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Price Change: Income and
Substitution Effects
THE IMPACT OF A PRICE
CHANGE
Economists often separate the
impact of a price change into two
components:
– the substitutio...
THE IMPACT OF A PRICE
CHANGE
The substitution effect involves the
substitution of good x1 for good x2 or viceversa due to ...
THE IMPACT OF A PRICE
CHANGE
The decomposition of the price effect
into the income and substitution
effect can be done in ...
THE HICKSIAN METHOD
Sir John R.Hicks (1904-1989)
Awarded the Nobel Laureate in
Economics (with Kenneth J. Arrrow)
in 1972 ...
THE HICKSIAN METHOD
Optimal bundle is Ea, on
indifference curve I1.

X2

Ea
I1
xa

X1
THE HICKSIAN METHOD
X2

A fall in the price of X1

P

The budget line pivots
out from P

*
Ea

I1
xa

X1
THE HICKSIAN METHOD
The new optimum is
Eb on I2.

X2

The Total Price
Effect is xa to xb
Ea

Eb

I2

I1
xa

xb

X1
THE HICKSIAN METHOD
To isolate the substitution effect we ask….
“what would the consumer’s optimal
bundle be if s/he faced...
THE HICKSIAN METHOD
The new optimum is
Eb on I2.

X2

The Total Price
Effect is xa to xb
Ea

Eb

I2

I1
xa

xb

X1
THE HICKSIAN METHOD
Draw a line parallel to
the new budget line and
tangent to the old
indifference curve

X2

Ea

Eb

I2
...
THE HICKSIAN METHOD
X2

Ea

The new optimum on I1 is
at Ec. The movement from
Ea to Ec (the increase in
quantity demanded ...
THE HICKSIAN METHOD
This is the
substitution effect.

X2

Ea

Xa

Eb
Ec

Substitution
Effect

I2

I1

Xc

X1
THE HICKSIAN METHOD
To isolate the income effect …
Look at the remainder of the total
price effect
This is due to a change...
THE HICKSIAN METHOD
The remainder of the total
effect is due to a change
in real income. The
increase in real income is
ev...
THE HICKSIAN METHOD
X2

Ea

Eb
Ec

xa xc

I2

I1
xb

Sub Income
Effect Effect

X1
HICKSIAN ANALYSIS and DEMAND CURVES
P

A fall in price
from p1 to p1*

M 1 = p1 x1 + p2 x 2

AC
P
P1
P1*

B
∗
M 1 = p1 x1 ...
HICKSIAN ANALYSIS and DEMAND
CURVES

Hicksian (compensated) demand
curves cannot be upward-sloping
(i.e. substitution effe...
THE SLUTSKY METHOD
Eugene Slutsky (1880-1948)
Russian economist expelled from the
University of Kiev for participating in
...
THE SLUTSKY METHOD
Optimal bundle is Ea, on
indifference curve I1.

X2

Ea
I1
xa

X1
THE SLUTSKY METHOD
X2

A fall in the price of X1

P

The budget line pivots
out from P

*
Ea
I1
xa

X1
THE SLUTSKY METHOD
The new optimum is
Eb on I2.

X2

The Total Price
Effect is xa to xb
Ea
xa

Eb
I1
xb

I2

X1
THE SLUTSKY METHOD
Slutsky claimed that if, at the new prices,
– less income is needed to buy the original
bundle then “re...
THE SLUTSKY METHOD
To isolate the substitution effect we
adjust the consumer’s money
income so that s/he change can just
a...
THE SLUTSKY METHOD
The new optimum is
Eb on I2.

X2

The Total Price
Effect is xa to xb
Ea
xa

Eb
I1
xb

I2

X1
THE SLUTSKY METHOD
Draw a line parallel
to the new budget
line which passes
through the point
Ea.

X2

Eb

Ea
xa

I1

xb

...
THE SLUTSKY METHOD
The new optimum
on I3 is at Ec. The
movement from Ea
to Ec is the
substitution effect

X2

Eb

Ea
Ec
xa...
THE SLUTSKY METHOD
The new optimum
on I3 is at Ec. The
movement from Ea
to Ec is the
substitution effect

X2

Eb

Ea
Ec
xa...
THE SLUTSKY METHOD
The remainder of
the total price effect
is the Income Effect.

X2

The movement from
Ec to Eb.
Eb

Ea
E...
THE SLUTSKY METHOD for NORMAL
GOODS
Most goods are normal (i.e. demand
increases with income).
The substitution and income...
THE SLUTSKY METHOD for
NORMAL GOODS

The income and
substitution effects
reinforce each
other.

X2

Eb

Ea
Ec
xa

xc

I2

...
THE SLUTSKY METHOD for NORMAL
GOODS
Since both the substitution and
income effects increase demand
when own-price falls, a...
THE SLUTSKY EQUATION
Let

M 1 = p1 x1 + p2 x 2

be the original budget constraint
and let
∗
M 2 = p1 x1 + p2 x 2

represen...
THE SLUTSKY EQUATION
X2

M2 < M1

Ea
xa
∗
M 2 = p1 x1 + p2 x2

Demand for x1 is

x1 = x ( p1 , p2 , M )
d

M 1 = p1 x1 + p...
THE SLUTSKY EQUATION
M2 - M1

∆M = M 2 − M 1 =

(

∆M = M 2 − M 1 =

∗
p1 x1

+ p2 x 2 - p1 x1 − p2 x 2

∆M = M 2 − M 1 =
...
THE SLUTSKY EQUATION
The demand curve holding M
constant is given by

∆x1 = x

d

(

∗
p1 ,

)

p2 , M 1 − x

d

( p1 , p2...
THE SLUTSKY EQUATION
The income effect is given by

(

)

(

∗
∗
∆x m = x d p1 , p2 , M 1 − x d p1 , p2 , M 2

)

(2)

The...
THE SLUTSKY EQUATION
Given

( p ,M )− x ( p , p ,M )
= x (p , p ,M )− x (p , p ,M )
= x (p , p ,M )− x ( p , p ,M )

∆x1 =...
THE SLUTSKY EQUATION
∆x1 = ∆x s + ∆x m
Divide across by ∆p1

∆x1 ∆x s ∆xm
=
+
∆p1 ∆p1 ∆p1
Recall
so

∆M = x1∆p1

∆p1 = (−)...
THE SLUTSKY EQUATION
Substituting

∆p1 = (−)∆M x1
∆x1 ∆xs ∆xm
=
+
∆p1 ∆p1 ∆p1
Gives

∆x1 ∆x s ∆x m
=
−
x1
∆p1 ∆p1 ∆M

THE
...
THE SLUTSKY METHOD: INFERIOR
GOODS
Some goods are (sometimes) inferior
(i.e. demand is reduced by higher
income).
The subs...
THE SLUTSKY METHOD: INFERIOR
GOODS
X2

Eb

I2

Ea
Ec
xa

xb xc

The substitution
effect is as per
usual. But, the
income e...
GIFFEN GOODS
In rare cases of extreme inferiority,
the income effect may be larger in
size than the substitution effect,
c...
THE SLUTSKY METHOD for
INFERIOR GOODS

In rare cases of
extreme incomeinferiority, the income
effect may be larger
in size...
SLUTSKY’S EFFECT FOR
GIFFEN GOODS
Slutsky’s decomposition of the effect
of a price change into a pure
substitution effect ...
DECOMPOSITION of TOTAL PRICE EFFECT:
PERFECT COMPLEMENTS
X2

A fall in the price of X1
I1

I2

B
Original
Budget
Constrain...
DECOMPOSITION of TOTAL PRICE EFFECT
PERFECT SUBSTITUTES
?
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Price change income and substittution effects

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Price change income and substittution effects

  1. 1. Price Change: Income and Substitution Effects
  2. 2. THE IMPACT OF A PRICE CHANGE Economists often separate the impact of a price change into two components: – the substitution effect; and – the income effect.
  3. 3. THE IMPACT OF A PRICE CHANGE The substitution effect involves the substitution of good x1 for good x2 or viceversa due to a change in relative prices of the two goods. The income effect results from an increase or decrease in the consumer’s real income or purchasing power as a result of the price change. The sum of these two effects is called the price effect.
  4. 4. THE IMPACT OF A PRICE CHANGE The decomposition of the price effect into the income and substitution effect can be done in several ways There are two main methods: (i) The Hicksian method; and (ii) The Slutsky method
  5. 5. THE HICKSIAN METHOD Sir John R.Hicks (1904-1989) Awarded the Nobel Laureate in Economics (with Kenneth J. Arrrow) in 1972 for work on general equilibrium theory and welfare economics.
  6. 6. THE HICKSIAN METHOD Optimal bundle is Ea, on indifference curve I1. X2 Ea I1 xa X1
  7. 7. THE HICKSIAN METHOD X2 A fall in the price of X1 P The budget line pivots out from P * Ea I1 xa X1
  8. 8. THE HICKSIAN METHOD The new optimum is Eb on I2. X2 The Total Price Effect is xa to xb Ea Eb I2 I1 xa xb X1
  9. 9. THE HICKSIAN METHOD To isolate the substitution effect we ask…. “what would the consumer’s optimal bundle be if s/he faced the new lower price for X1 but experienced no change in real income?” This amounts to returning the consumer to the original indifference curve (I1)
  10. 10. THE HICKSIAN METHOD The new optimum is Eb on I2. X2 The Total Price Effect is xa to xb Ea Eb I2 I1 xa xb X1
  11. 11. THE HICKSIAN METHOD Draw a line parallel to the new budget line and tangent to the old indifference curve X2 Ea Eb I2 I1 xa xb X1
  12. 12. THE HICKSIAN METHOD X2 Ea The new optimum on I1 is at Ec. The movement from Ea to Ec (the increase in quantity demanded from Xa to Xc) is solely in response to a change in Eb relative prices I2 Ec I1 xa xc xb X1
  13. 13. THE HICKSIAN METHOD This is the substitution effect. X2 Ea Xa Eb Ec Substitution Effect I2 I1 Xc X1
  14. 14. THE HICKSIAN METHOD To isolate the income effect … Look at the remainder of the total price effect This is due to a change in real income.
  15. 15. THE HICKSIAN METHOD The remainder of the total effect is due to a change in real income. The increase in real income is evidenced by the movement from I1 to I2 X2 Ea Xc Eb Ec I2 I1 X1 Income Effect Xb
  16. 16. THE HICKSIAN METHOD X2 Ea Eb Ec xa xc I2 I1 xb Sub Income Effect Effect X1
  17. 17. HICKSIAN ANALYSIS and DEMAND CURVES P A fall in price from p1 to p1* M 1 = p1 x1 + p2 x 2 AC P P1 P1* B ∗ M 1 = p1 x1 + p2 x2 X1 Marshallian Demand Curve (A & B) A C B Hicksian Demand Curve (A & C) X1
  18. 18. HICKSIAN ANALYSIS and DEMAND CURVES Hicksian (compensated) demand curves cannot be upward-sloping (i.e. substitution effect cannot be positive)
  19. 19. THE SLUTSKY METHOD 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 the Budget of the Consumer” he introduced “Slutsky Decomposition”.
  20. 20. THE SLUTSKY METHOD Optimal bundle is Ea, on indifference curve I1. X2 Ea I1 xa X1
  21. 21. THE SLUTSKY METHOD X2 A fall in the price of X1 P The budget line pivots out from P * Ea I1 xa X1
  22. 22. THE SLUTSKY METHOD The new optimum is Eb on I2. X2 The Total Price Effect is xa to xb Ea xa Eb I1 xb I2 X1
  23. 23. THE SLUTSKY METHOD Slutsky 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” 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 so that, at the new prices, s/he can just afford to buy the original bundle?”
  24. 24. THE SLUTSKY METHOD To isolate the substitution effect we adjust the consumer’s money income so that s/he change can just afford the original consumption bundle. In other words we are holding purchasing power constant.
  25. 25. THE SLUTSKY METHOD The new optimum is Eb on I2. X2 The Total Price Effect is xa to xb Ea xa Eb I1 xb I2 X1
  26. 26. THE SLUTSKY METHOD Draw a line parallel to the new budget line which passes through the point Ea. X2 Eb Ea xa I1 xb I2 X1
  27. 27. THE SLUTSKY METHOD The new optimum on I3 is at Ec. The movement from Ea to Ec is the substitution effect X2 Eb Ea Ec xa xc xb I2 I3 X1
  28. 28. THE SLUTSKY METHOD The new optimum on I3 is at Ec. The movement from Ea to Ec is the substitution effect X2 Eb Ea Ec xa I2 I3 xc Substitution Effect X1
  29. 29. THE SLUTSKY METHOD The remainder of the total price effect is the Income Effect. X2 The movement from Ec to Eb. Eb Ea Ec xc I2 I3 xb Income Effect X1
  30. 30. THE SLUTSKY METHOD for NORMAL GOODS Most goods are normal (i.e. demand increases with income). The substitution and income effects reinforce each other when a normal good’s own price changes.
  31. 31. THE SLUTSKY METHOD for NORMAL GOODS The income and substitution effects reinforce each other. X2 Eb Ea Ec xa xc I2 I3 xb X1
  32. 32. THE SLUTSKY METHOD for NORMAL GOODS Since both the substitution and income effects increase demand when own-price falls, a normal good’s ordinary demand curve slopes downwards. The “Law” of Downward-Sloping Demand therefore always applies to normal goods.
  33. 33. THE SLUTSKY EQUATION Let M 1 = p1 x1 + p2 x 2 be the original budget constraint and let ∗ M 2 = p1 x1 + p2 x 2 represent the budget constraint after the Slutsky compensating variation in income has been carried out.
  34. 34. THE SLUTSKY EQUATION X2 M2 < M1 Ea xa ∗ M 2 = p1 x1 + p2 x2 Demand for x1 is x1 = x ( p1 , p2 , M ) d M 1 = p1 x1 + p2 x2 X1
  35. 35. THE SLUTSKY EQUATION M2 - M1 ∆M = M 2 − M 1 = ( ∆M = M 2 − M 1 = ∗ p1 x1 + p2 x 2 - p1 x1 − p2 x 2 ∆M = M 2 − M 1 = ∗ p1 x1 - p1 x1 ∗ p1 x1 ( ) + p2 x 2 - ( p1 x1 + p2 x 2 ) ∗ ∆M = M 2 − M 1 = x1 p1 - p1 ∆M = x1∆p1 as ( ∗ p1 ) ) - p1 = ∆p1 gives the change in money income needed to consume the original bundle of goods (at EA) ∆M=x1∆p1
  36. 36. THE SLUTSKY EQUATION The demand curve holding M constant is given by ∆x1 = x d ( ∗ p1 , ) p2 , M 1 − x d ( p1 , p2 , M 1 ) (1) which is the change in demand for x1 due to the change in its own price, holding M and the price of x2 constant
  37. 37. THE SLUTSKY EQUATION The income effect is given by ( ) ( ∗ ∗ ∆x m = x d p1 , p2 , M 1 − x d p1 , p2 , M 2 ) (2) The change in demand due to the Slutsky substitution effect is given by ( ) ∗ ∆x s = x d p1 , p2 , M 2 − x d ( p1 , p2 , M 1 ) (3)
  38. 38. THE SLUTSKY EQUATION Given ( p ,M )− x ( p , p ,M ) = x (p , p ,M )− x (p , p ,M ) = x (p , p ,M )− x ( p , p ,M ) ∆x1 = x d ∗ p1 , ∆x m d ∗ 1 ∆x s d ∗ 1 2 2 2 1 1 2 d d d 1 2 1 (1) ∗ 1 2 2 (2) 1 2 1 (3) Claim ∆x1 = ∆x s + ∆x m (4) Show this by substituting equations (1), (2) and (3) into equation (4)
  39. 39. THE SLUTSKY EQUATION ∆x1 = ∆x s + ∆x m Divide across by ∆p1 ∆x1 ∆x s ∆xm = + ∆p1 ∆p1 ∆p1 Recall so ∆M = x1∆p1 ∆p1 = (−) ∆M x1
  40. 40. THE SLUTSKY EQUATION Substituting ∆p1 = (−)∆M x1 ∆x1 ∆xs ∆xm = + ∆p1 ∆p1 ∆p1 Gives ∆x1 ∆x s ∆x m = − x1 ∆p1 ∆p1 ∆M THE SLUTSKY EQUATION
  41. 41. THE SLUTSKY METHOD: INFERIOR GOODS Some goods are (sometimes) inferior (i.e. demand is reduced by higher income). The substitution and income effects “oppose” each other when an inferior good’s own price changes.
  42. 42. THE SLUTSKY METHOD: INFERIOR GOODS X2 Eb I2 Ea Ec xa xb xc The substitution effect is as per usual. But, the income effect is in the opposite direction. I3 X1 xa to xc xc to xb
  43. 43. GIFFEN GOODS In rare cases of extreme inferiority, the income effect may be larger in size than the substitution effect, causing quantity demanded to rise as own price falls. Such goods are Giffen goods. Giffen goods are very inferior goods.
  44. 44. THE SLUTSKY METHOD for INFERIOR GOODS In rare cases of extreme incomeinferiority, the income effect may be larger in size than the substitution effect, causing quantity demanded to fall as own-price falls. X2 Eb I2 Ea Ec xa to xc xb xa xc I3 X1 xc to xb
  45. 45. SLUTSKY’S EFFECT FOR GIFFEN GOODS Slutsky’s decomposition of the effect of a price change into a pure substitution effect and an income effect thus explains why the “Law” of Downward-Sloping Demand is violated for very inferior goods.
  46. 46. DECOMPOSITION of TOTAL PRICE EFFECT: PERFECT COMPLEMENTS X2 A fall in the price of X1 I1 I2 B Original Budget Constraint A=C No substitution effect New Budget Constraint X1
  47. 47. DECOMPOSITION of TOTAL PRICE EFFECT PERFECT SUBSTITUTES ?

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