Income and substitution effect in economics

Income and substitution effect in economics

1. PriceChange:
Incomeand
Price
Change:

Income
and

Substitution Effects

2. THE IMPACT OF A PRICE
CHANGE

Economists often separate the impactofapricechangeintotwo impact

of

a

price

change

into

two

components:
h
bii ff
d
–
t
h
e su
b
st
i
tut
i
on e
ff
ect; an
d
–
the
incomeeffect
.
the

income

effect
.

3. THE IMPACT OF A PRICE
CHANGE

The substitution effectinvolves the
substitution of good x
1
for good x
2
or vice-
versa due to a change in relative pricesof
the two goods.
ff
f

The income e
ff
ect results
f
rom an increase
or decrease in the consumer’s real income
or
purchasingpower
asaresultofthe
or
purchasing

power
as

a

result

of

the

price change.

Thesumofthesetwoeffectsiscalledthe

The

sum

of

these

two

effects

is

called

the

price effect.

4. THE IMPACT OF A PRICE
CHANGE

The decomposition of the price effect intotheincomeandsubstitution into

the

income

and

substitution

effect can be done in several ways
Th i h d

Th
ere are two ma
i
n met
h
o
d
s:
(i)The
Hicksian
method;and
(i)

The

Hicksian

method;

and
(ii) The Slutskymethod

5. THEHICKSIANMETHOD THE
HICKSIAN

METHOD

SirJohnR.Hicks(1904
-
1989)

Sir

John

R.Hicks

(1904
1989)

Awarded the Nobel Laureate in Ei(ithKthJA) E
conom
i
cs
(
w
ith

K
enne
th

J
.
A
rrrow
)

in 1972 for work on general
equilibrium theory and welfare economics.

6. THEHICKSIANMETHOD THE
HICKSIAN

METHOD
X
2
Optimal bundle is E
a
, on
indifference curve I
1.
E
a
E
a
I
1
X
1
1
x
a

7. THEHICKSIANMETHOD THE
HICKSIAN

METHOD
Aflli th i fX
X
2
A

f
a
ll

i
n
th
e pr
i
ce o
f

X
1
The bud
g
et line
p
ivots
*
gp
out from P
P
*
E
a
I
1
E
a
X
1
1
x
a

8. THEHICKSIANMETHOD THE
HICKSIAN

METHOD
Thenewoptimumis
X
2
The

new

optimum

is

E
b
on I
2
.
The Total Price Effect is x
a
to x
b
E
b
I
2
E
a
I
1
I
2
E
a
X
1
1
x
a
x
b

9. THEHICKSIANMETHOD THE
HICKSIAN

METHOD

To isolate the substitution effect we ask….
“
whatwouldtheconsumer
’
soptimal
what

would

the

consumers

optimal

bundle be if s/he faced the new lower price
forX
1
butexperiencednochangeinreal
for

X
1
but

experienced

no

change

in

real

income?”

Thisamountstoreturningtheconsumer

This

amounts

to

returning

the

consumer

to the original indifference curve (I
1
)

10. THEHICKSIANMETHOD THE
HICKSIAN

METHOD
Thenewoptimumis
X
2
The

new

optimum

is

E
b
on I
2
.
The Total Price Effect is x
a
to x
b
E
b
I
2
E
a
I
1
I
2
E
a
X
1
1
x
a
x
b

11. THEHICKSIANMETHOD THE
HICKSIAN

METHOD
Drawalineparallelto
X
2
Draw

a

line

parallel

to

the new budget line and
tangenttotheold tangent

to

the

old

indifference curve
I
2
E
a
E
b I
1
I
2
E
a
X
1
1
x
a
x
b

12. THEHICKSIANMETHOD THE
HICKSIAN

METHOD
ThenewoptimumonI
1
is
X
2
The

new

optimum

on

I
1
is

at Ec. The movement from
EatoEc
(
theincreasein
Ea

to

Ec

(
the

increase

in

quantity demanded from
XatoXc
)
issolelyin
I
2
E
a
E
b
Xa

to

Xc
)

is

solely

in

response to a change in
relativeprices
E
c
I
1
I
2
E
a
relative

prices
X
1
x
a
x
c
x
b

13. THEHICKSIANMETHOD THE
HICKSIAN

METHOD
Thi i th
X
2
Thi
s
i
s
th
e
substitution effect.
I
2
E
a
E
b I
1
I
2
E
a
E
c
X
1
1
Sbtitti
X
a
X
S
u
b
s
tit
u
ti
on
Effect
X
a
X
c

14. THEHICKSIANMETHOD THE
HICKSIAN

METHOD

To isolate the income effect …

Lookattheremainderofthetotal

Look

at

the

remainder

of

the

total

price effect

This is due to a change in real income. income.

15. THEHICKSIANMETHOD THE
HICKSIAN

METHOD
The remainder of the total
X
2
effect is due to a change
in real income. The
increase in real income is
evidenced b
y
the
I
2
E
a
E
b
y
movement from I
1
to I
2
I
1
I
2
E
a
E
c
X
1
1
ff
X
c
Income E
ff
ect
X
c
X
b

16. THEHICKSIANMETHOD THE
HICKSIAN

METHOD
X
2
I
2
E
a
E
b I
1
I
2
E
a
E
c
X
1
1
x
a
x
c
x
b
Sb
I
S
u
b

Effect
I
ncome
Effect

17. HICKSIAN ANALYSIS and DEMAND CURVES
P
A fall in price
fromp
top
*

22 11 1
xp xp M

B
from

p
1
to

p
1

22 11 1
xp xp M 

A
B
C
A
MarshallianDemand
X
1
PP
1
A
B
Marshallian

Demand

Curve (A &B)
P
1
*
B
Hicksian Demand Curve(A & C)
C
X
1

18. HICKSIAN ANALYSIS and DEMAND
CURVES
Hicksian (compensated) demand curvescannotbeupward
-
sloping
curves

cannot

be

upward
sloping

(i.e. substitution effect cannot be
positive) positive)

19. THESLUTSKYMETHOD THE
SLUTSKY

METHOD

EugeneSlutsky(1880
-
1948)

Eugene

Slutsky

(1880
-
1948)


Russian economist expelled from the University of Kiev for participating in
student revolts.

In his 1915 paper, “On the theory of theBudgetoftheConsumer
”
he
the

Budget

of

the

Consumer

he

introduced “Slutsky Decomposition”.

20. THESLUTSKYMETHOD THE
SLUTSKY

METHOD
X
2
Optimal bundle is E
a
, on
indifference curve I
1.
E
a
E
a
I
1
X
1
1
x
a

21. THESLUTSKYMETHOD THE
SLUTSKY

METHOD
Aflli th i fX
X
2
A

f
a
ll

i
n
th
e pr
i
ce o
f

X
1
The bud
g
et line
p
ivots
*
gp
out from P
P
*
E
a
I
1
E
a
X
1
x
a

22. THESLUTSKYMETHOD THE
SLUTSKY

METHOD
Thenewoptimumis
X
2
The

new

optimum

is

E
b
on I
2
.
The Total Price Effect is x
a
to x
b
E
b
I
2
E
a
I
1
I
2
E
a
X
1
x
a
x
b

23. THE SLUTSKY METHOD

Slutsky claimed that if, at the new prices,
–
lessincomeisneededtobuytheoriginal less

income

is

needed

to

buy

the

original

bundle then “real income” has increased
–
moreincomeisneededtobuythe more

income

is

needed

to

buy

the

original bundle then “real income” has
decreased

Slutsky isolated the change in demand due only to the change in relative prices by asking “What is the change in demand when the consumer’s income is adjusted
th t tth i /h j t
so
th
a
t
, a
t

th
e new pr
i
ces, s
/h
e can
j
us
t

afford to buy the original bundle?”

24. THESLUTSKYMETHOD THE
SLUTSKY

METHOD

To isolate the substitution effect we adjusttheconsumer
’
smoney
adjust

the

consumers

money

income so that s/he change can just
affordtheoriginalconsumption afford

the

original

consumption

bundle.

In other words we are holding purchasingpowerconstant. purchasing

power

constant.

25. THESLUTSKYMETHOD THE
SLUTSKY

METHOD
Thenewoptimumis
X
2
The

new

optimum

is

E
b
on I
2
.
The Total Price Effect is x
a
to x
b
E
b
I
2
E
a
I
1
I
2
E
a
X
1
x
a
x
b

26. THESLUTSKYMETHOD THE
SLUTSKY

METHOD
Drawalineparallel
X
2
Draw

a

line

parallel

to the new budget
line
whichpasses
line

which

passes

through
the point
Ea
E
b
I
2
E
a
Ea
.
I
1
I
2
E
a
X
1
I
1
x
a
x
b

27. THESLUTSKYMETHOD THE
SLUTSKY

METHOD
The new optimum
I
itETh
X
2
on
I
3
i
s a
t

E
c.
Th
e
movement from Ea
tEith t
o
E
c
i
s
th
e
substitution effect
E
b
I
2
E
a
I
3
I
2
E
a
E
c
X
1
3
x
a
x
b
x
c

28. THESLUTSKYMETHOD THE
SLUTSKY

METHOD
The new optimum
I
itETh
X
2
on
I
3
i
s a
t

E
c.
Th
e
movement from Ea
tEith t
o
E
c
i
s
th
e
substitution effect
E
b
I
2
E
a
I
3
I
2
E
a
E
c
X
1
3
x
a
x
c
Substitution Effect

29. THESLUTSKYMETHOD THE
SLUTSKY

METHOD
The remainder of
th t t l i ff t
X
2
th
e
t
o
t
a
l
pr
i
ce e
ff
ec
t

is theIncomeEffect.
The movement from
EctoEb.
E
b
I
2
E
a
Ec

to

Eb.
I
3
I
2
E
a
E
c
X
1
3
x
c
IncomeEffect
x
b
Income

Effect

30. THE SLUTSKY METHOD for NORMAL
GOODS

Most goods are normal (i.e. demand increaseswithincome) increases

with

income)
.

The substitution and income effects
if h h h l
re
i
n
f
orce eac
h
ot
h
er w
h
en a norma
l

g
ood’s own price chan
g
es.
gg

31. THE SLUTSKY METHOD for
NORMALGOODS NORMAL

GOODS
The income and
b tit ti ff t
X
2
su
b
s
tit
u
ti
on e
ff
ec
t
s
reinforce each
th
o
th
er.
E
b
I
2
E
a
I
3
I
2
E
a
E
c
X
1
3
x
c
x
b
x
a

32. THE SLUTSKY METHOD for NORMAL
GOODS

Since both the substitution and incomeeffectsincreasedemand income

effects

increase

demand

when own-price falls, a normal
good’sordinarydemandcurve good’s

ordinary

demand

curve

slopes downwards.

The “Law” of Downward-Sloping Demandthereforealwaysappliesto Demand

therefore

always

applies

to

normal goods.

33. THE SLUTSKY E
Q
UATION
Q
LetLet


2 2 1 1 1
x
p
x
p
M


be the original budget constraint andlet and

let


2 2 1 1 2
xp xp M 

represent the budget constraint after the Slutsky compensating variation in income
has been carried out.

34. THE
S
L
U
T
S
KY E
QU
ATI
ON
SUS QU ON
Demandforx
1
is
X
2
Demand

for

x
1
is



M
p
p
x
x
d
,
,
2
1
1

M
2
< M
1


p
p
,
,
2
1
1
E
a

22 11 1
xp xp M


E
a
X
1
x
a
x
p
x
p
M




22 11 2
x
p
x
p
M



35. THE SLUTSKY EQUATION
M
2
-M
1




M
x
p
x
p
x
p
x
p
M
M










2
2
1
1
2
2
1
1
1
2
22 11 22 11 1 2
-
M
-
M
x
p
x
p
x
p
x
p
M
M
x
p
x
p
x
p
x
p
M
M













1
1
1
1
1
2
2
2
1
1
2
2
1
1
1
2
- M
M
x
p
x
p
M
M
x
p
x
p
x
p
x
p
M
M









1 1 1 1 2
1
1
1
1
1
2
- Mp px M Mp
p
   



1 1 1 1 1
- p p p as px M   

ithh i

M=x
1

p
1
g
i
ves
th
e c
h
ange
i
n money
income needed to
consumetheoriginal
1
p
1
consume

the

original

bundle of goods (at E A
)

36. THE
S
L
U
T
S
KY E
QU
ATI
ON
SUS QU ON
The demand curve holdin
g
M
g
constant is given by




1 2 1 1 2 1 1
, , , ,Mpp x Mp p x x
d d
  

(1)
whichisthechangeindemandforx
1
dueto
which

is

the

change

in

demand

for

x
1
due

to

the change in its own price, holding M and
thepriceofx
2
constant
the

price

of

x
2
constant

37. THE SLUTSKY E
Q
UATION
Q




The income effect is given by



 , , , ,
2 2 1 1 2 1
Mp p x Mp p x x
d d
m





(2)
ThechangeindemandduetotheSlutsky The

change

in

demand

due

to

the

Slutsky

substitution effect is given by



, , , ,
1 2 1 2 2 1
Mpp x Mp p x x
d d
s
  

(3)

38. THESLUTSKYEQUATION THE
SLUTSKY

EQUATION


Given








1 2 1 1 2 1 1
, , , ,Mpp x Mp p x x
d d
  

(1)


d
d




2 2 1 1 2 1
, , , ,Mp p x Mp p x x
d d
m





(2)



1 2 1 2 2 1
, , , ,Mpp x Mp p x x
d
d
s




(3)
x
x
x





1
Claim
(4)
m s
x
x
x





1
Showthisbysubstitutingequations(1),(2)
(4)
Show

this

by

substituting

equations

(1),

(2)

and (3) into equation (4)

39. THE SLUTSKY E
Q
UATION
Q m s
x x x





1
Divideacrossby

p
1
Divide

across

by


p
1
1
x x x
m
s



1 1 1
1
p p p
m
s





Recall
1 1
px M



so
1
1
)
(
x
M
p




1
1
)
(
p

40. THE SLUTSKY E
Q
UATION
Q
Substituting Substituting
1
1
)
(
x
M
p




1
1
)
(
p
1
x x x
m
s



1 1 1
1
p p p
m
s





Gives
1
x
x x x
m s




THE SLUTSKY
1
1 1
x
M p p




SLUTSKY

EQUATION

41. THE SLUTSKY METHOD: INFERIOR
GOODS

Some goods are (sometimes) inferior (ie demandisreducedbyhigher (i
.
e
.
demand

is

reduced

by

higher

income).
Th b i i di ff

Th
e su
b
st
i
tut
i
on an
d

i
ncome e
ff
ects
“oppose” each other when an
inferior good’s own price changes.

42. THE SLUTSKY METHOD: INFERIOR
GOODS GOODS
The substitution
ff ti
X
2
e
ff
ec
t

i
s as per
usual. But, the
iffti i
ncome e
ff
ec
t

i
s
in the opposite
di ti
E
b
I
2
E
a
di
rec
ti
on.
I
3
E
a
E
c
X
1
3
x
c
x
b
x
a
x
a
to
x
c
a
to
c
x
c
to x
b

43. GIFFENGOODS GIFFEN
GOODS

In rare cases of extreme inferiority, theincomeeffectmaybelargerin the

income

effect

may

be

larger

in

size than the substitution effect,
causingquantitydemandedtorise causing

quantity

demanded

to

rise

as own price falls.

Such goods are Giffen goods.

Giffengoodsareveryinferiorgoods

Giffen

goods

are

very

inferior

goods
.

44. THE SLUTSKY METHOD for
INFERIORGOODS INFERIOR
GOODS
In rare cases of
ti
X
2
ex
t
reme
i
ncome-
inferiority, the income
effectmaybelarger
E
b
I
2
effect

may

be

larger

in size than the
substitutioneffect
I
2
E
a
substitution

effect
,
causing quantity
de
m
a
n
ded

to
f
a
ll
as

I
3
E
a
de a dedto a as
own-price falls.
E
c
X
1
3
x
b
x
c
x
a
x
a
to x
c
x
c
to x
b

45. SLUTSKY’S EFFECT FOR
GIFFEN GOODS

Slutsky’s decomposition of the effect ofapricechangeintoapure of

a

price

change

into

a

pure

substitution effect and an income
effectthusexplainswhythe“Law”of effect

thus

explains

why

the

“Law”

of

Downward-Sloping Demand is
violatedfor very inferior goods.

46. DECOMPOSITION of TOTAL PRICE EFFECT:
PERFECT COMPLEMENTS
X
I
1
I
2
Nosubstitution
X
2
A
fall in the price of X
1
I
2
No

substitution

effect
B
New Budget
A=C
Original
Budget
Constraint
Budget

Constraint
Constraint
X
1

47. DECOMPOSITION of TOTAL PRICE EFFECT
PERFECT
SUBSTITUTES
PERFECT
SUBSTITUTES
?