in

relative price of good-1 after compensating (here, reduce income e.g., by income tax) for the

change in income so that the consumerâ€™s purchasing power remains unchanged, i.e., he can

afford the previous commodity bundle if he wish.

Income effect: it measures change in demand for good-1 due to having more purchasing

power (in our case, let the govt. returns the same taxed amount by lump-sum transfers),

relative price remains unchanged.

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Compiled by: Nilanjan Patra

Compiled by: Nilanjan Patra

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Hicks & Slutsky Decomposition of Price Effect

Hicks & Slutsky Decomposition of Price Effect

Figure-1: Decomposition of Price Effect ( Hicks & Slutsky)

A

B

B'

X1

X2

P1falls, ceteris paribus

e0

.

O

e1

.

x10

x11

eH

x1H

.

.eS

x1S

C

C'

D D'

..

.

. .

.

..

.

.

F

..G

.

H

IC0

IC1

ICS

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Compiled by: Nilanjan Patra

Compiled by: Nilanjan Patra

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Hicks & Slutsky Decomposition of Price Effect

Hicks & Slutsky Decomposition of Price Effect

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AB initial budget line. Consumer is on

AB initial budget line. Consumer is on IC0. Equilibrium at e0consuming 0x10 of x1.

After P1falls, new budget line becomes AB'. Consumer is on IC1. Equilibrium at e1

consuming 0x11 of x1.

So, price effect of fall in P1 (movement from e0to e1)is rise in consumption of x1by x10 x11

(negative for normal good).

S.E. (Hicks): Draw a budget line CD tangential to IC0and parallel to AB'. Point of tangency

is at eH. Movement from e0to eHis due to Hicksian S.E. (negative), which raises demand by

x10 x1H .

S.E. (Slutsky): Draw a budget line C'D' that passes through e0and parallel to AB'. Consumer

will now reach a higher utility level given by ICS. Point of tangency is at eS. Movement from

e0to eSis due to Slutsky S.E. (negative), which raises demand by x10 x1S .

Income effect: For Hicksian (Slutsky) case I.E. is given by a movement from eH (eS) to e1and

demand increases by x1H x11 (x1S x11 ). So as P1 falls, real income or purchasing power goes up

that in turn raises demand for the normal good x1.Thus I.E. is also negative for a normal

good.

As income elasticity for a normal good is positive, point e1 must lie on AB' to the right of

point F (G) in Hicksian (Slutsky) case.

As income elasticity for an inferior good is negative, point e1 must lie on AB' between HF

(HG) in Hicksian (Slutsky) case. Thus I.E. is positive but weaker than the negative S.E.

Hence P.E. is still negative.

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Compiled by: Nilanjan Patra

Compiled by: Nilanjan Patra

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Hicks & Slutsky Decomposition of Price Effect

Hicks & Slutsky Decomposition of Price Effect

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As income elasticity for a Giffen (also an inferior good) good is negative, point e1 must lie on

AB' to the left of H in both cases. Thus I.E. is positive but stronger than the negative S.E.

Hence P.E. becomes positive. In this case we will get an upward sloping demand curve.

Summary

Substitution

Effect

Negative

Negative

Negative

Income

Effect

Negative

Positive

Positive

Price

Effect

Negative

Normal Good

Inferior Good

Giffen Good

Negative (S.E. > I.E.)

Positive (S.E. < I.E.)