Lectures, week 3
Topic 1.
Consumer Theory 3
(continued)
Econ20002 semester 1
Intermediate Microeconomics
Svetlana Danilkina
W3-1
Overview
4. Consumer’s (Individual) Demand
a. income changes: income-consumption curve;
normal and inferior goods; Engel Curve; income
elasticity of demand
b. price changes – demand curve; price-consumption
curve; ordinary and Giffen goods; gross
complements and gross substitutes
c. Income and substitution effects
d. How much to compensate? Cost-of-living
adjustments, CPI substitution bias
next lecture:
e. revealed preferences
f. paying nurses (labour supply).
g. taxation and labour supply
W3-2
Change in income – summary:
When income increases:
 normal good - consumption increases (that means
that Engel curve is upward sloping)
 inferior good - consumption decreases (that means
that Engel curve is downward sloping)
W3-3
Income
Qbeer
Δ
Δ
< 0

< 0
Income
Qbeer
Engel curve:
Beer is an
inferior good
Engel curve:
Beer is a
normal good
Δ
Δ
> 0

> 0
Change in income – summary:
When income increases:
 normal good - consumption increases (that means
that demand curve shift to the right)
 inferior good - consumption decreases (that means
that demand curve shift to the left)
W3-4
pbeer
Qbeer
Demand curve
shifts right:
Beer is a
normal good
0BeerQ
I
∆
>
∆
pbeer
Qbeer
Demand curve
shifts left:
Beer is an
inferior good
0BeerQ
I
∆
<
∆
Income elasticity of demand
W3-5
By definition, income elasticity of demand:
it shows by how many % quantity demanded will increase if
income increases by 1%.
 normal good - consumption increases with income =>
income elasticity is positive
 inferior good - consumption decreases with income =>
income elasticity is negative
% change in quantity demanded
% change in income
I Q Q Q I
I I I Q
ε
∆ ∆
= = =
∆ ∆
for calculus−lovers: =

/

=



Income-consumption curve and
normal/inferior goods
 If income – consumption curve is upward
sloping, both goods are normal:
W3-6
Qbeer
Qdoughnuts
Income
Qbeer
Engel curve:
Beer is a
normal good
Income
Qdoughnuts
Engel curve:
doughnuts is a
normal good
Income-consumption curve and
normal/inferior goods
 If income – consumption curve is downward sloping,
one good is normal and the other is inferior:
W3-7
Income
q1
Engel curve:
expensive
restaurants is
a normal good
Income
q2
Engel curve:
fast food is an
inferior good
q2, fast food
q1, expensive restaurants
income – consumption curve
Here good 1 is a normal good and
good 2 is an inferior good
Income-consumption curve and
normal/inferior goods
 If income – consumption curve is downward sloping, one
good is normal and the other is inferior:
W3-8
Income
q1
Engel curve:
DVDs is an
inferior good
Income
q2
Engel curve:
Blu-rays is a
normal good
q2, Blu-ray
q1, DVD
income – consumption curve
Here good 2 is a normal good and
good 1 is an inferior good
4b. Change in price:
When price of a good increases:
 ordinary good - its consumption decreases (that
means that demand curve is downward sloping)
 Giffen good – its consumption increases (that
means that demand curve is upward sloping)
W3-9
pbeer
Qbeer
Demand curve
is downward
sloping:
Beer is an
ordinary good
Δ
Δ
> 0

> 0
pbeer
Qbeer
Demand curve
is upward
sloping:
Beer is a
Giffen good
Δ
Δ
< 0

< 0
Price elasticity of demand
W3-10
By definition, price elasticity of demand:
It shows by how many % quantity demanded for a particular good will
increase if its own price increases by 1%.
 ordinary good - consumption decreases with price => price elasticity
is negative: < 0
 Giffen good - consumption increases with price => price elasticity is
positive: > 0
Demand is
 elastic if absolute value of price elasticity is greater than 1
 unit-elastic if the absolute value of price elasticity = 1
 inelastic if absolute value of price elasticity is smaller than 1
 and demand is isoelastic if price elasticity is constant.
% change in quantity demanded
% change in price
price Q Q Q p
p p p Q
ε ∆ ∆= = =
∆ ∆
for calculus−lovers : =

/

=



price-consumption curve; ordinary
good
Qdoughnuts
Homer’s price-consumption curve when
price of doughnuts (good 1) changes
50
W3-11
8 18 10040
Qbeer
As the price of doughnuts decreases,
Homer buys more doughnuts.
Therefore, doughnuts (good 1) are
ordinary (not Giffen) good
Pdoughnuts
Qdoughnuts
Demand curve
Giffen goods
Qbeer
Qdoughnuts
Here the price-consumption
curve (for doughnuts) goes the
‘normal’ way
But here it ‘turns back on
itself’. Doughnuts are a Giffen
good for these choices – the
lower the price the fewer
doughnuts Homer buys.
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pd
pd
0d
d
Q
p
∆
<
∆
0d
d
Q
p
∆
>
∆
What if the price-consumption
curve look like this?
Here doughnuts (good 1)
is a Giffen good
pd
price-consumption curve when
price of doughnuts (good 1) changes
price-consumption curve with
Giffen good
pd
W3-13
Qbeer
Qdoughnuts
0d
d
Q
p
∆
>
∆
Change in price for good 1: can I say
something about the other good?
When price of good 1 increases:
 good 2 is a gross complement to the good 1
if its consumption decreases
 good 2 is a gross substitute to the good 1
if its consumption increases
W3-14
2
1
0Q
p
∆
<
∆
2
1
0Q
p
∆
>
∆
 You would assume, naturally, that if good 2 is a gross complement
to good 1, then good 1 is a gross complement to good 2, and the
same for substitutes. Unfortunately, and amazingly, this is not the
case! It is possible for good 2 to be a gross substitute to the good
1 and, at the same time, for good 1 to be a gross complement to
the good 2. I know, I know – it is mind boggling. There is nothing
you can do about it – just another mystery of life (or do PhD).
2 1
1 2
possible to have 0 but 0Q Q
p p
∆ ∆
> <
∆ ∆
Complements and substitutes
Qdoughnuts
Homer’s price-consumption curve when
price of doughnuts changes
W3-15
Qbeer
Here it slopes down. As the price of
doughnuts decreases (we move to the
right along the curve), Homer buys more
doughnuts and less beer.
So doughnuts is an ordinary good.
pd
0beer
doughnuts
Q
p
∆
>
∆
Here beer is a gross substitute for
doughnuts:
Complements and substitutes
Qdoughnuts
Homer’s price-consumption curve when
price of doughnuts changes
W3-16
Qbeer
Here it slopes up. As the price of doughnuts decreases,
(we move to the right along the curve), Homer buys
more doughnuts and more beer.
So doughnuts is an ordinary good.
0beer
doughnuts
Q
p
∆
<
∆
Here beer is a gross complement for doughnuts:
pd
Summary
 A price - consumption curve shows us how an
individual’s choice will alter as the price of one
product alters given income and the prices of all
other products.
 The price-consumption curve gives us the
information to draw the demand curve for a good
which price changes.
 For a Giffen good, when its own price changes, the
price-consumption curve ‘turns back on itself’.
 The slope of the price-consumption curve, when
price of good one changes, tells us whether the
good two is a gross substitute or a gross
complement for the good one.
W3-17
W3-18
New optimal bundle
Initial optimal bundle
18
32
30
40
TE = - 22
4c. Income and Substitution Effects.
This is the total effect of
price change (TE)
q2
q1
TE = the change in the quantity of a good demanded when price
changes, holding other prices and income constant.
TE = 18 - 40 = - 22 (for good 1) => good 1 is ordinary (not Giffen)
(TE for good 2 = 32 – 30 = 2)
Suppose the price of good 1 increased from
$15 to $20.
A
B
Total effect
u0
u1
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Total effect (TE):
• negative for ordinary good (Law of
demand: buy less for a higher price)
• positive for Giffen good (Law of
demand does not hold: buy more for
higher price.)
TE:
ordinary good: q1 (buy less)
Giffen good: q1 (buy more)
Total effect for ordinary and
Giffen goods.
p1 ⟹ q1 ?
∆
∆
> 0

> 0
∆
∆
< 0

< 0
Δ1
Δ1 < 0
Δ1
Δ1 > 0
W3-20
If a price of a good increases, it affects the demand
for the good through two channels:
– A substitution effect: the change in the quantity of a good
demanded when price changes, holding other prices and the
consumer’s utility constant.
(The good becomes relatively more expensive than before =>
an incentive to substitute for another good)
– An income effect: the change in the quantity of a good
demanded due to the change in income, holding prices
constant.
Real income (purchasing power) decreases when price
increases. => you will buy
• less if it is a normal good; remember that for normal good:
• more if it is an inferior good. for an inferior good:
Income and substitution effects
total effect of price change =
substitution effect + income effect TE = SE + IE
Δ1
Δ
< 0
Δ1
Δ
> 0
W3-2122
35
30
40
SE
Suppose the price of good 1 increased from $15 to $20. As price of good 2
stays the same, good 2 becomes relatively more attractive, and the consumer
will want to buy more of it. We want to capture only relative price change effect,
not income (purchasing power) effect, so we will assume that the consumer will
“choose” intermediate bundle D (note that consumer cannot actually afford it, given
their income and prices!)
initial optimal bundle
Intermediate
bundle
q2
q1
The move from bundle A to D gives us
substitution effect: SE = 22 – 40 = - 18.
A
D
How do we define Substitution Effect?
u0
It is on the initial indifference curve, but on the “fake” budget line
with slope corresponding to new prices. Bundle D is the optimal
bundle the consumer would have chosen had s/he had just
enough income to achieve the initial utility (to reach the initial
indifference curve) at the new prices.
initial budget line
new budget line
“fake” budget line
W3-22
TE = SE + IE
18 22
35
32
30
40
IE SE
TE
Initial optimal bundle
Intermediate bundle
q2
q1
TE = - 22, SE = - 18, IE = - 4
New optimal bundle
AB
D
Whatever is left must be due to the income effect, which is move from D to B.
Both bundles are on the parallel budget lines – so the relative prices are the
same, and the only change when you move from the “fake” budget line to the
new budget line is decrease in income. So it make sense that this is the IE.
initial budget line
new budget line
“fake” budget line
good 1 is normal
W3-23
IE SE
TE
food
cigarettes
Initial optimal bundle
Intermediate bundle
New optimal
bundle
Tax on our sins (tobacco, alcohol, sugar, fast foods, gambling)
Average low-income family of smokers spends $1,018 per year on
cigarettes (5.1% of their total annual expenditures) and $4,291 on food
(21.5%). Data from Busch et al. (2004)
The government wants to increase taxes on cigarettes to discourage
people from smoking.
10% increase in price of cigarettes causes 9% reduction in cigarette
consumption. They spend more on cigarettes now than before price
increase! Therefore, to pay for this now more expensive habit, they cut
on consumption of food (by 17%), health care (by 12%) and so on...
17%
9%
A
B
D
W3-24
SE
Initial optimal bundle
Intermediate bundle
When price of good 1 increases, the new and “fake” budget lines will be
steeper, so you will always choose the intermediate bundle with less of
good 1 and more of good 2.
Substitution Effect is always negative
A
D
q2
q1
initial budget line
new budget line
“fake” budget line
22 40
35
30
u0
p1 ⟹ q1 (buy less)SE:
�
Δ1
Δ1 =0
< 0 Goods are always net substitutes (as long as preferences are convex).
W3-25
When you move from bundle D to the new optimal bundle B, it is equivalent
to reduction in your income.
• you will buy less if it is a normal good;
• more if it is an inferior good
Income Effect is positive or negative
IE
Intermediate bundle
New optimal bundle
D
B
q2
q1
Here good 1 is normal: IE < 0.
new budget line
“fake” budget line
p1 ⟹ q1 (buy less)
IE for normal good:
Δ1
Δ
< 0
Δ1
Δ
> 0
W3-26
When you move from bundle D to the new optimal bundle B, it is equivalent
to reduction in your income.
• you will buy less if it is a normal good;
• more if it is an inferior good
Income Effect is positive or negative
IE
Intermediate bundle
New optimal bundle
D
B
q2
q1
Here good 1 is inferior: IE > 0.
new budget line
“fake” budget line
p1 ⟹ q1 (buy more)
IE for inferior good:
Δ1
Δ
< 0
Δ1
Δ
> 0
W3-27
A substitution effect: always negative: p1 ⟹ q1
An income effect: (increase in price => decrease in income)
• negative for normal good: I ⟹ q1
• positive for an inferior good: I ⟹ q1
Total effect = substitution effect + income effect:
• negative for ordinary goods : p1 ⟹ q1
• positive for Giffen goods: p1 ⟹ q1
TE = SE + IE
SE and IE work in the same direction
SE dominates (opposite directions)
IE dominates (opposite directions)
Income and substitution effects
p1 ⟹ q1 ?
So, there are three possible cases. If good is normal, then TE is negative;
but if good is inferior, the total effect could be either positive or negative.
W3-28
Income and substitution effects
p1 ⟹ q1 ?
Ordinary good could be either normal or inferior, but Giffen good must be inferior.
Normal good is ordinary, but inferior good could be either Giffen or ordinary.
TE = SE + IE
Inferior good
Giffen good
Normal good
Ordinary good
• Ordinary/Giffen goods: it is about total effect (TE) – how price affects
consumption.
• Normal/inferior goods: it is about income effect (IE) – how income
affect consumption.
= +
=
= +
+
W3-29
Normal/inferior goods vs.
ordinary/Giffen goods
• Normal/inferior goods: it is about how income affect consumption.
• Ordinary/Giffen goods: it is about how price affects consumption.
Inferior
goodsNormal goods
Ordinary (non-Giffen)
goods
income price
W3-30
Normal/inferior goods vs.
ordinary/Giffen goods
All normal goods are ordinary.
Some inferior goods are Giffen and some are ordinary.
Some ordinary goods are normal and some are inferior.
All Giffen goods are inferior.
• Normal/inferior goods: it is about how income affect consumption.
• Ordinary/Giffen goods: it is about how price affects consumption.
Inferior
goodsNormal goods
Ordinary (non-Giffen)
goods
income price
4d. Application – how much to compensate?
QOG
Qhousing
1000
105
Sheldon and Leonard have $1,000
per week that they can spend on
housing or ‘other goods’. Let the
price of ‘other goods’ be $1. Initially
the price of ‘housing’ is $100 per
week (this is the price of a ‘unit of
housing quality’). But due to a
housing boom, the price of ‘housing’
rises to $200 per week.
Rotation of the budget line due
to rise in the price of housing
W3-31
Application – how much compensation?
QOG
Qhousing
1000
104
Initially they have a nice apartment that
they rent for $400 per week. This
leaves them $600 to spend on OGs.
But because of the boom their
apartment rent has risen to $800 per
week. This only leaves $200 per week
for OG. Looks like Sheldon and
Leonard will have to move to a
cheaper (lower quality) apartment.
5
600
200
W3-32
A
Application – how much compensation?
 But luckily for Sheldon and Leonard their
university, Caltex, offers to give them a ‘rent
compensation payment’ of $400 per week.
 This means that after the compensation Sheldon
and Leonard only pay $400 per week in rent on
their apartment like before. So Sheldon and
Leonard can stay in their apartment.
 Will they stay?
W3-33
QOG
Qhousing
1000
104
Note that Sheldon and Leonard’s
budget line after the $400 per week
compensation is not the same as
their original budget line. While they
can still afford their original bundle,
they now face a different price ratio.
At their old bundle, their MRSh,OG is
less than the price ratio. They will
still think that their old apartment is
‘too expensive’ relative to other
goods.
5
600
200
7
1400
W3-34
A
QOG
Qhousing
1000
104
So we can make two predictions:
1. Sheldon and Leonard will still
‘downgrade’ their apartment and
2. They are better off after the rent
rise and compensation than before.
Caltex has overcompensated them.
5
600
200
7
1400
800
3
U = 111
U = 173
W3-35
Initial optimal bundle
F
A
 If you provide a compensation for a price rise in
such a way that the original bundle is still
affordable, you are overcompensating – you make
consumers better off, as they are going to substitute
for cheaper goods to increase their utility.
 Popular application: cost-of-living adjustments, for
example, CPI indexing.
 Assume that inflation was 4% this year. If I increase
your salary/pension/unemployment benefits/child
care payments by 4%, will you be
 compensated
 overcompensated
 not compensated enough?
W3-36
 Consider a situation when, though your living
expenses increased by 4% overall, price of some
goods and services went up by more than 4% and
some by less. So, with 4% compensation, you still
can afford the initial living expenses. But why would
you? You will increase consumption of goods and
services which prices went up less, and decrease
the consumption of goods and services which
prices went up more (substitution effect). Therefore,
you will end up better off!
 Indexing living expenses compensation by CPI
usually leads to overcompensation (CPI substitution
bias)
Reading: PR, Ch. 3.6
W3-37
QOG
Qhousing104
Just enough – you need to give them enough
money so that they can afford the initial utility –
the bundle D. This monetary transfer (required to
restore the original utility) is called compensating
variation.
5 73
U = 111
U = 173
W3-38
How should you compensate?
1000
600
200
1400
D Intermediate bundle (same as in
the substitution effect)
Initial optimal bundle A
F
W3-39
If you ever see anything
mysterious or unusual, like
the Slutsky Equation,
just enjoy it while you can
(if you are seeing double,
check your alcohol level)
rephrased from Leunig
*
p p I
U U
ε ε θε
=
= −1
1
= �1
1 =∗
− 1
1

Slutsky Equation: TE = SE + IE
Evgeny Slutsky
(1880-1948)