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Chapter Eight
Slutsky’s Equation
Effects of a Price Change
 What
happens when the price of a
commodity decreases?
 First, the commodity becomes
relatively cheaper, so consumers
substitute towards it and away from
now relatively more expensive other
commodities. This is the
substitution effect of the price
change.
Effects of a Price Change
 Second,
the consumer’s budget of $y
can purchase larger bundles than
before. It is as if the consumer
received an increase in income.
 The consequent changes in
quantities demanded are the income
effects of the price change.
Effects of a Price Change
x2
y
p2
Consumer’s budget is $y.
Original choice
x1
Effects of a Price Change
x2
y
p2
Consumer’s budget is $y.
Lowered price for commodity 1
pivots outwards the budget constraint.
x1
Effects of a Price Change
x2
y
p2
y'
p2
Consumer’s budget is $y.
Lowered price for commodity 1
pivots outwards the budget constraint.
Now only $y’ are needed to buy the
original bundle at the new prices. It is
as if the consumer’s income has
increased by $y - $y’.
x1
Effects of a Price Change
 The
change to quantities demanded
due to this ‘extra’ income is the
income effect of the price change.
Effects of a Price Change
 Slutsky’s
insight was that the effects
on quantities demanded of any price
change can always be decomposed
into a pure substitution effect and an
income effect.
 The overall change in quantities
demanded due to a price change is
the sum of the substitution and
income effects.
Pure Substitution Effect
 Slutsky
isolated the change in
quantities demanded due only to the
change in relative prices by asking
“What is the change in quantities
demanded when the consumer’s
income is adjusted so that, at the
new prices, she can only just buy the
original bundle?”
Pure Substitution Effect Only
x2
x 2’
x 1’
x1
Pure Substitution Effect Only
x2
x 2’
x 1’
x1
Pure Substitution Effect Only
x2
x 2’
x 1’
x1
Pure Substitution Effect Only
x2
Lowering p1 makes good 1 relatively
cheaper and causes a substitution
from good 2 to good 1. The change
from (x1’,x2’) to (x1’’,x2’’) is the
pure substitution effect.
x 2’
x2’’
x 1’
x1’’
x1
And Now The Income Effect
x2
The income effect is the change
from (x1’’,x2’’) to (x1’’’,x2’’’).
(x1’’’,x2’’’)
x 2’
x2’’
x 1’
x1’’
x1
The Overall Change in Demand
x2
The overall effect on demands
of the change in p1 is the sum
of the income and substitution
effects. This is the
(x1’’’,x2’’’)
change from
(x1’,x2’) to (x1’’’,x2’’’).
x 2’
x2’’
x 1’
x1’’
x1
Slutsky’s Effects for Normal Goods
x2
Good 1 is normal because an
increase to income causes
demand to rise.
(x1’’’,x2’’’)
x 2’
x2’’
x 1’
x1’’
x1
Slutsky’s Effects for Normal Goods
x2
Good 1 is normal because an
increase to income causes
demand to rise. So the income
and substitution
(x1’’’,x2’’’)
effects reinforce
each other.
x 2’
x2’’
x 1’
x1’’
x1
Slutsky’s Effects for Normal Goods
 Since
both the substitution and
income effects increase demand
when own-price decreases, the
ordinary demand curve for a normal
good must slope downwards.
 The Law of Downward-Sloping
Demand therefore always applies to
normal goods.
Slutsky’s Effects for Income-Inferior
Goods
 Some
goods are income-inferior; that
is, demand is reduced by an increase
in income.
 Slutsky showed that, for incomeinferior goods, the substitution and
income effects oppose each other
when a good’s own price changes.
Slutsky’s Effects for Income-Inferior
Goods
x2
The pure substitution effect is as for
a normal good. But, ….
x 2’
x2’’
x 1’
x1’’
x1
Slutsky’s Effects for Income-Inferior
Goods
x2
x 2’
The pure substitution effect is as for a
normal good. But, the income effect is
in the opposite direction.
(x1’’’,x2’’’)
x2’’
x 1’
x1’’
x1
Slutsky’s Effects for Income-Inferior
Goods
x2
x 2’
x2’’
The pure substitution effect is as for a
normal good. But, the income effect is
in the opposite direction. Good 1 is
(x1’’’,x2’’’)
income-inferior
because an
increase to income
causes demand to
fall.
x 1’
x1’’
x1
Slutsky’s Effects for Income-Inferior
Goods
x2
The overall changes to demand are
the sums of the substitution and
income effects.
(x ’’’,x ’’’)
1
x 2’
2
x2’’
x 1’
x1’’
x1
Giffen Goods
 In
the rare case of extreme incomeinferiority, the income effect may be
larger in size than the substitution
effect, causing quantity demanded to
decrease as own-price decreases.
 Such goods are called Giffen goods.
Slutsky’s Effects for Giffen Goods
x2
A decrease in p1 causes a
decrease in the quantity
demanded of good 1.
x 2’
x 1’
x1
Slutsky’s Effects for Giffen Goods
x2
A decrease in p1 causes a
decrease in the quantity
demanded of good 1.
x2’’’
x 2’
x1’’’ x1’
x1
Slutsky’s Effects for Giffen Goods
x2
A decrease in p1 causes a
decrease in the quantity
demanded of good 1.
x2’’’
x 2’
x2’’
x1’’’ x1’
x1’’
x1
Substitution effect
Income effect
Slutsky’s Effects 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 extremely incomeinferior goods.