Transcript Comparing the Hicks and Slutsky Method

THE HICKSIAN METHOD
Optimal bundle is Ea, on
indifference curve U1.
Y
Ea
U1
xa
X
*Slides adapted from Suzanne O’neil, TCD
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THE HICKSIAN METHOD
A fall in the price of X
Y
The budget line pivots
out from P
*
P
Ea
U1
xa
X
2
THE HICKSIAN METHOD
The new optimum is
Eb on U2.
Y
The Total Price
Effect is xa to xb
Ea
Eb
U2
U1
xa
xb
X
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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 (U1)
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THE HICKSIAN METHOD
The new optimum is
Eb on U2.
Y
The Total Price
Effect is xa to xb
Ea
Eb
U2
U1
xa
xb
X
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THE HICKSIAN METHOD
Draw a line parallel to
the new budget line and
tangent to the old
indifference curve
Y
Ea
Eb
U2
U1
xa
xb
X
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THE HICKSIAN METHOD
The new optimum on U1 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
Y
Eb
Ea
Ec U1
xa xc
xb
U2
X
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THE HICKSIAN METHOD
This is the
substitution effect.
Y
Eb
Ea
U2
Ec
U1
Xa
X
Substitution
Effect
Xc
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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.
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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 U1 to U2
Y
Eb
Ea
U2
Ec
UI1
Xc
X
Income Effect
Xb
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THE HICKSIAN METHOD
Y
Eb
Ea
U2
Ec
U1
xa xc
xb
Sub Income
Effect Effect
X
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HICKSIAN ANALYSIS and DEMAND CURVES
P
A fall in price
from p1 to p1*
M  p1x1  p2 x2
AC
P
P1
P1*
B
M  p1 x1  p2 x2
X
Marshallian Demand
Curve (A & B)
A
B
C
Hicksian Demand
Curve (A & C)
X
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THE SLUTSKY METHOD
Optimal bundle is Ea, on
indifference curve U1.
Y
U1
Ea
xa
X
13
THE SLUTSKY METHOD
A fall in the price of X
Y
The budget line pivots
out from P
*
P
U1
Ea
xa
X
14
THE SLUTSKY METHOD
The new optimum is
Eb on U2.
Y
The Total Price
Effect is xa to xb
U1
Ea
xa
Eb
xb
U2
X
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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?”

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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.
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THE SLUTSKY METHOD
The new optimum is
Eb on U2.
Y
The Total Price
Effect is xa to xb
U1
Ea
xa
Eb
xb
U2
X
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THE SLUTSKY METHOD
Draw a line
parallel to the new
budget line which
passes through
the point Ea.
Y
U1
Ea
xa
Eb
xb
U2
X
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THE SLUTSKY METHOD
The new optimum
on I3 is at Ec. The
movement from Ea
to Ec is the
substitution effect
Y
Eb
Ea
Ec
xa
xc xb
U2
U3
X
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THE SLUTSKY METHOD
The new optimum
on I3 is at Ec. The
movement from Ea
to
Ec
is
the
substitution effect
Y
U1
Eb
Ea
Ec
xa
U2
U3
xc
Substitution Effect
X
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THE SLUTSKY METHOD
The remainder of
the total price effect
is the Income Effect.
Y
The movement from
Ec to Eb.
U1
Eb
Ea
Ec
xc
U2
U3
xb
X
Income Effect
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THE SLUTSKY METHOD for
NORMAL GOODS
Y
The income and
substitution effects
reinforce each other.
U1
Eb
Ea
Ec
xa
xc
U2
U3
xb
X
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