Chapter Eight

1
Chapter Eight

• Slutsky Equation

2
Effects of a Price Change

• What happens when a commoditys price decreases?
• Substitution effect the commodity is relatively
  cheaper, so consumers substitute it for now
  relatively more expensive other commodities.

3
Effects of a Price Change

• Income effect the consumers budget of y can
  purchase more than before, as if the consumers
  income rose, with consequent income effects on
  quantities demanded.

4
Effects of a Price Change

• Slutsky discovered that changes to demand from a
  price change are always the sum of a pure
  substitution effect and an income effect.

5
Real Income Changes

• Slutsky asserted that if, at the new prices,
• less income is needed to buy the original bundle
  then real income is increased
• more income is needed to buy the original bundle
  then real income is decreased

6
Real Income Changes
x2
Original budget constraint and choice
x1
7
Real Income Changes
x2
Original budget constraint and choice
New budget constraint
x1
8
Real Income Changes
x2
Original budget constraint and choice
New budget constraint real income has risen
x1
9
Pure Substitution Effect

• Slutsky isolated the change in demand due only to
  the change in relative prices by asking What is
  the change in demand when the consumers income
  is adjusted so that, at the new prices, she can
  only just buy the original bundle?

10
Pure Substitution Effect Only
x2
x2
x1
x1
11
Pure Substitution Effect Only
x2
x2
x1
x1
12
Pure Substitution Effect Only
x2
x2
x1
x1
13
Pure Substitution Effect Only
x2
x2
x2
x1
x1
x1
14
And Now The Income Effect
x2
(x1,x2)
x2
x2
x1
x1
x1
15
And Now The Income Effect
x2
The income effect is (x1,x2) ?
(x1,x2).
(x1,x2)
x2
x2
x1
x1
x1
16
The Overall Change in Demand
The change to demand due to lower p1 is the sum
of the income and substitution effects,
(x1,x2) ? (x1,x2).
x2
(x1,x2)
x2
x2
x1
x1
x1
17
Slutskys Effects for Normal Goods

• Most goods are normal (i.e. demand increases with
  income).
• The substitution and income effects reinforce
  each other when a normal goods own price changes.

18
Slutskys Effects for Normal Goods
x2
Good 1 is normal becausehigher income
increasesdemand
(x1,x2)
x2
x2
x1
x1
x1
19
Slutskys Effects for Normal Goods

• Since both the substitution and income effects
  increase demand when own-price falls, a normal
  goods ordinary demand curve slopes down.
• The Law of Downward-Sloping Demand therefore
  always applies to normal goods.

20
Slutskys Effects for Income-Inferior Goods

• Some goods are income-inferior (i.e. demand is
  reduced by higher income).
• The substitution and income effects oppose each
  other when an income-inferior goods own price
  changes.

21
Slutskys Effects for Income-Inferior Goods
x2
x2
x2
x1
x1
x1
22
Slutskys Effects for Income-Inferior Goods
The pure substitution effect is as for a normal
good. But, the income effect is in the
opposite direction.
x2
(x1,x2)
x2
x2
x1
x1
x1
23
Slutskys Effects for Income-Inferior Goods
The pure substitution effect is as for a normal
good. But, the income effect is in the
opposite direction. Good 1 is
income-inferior
because an
increase to income
causes demand to
fall.
x2
(x1,x2)
x2
x2
x1
x1
x1
24
Slutskys Effects for Income-Inferior Goods
x2
The overall changes to demand arethe sums of the
substitution and
income effects.
(x1,x2)
x2
x2
x1
x1
x1
25
Giffen Goods

• In rare cases of extreme income-inferiority, the
  income effect may be larger in size than the
  substitution effect, causing quantity demanded to
  fall as own-price rises.
• Such goods are Giffen goods.

26
Walt considers x and y to be perfect substitutes.
They originally cost 10 and 9 respectively. His
income is 720. One day the price of x drops to
8. Which of the following is true?

• The income effect increases the quantity of y by
  90.
• The substitution effect increases the quantity of
  y by 80.
• The substitution effect increases the quantity of
  x by 90.
• The income effect increases the quantity of x by
  80.
• None of the above.

27
Rob consumes two goods, x and y. He has an
allowance of 50 per week and is not endowed with
either of the goods. If the price of good x
increases and his substitution and income effects
change demand in opposite directions

• good x must be a Giffen good.
• good x must be an inferior good.
• WARP is violated.
• good x must be a normal good.
• There is not enough information to judge whether
  good x is a normal or inferior good.

28
Charlies utility function is xAxB. The price of
apples used to be 1 and the price of bananas
used to be 2, and his income used to be 40. If
the price of apples increased to 8 and the price
of bananas stayed constant, the substitution
effect on Charlies apple consumption reduces his
consumption by

• 17.5 apples
• 7 apples
• 8.75 apples
• 13.75 apples
• None of the above is correct.