lecture 7 micro eco

8/9/2019 Lecture 7 micro eco

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Price Change: Income andSubstitution Effects


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THE IMPACT OF A PRICE

CHANGEEconomists often separate theimpact of a price change into two

components: the substitution effect; and the income effect.


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THE IMPACT OF A PRICE

CHANGET he substitution effect involves thesubstitution of good x 1 for good x 2 or vice-versa due to a change in relative prices of the two goods.T he income effect results from an increaseor decrease in the consumers real incomeor purchasing power as a result of the

price change.T he sum of these two effects is called theprice effect .


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THE HICKSIAN METHODSir John R.Hicks (1904-1989)Awarded the Nobel Laureate inEconomics (with Kenneth J. Arrrow)in 1972 for work on generalequilibrium theory and welfareeconomics.


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THE HICKSIAN METHOD

X 2

X 1

E a

I1xa

Optimal bundle is E a , onindifference curve I 1.


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THE HICKSIAN METHOD

X 2

X 1

I1xa

E a

A fall in the price of X 1

T he budget line pivotsout from PP*


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THE HICKSIAN METHOD

X 2

X 1

Eb

I1

I2

xa xb

E a

T he new optimum isEb on I 2.

T he Total PriceEffect is x a to x b


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THE HICKSIAN METHOD

T o isolate the substitution effect we ask.what would the consumers optimal

bundle be if s/he faced the new lower pricefor X 1 but experienced no change in realincome?T his amounts to returning the consumer

to the original indifference curve (I 1)


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THE HICKSIAN METHOD

X 2

X 1

Eb

I1

I2

xa xb

E a




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THE HICKSIAN METHOD

X 2

X 1

I1

I2

xa xb

E aEb

Draw a line parallel tothe new budget line andtangent to the old

indifference curve


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THE HICKSIAN METHOD

X 2

X 1

E c I1

I2

xa xc xb

E aEb

T he new optimum on I 1 isat Ec. T he movement from

Ea to Ec (the increase in

quantity demanded fromX a to X c) is solely inresponse to a change in

relative prices


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THE HICKSIAN METHOD

X 2

X 1

I1

I2

SubstitutionEffect

E aEb

E c

T his is thesubstitution effect.

X a X c


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THE HICKSIAN METHOD

T o isolate the income effect Look at the remainder of the total

price effectT his is due to a change in realincome.


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THE HICKSIAN METHOD

X 2

X 1

I1

I2

Income Effect

E aEb

E c

T he remainder of the totaleffect is due to a change

in real income. T heincrease in real income is

evidenced by themovement from I 1 to I 2

X cX

b


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THE HICKSIAN METHOD

X 2

X 1

I1

I2

xa xc xb

Sub

Effect

Income

Effect

E aEb

E c


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HICKSIAN ANALYSIS and DEMAND CURVES

22111 x p x p M !

P 1

P 1*

22111 x p x p!A

A

B

B

C

Hicksian DemandCurve (A & C)

Marshallian Demand

Curve (A & B)

P

X 1

X1

P

A fall in pricefrom p 1 to p 1*

C


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HICKSIAN ANALYSIS and DEMANDCURVES

Hicksian (compensated) demandcurves cannot be upward-sloping

(i.e. substitution effect cannot bepositive)


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THE SLUTSKY METHODEugene Slutsky (1880-1948)Russian economist expelled from theUniversity of Kiev for participating instudent revolts.In his 1915 paper, On the theory of the Budget of the Consumer he

introduced Slutsky Decomposition.


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THE SLUTSKY METHOD

X 2

X 1

E a

I1xa

Optimal bundle is E a , onindifference curve I 1.


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THE SLUTSKY METHOD

X 2

X 1

I1xa

E a


T he budget line pivotsout from PP*


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THE SLUTSKY METHOD

X 2

X 1

Eb

I1

I2

xa xb

E a




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THE SLUTSKY METHODSlutsky claimed that if, at the new prices, less income is needed to buy the original

bundle then real income has increased more income is needed to buy the

original bundle then real income hasdecreased

Slutsky isolated the change in demand dueonly to the change in relative prices byasking What is the change in demandwhen the consumers income is adjustedso that, at the new prices, s/he can justafford to buy the original bundle?


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THE SLUTSKY METHOD

T o isolate the substitution effect weadjust the consumers money

income so that s/he change can justafford the original consumptionbundle.In other words we are holdingpurchasing power constant.


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THE SLUTSKY METHOD

X 2

X 1

Eb

I1

I2

xa xb

E a




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THE SLUTSKY METHOD

X 2

X 1

Eb

I1

I2

xa xb

E a

Draw a line parallelto the new budgetline which passes

through the point Ea.


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THE SLUTSKY METHOD

X 2

X 1

Eb

I3

I2

xa xb

E a

T he new optimumon I 3 is at Ec. T he

movement from Eato Ec is the

substitution effect

E c

xc


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THE SLUTSKY METHOD

X 2

X 1

Eb

I3

I2

xa

E a

T he new optimumon I 3 is at Ec. T he

movement from Eato Ec is the

substitution effect

E c

xc

Substitution Effect


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THE SLUTSKY METHOD

X 2

X 1

Eb

I3

I2E a

T he remainder of the total price effectis the Income Effect.

T he movement fromEc to Eb.

E c

xc

Income Effect

xb


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THE SLUTSKY METHOD for NORMALGOODS

Most goods are normal (i.e. demandincreases with income).

T he substitution and income effectsreinforce each other when a normalgoods own price changes.


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THE SLUTSKY METHOD for NORMAL GOODS

X 2

X 1

Eb

I3

I2E a

T he income andsubstitution effects

reinforce eachother.

E cxc xbxa


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Since both the substitution andincome effects increase demand

when own-price falls, a normalgoods ordinary demand curveslopes downwards.T he Law of Downward-SlopingDemand therefore always applies tonormal goods.

THE SLUTSKY METHOD for NORMALGOODS


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THE SLUTSKY EQUATION

Let

be the original budget constraintand let

22111 x p x p M !

22112 x p x p!

represent the budget constraint after theSlutsky compensating variation in incomehas been carried out.


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X 2

X 1

E a

xa

22111 x p x p M !

22112 x p x p M !

Demand for x 1 is

M p p x x d ,, 211 !M2 < M1


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TH E SLU T SKY EQUA T IONM2 - M1

1111111112

111112

2211221112

2211221112

-

-M

-M

-M

-M

p p pas p x M

p p x M M

x p x p M M

x p x p x p x p M M

x p x p x p x p M M

(!(!(

!!(

!!(

!!(

!!(

( M=x 1( p 1gives the change in moneyincome needed toconsume the original

bundle of goods (at E A)


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1211211 ,,,,M

p p x M

p p x x d d !(

T he demand curve holding Mconstant is given by

which is the change in demand for x 1 due to

the change in its own price, holding M andthe price of x 2 constant

(1)


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,,,, 121221 M p p x M p p x x d d s !(

T he change in demand due to the Slutsky

substitution effect is given by

(3)

,,,, 221121 M p p x M p p x x d d m !(

T he income effect is given by

(2)


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ms x x x ((!( 1Divide across by ( p 1

111

1

p x

p x

p x ms

(

(

(

(!

(

(

Recall 11 p x M (!(

so 11 )( x M p (!(


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Substituting

11 )( x p (!(

111

1

p x

p x

p x m s

(

(

(

(!

(

(

G ives1

11

1 x M x

p x

p x ms

((

((!

(( T HESLU T SKY

EQUA T ION


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THE SLUTSKY METHOD: INFERIOR GOODS

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

income).T he substitution and income effectsoppose each other when aninferior goods own price changes.


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THE SLUTSKY METHOD: INFERIOR GOODS

X 2

X 1

Eb

I3

I2E a

T he substitutioneffect is as per usual. But, the

income effect is

in the oppositedirection.

E cxcxbxa

xa to x cxc to x b


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GIFFEN GOODS

In rare cases of extreme inferiority,the income effect may be larger in

size than the substitution effect,causing quantity demanded to riseas own price falls.Such goods are G iffen goods.G iffen goods are very inferior goods.


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THE SLUTSKY METHOD for INFERIOR GOODS

X 2

X 1

Eb

I3

I2

E a

In rare cases of extreme income-inferiority, the income

effect may be larger in size than the

substitution effect,causing quantity

demanded to fall asown-price falls.

E cxb xcxa

xa to x c

xc to x b


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SLUTSKYS EFFECT FOR GIFFEN GOODS

Slutskys decomposition of the effectof a price change into a pure

substitution effect and an incomeeffect thus explains why the Law of Downward-Sloping Demand isviolated for very inferior goods.


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D ECO POSI T ION of T O T AL PRICE EFFEC T :PERFEC T CO PLE EN T S

I1 I2 No substitutioneffect

X 2

X 1

A=C

BOriginal

BudgetConstraint

NewBudgetConstraint



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D ECO POSI T ION of T O T AL PRICE EFFEC T PERFEC T SUBS T IT UT ES

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lecture 7 micro eco

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