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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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8/9/2019 Lecture 7 micro eco
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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
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
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
A fall in the price of X 1
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
T he new optimum isEb on I 2.
T he Total PriceEffect is x a to x b
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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
T he new optimum isEb on I 2.
T he Total PriceEffect is x a to x b
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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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THE SLUTSKY EQUATION
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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THE SLUTSKY EQUATION
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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THE SLUTSKY EQUATION
,,,, 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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THE SLUTSKY EQUATION
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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THE SLUTSKY EQUATION
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
A fall in the price of X 1
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D ECO POSI T ION of T O T AL PRICE EFFEC T PERFEC T SUBS T IT UT ES
?