Y
THE HICKSIAN METHOD
Optimal bundle is E a
, on indifference curve U
1.
x a
E a
U
1
X
*Slides adapted from Suzanne O’neil, TCD
1

Y
P
*
THE HICKSIAN METHOD
A fall in the price of X
The budget line pivots out from P x a
E a
U
1
X
2

Y
THE HICKSIAN METHOD
The new optimum is
E b on U
2
.
The Total Price
Effect is x a to x b
E b
E a
U
2 x a x b
U
1
X
3

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 X but experienced no change in real income?”
 This amounts to returning the consumer to the original indifference curve (U
1
)
4

Y
THE HICKSIAN METHOD
The new optimum is
E b on U
2
.
The Total Price
Effect is x a to x b
E b
E a
U
2 x a x b
U
1
X
5

Y
THE HICKSIAN METHOD
Draw a line parallel to the new budget line and tangent to the old indifference curve x a
E a
E b
U
2 x b
U
1
X
6

Y
THE HICKSIAN METHOD
The new optimum on U
1 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 relative prices
E b
E a
E c U
1 x a x c x b
U
2
X
7

Y
THE HICKSIAN METHOD
This is the substitution effect.
X a
E a
E c
E b
U
1
U
2
Substitution
Effect
X c
X
8

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.
9

Y
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 U
1 to U
2
X c
E a
E c
E b
UI
1
U
2
Income Effect X b
X
10

Y
THE HICKSIAN METHOD
E b
E a
E c x a x c x b
U
1
U
2
Sub
Effect
Income
Effect
X
11

P
M
 p x
1 1
 p x
2 2
A fall in price from p
1 to p
1
*
A
C
B
M
  p x
1 1
 p x
2 2
P
P
1
P
1
*
C
A
B
X
Marshallian Demand
Curve (A & B)
Hicksian Demand
Curve (A & C)
X
12

Y
THE SLUTSKY METHOD
Optimal bundle is E a
, on indifference curve U
1.
U
1
E a x a X
13

Y
P
*
THE SLUTSKY METHOD
A fall in the price of X
The budget line pivots out from P
U
1
E a x a X
14

Y
THE SLUTSKY METHOD
The new optimum is
E b on U
2
.
The Total Price
Effect is x a to x b
U
1
E a
E b
U
2 x a x b X
15

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?”
16

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.
17

Y
THE SLUTSKY METHOD
The new optimum is
E b on U
2
.
The Total Price
Effect is x a to x b
U
1
E a
E b
U
2 x a x b X
18

Y
THE SLUTSKY METHOD
Draw a line parallel to the new budget line which passes through the point Ea.
U
1
E a
E b
U
2 x a x b X
19

Y
THE SLUTSKY METHOD
The new optimum on I
3 is at Ec. The movement from Ea to Ec is the substitution effect x a
E a
E b
E c x c x b
U
3
U
2
X
20

Y
THE SLUTSKY METHOD
The new optimum on I
3 is at Ec. The movement from Ea to Ec is the substitution effect
U
1
E b
E a
U
2
E c
U
3 x a x c X
Substitution Effect
21

Y
THE SLUTSKY METHOD
The remainder of the total price effect is the Income Effect.
U
1
E a
E b x c
E c x b
U
3
Income Effect
U
2
The movement from
Ec to Eb.
X
22

Y
The income and substitution effects reinforce each other.
U
1
E a x a
E b
E c x c x b
U
3
U
2
X
23