Lecture # 08
The Theory of Demand
(conclusion)
Lecturer: Martin Paredes
1. Individual Demand Curves
2. Income and Substitution Effects and the
Slope of Demand
3. Applications: the Work-Leisure Trade-off
4. Consumer Surplus
5. Constructing Aggregate Demand
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Definition: The income-consumption curve of
good X is the set of optimal baskets for every
possible income level.
 Assumes all other variables remain constant.
3
Y (units)
I=40
U1
0
10
X (units)
4
Y (units)
I=68
I=40
U1
0
10
18
U2
X (units)
5
Y (units)
I=92
I=68
U3
I=40
U1
0
10
18
U2
24
X (units)
6
Y (units)
I=92
Income consumption curve
I=68
U3
I=40
U1
0
10
18
U2
24
X (units)
7
Note:
 The points on the income-consumption curve
can be graphed as points on a shifting demand
curve.
8
Y (units)
I=40
0
Income consumption curve
U1
10
X (units)
PX
$2
I=40
10
X (units)
9
Y (units)
I=68
I=40
0
Income consumption curve
U2
U1
10
18
X (units)
PX
$2
I=68
I=40
10
18
X (units)
10
Y (units)
I=92
I=68
I=40
0
U3
Income consumption curve
U2
U1
10
18
X (units)
24
PX
$2
I=68
I=40
10
18
24
I=92
X (units)
11
 The income-consumption curve for good X can
also be written as the quantity consumed of good
X for any income level.
 This is the individual’s Engel curve for good X.
12
I (€)
40
0
10
X (units)
13
I (€)
68
40
0
10
18
X (units)
14
I (€)
92
68
40
0
10
18
24
X (units)
15
I (€)
Engel Curve
92
68
40
0
10
18
24
X (units)
16
Note:
 When the slope of the income-consumption
curve is positive, then the slope of the Engel
curve is also positive.
17
Normal Good:
 If the income consumption curve shows that
the consumer purchases more of good X as her
income rises, good X is a normal good.
 Equivalently, if the slope of the Engel curve is
positive, the good is a normal good.
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Inferior Good:
 If the income consumption curve shows that
the consumer purchases less of good X as her
income rises, good X is a inferior good.
 Equivalently, if the slope of the Engel curve is
negative, the good is a normal good.
Note: A good can be normal over some ranges of
income, and inferior over others.
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Y (units)
Example: Backward Bending Engel Curve
I=200
0
U1
•
13
X (units)
I (€)
200
•
13
X (units)
20
Y (units)
Example: Backward Bending Engel Curve
I=300
I=200
0
U1
U2
•
•
13
18
X (units)
I (€)
300
200
•
13
•
18
X (units)
21
Y (units)
U3
I=300
I=200
0
Example: Backward Bending Engel Curve
I=400
U1
•
•
•
U2
13 16 18
X (units)
I (€)
•
400
300
200
•
•
13 16 18
X (units)
22
Y (units)
U3
I=300
I=200
0
Example: Backward Bending Engel Curve
I=400
U1
•
•
•
Income consumption curve
U2
13 16 18
X (units)
I (€)
•
400
300
200
•
• Engel Curve
13 16 18
X (units)
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 There are two effects:
1. Income Effect
2. Substitution Effect
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Definition: When the price of good X falls,
purchasing power rises. This is called the
income effect of a change in price.
 It assumes all else remain constant
 The income effect may be:
1. Positive (normal good)
2. Negative (inferior good).
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Definition: When the price of good X falls, good X
becomes cheaper relative to good Y. This
change in relative prices alone causes the
consumer to adjust his consumption basket.
This effect is called the substitution effect.
 It assumes all else remain constant
 The substitution effect is always negative
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 Usually, a move along a demand curve will be
composed of both effects.
 Let’s analyze both effects for the cases of:
 Normal good
 Inferior good
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Y
Example: Normal Good: Income and Substitution Effects
BL1 has slope
-PX1/PY
A
•
U1
0
XA
X
28
Y
Example: Normal Good: Income and Substitution Effects
BL2 has slope
-PX2/PY
A
•
C
•
U2
U1
0
XA
XC
X
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Y
Example: Normal Good: Income and Substitution Effects
A
•
C
•
B
0
XA
XB
•
U2
BLd has slope
-PX2/PY
U1
XC
X
30
Y
Example: Normal Good: Income and Substitution Effects
Substitution Effect: XB-XA
A
•
C
•
B
0
XA
XB
•
U2
U1
XC
X
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Y
Example: Normal Good: Income and Substitution Effects
Substitution Effect: XB-XA
Income Effect:
XC-XB
A
•
C
•
B
0
XA
XB
•
U2
U1
XC
X
32
Y
Example: Normal Good: Income and Substitution Effects
Substitution Effect: XB-XA
Income Effect:
XC-XB
Overall Effect:
XC-XA
A
•
C
•
B
0
XA
XB
•
U2
U1
XC
X
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Y
Example: Inferior Good: Income and Substitution Effects
BL1 has slope
-PX1/PY
A
•
U1
0
XA
X
34
Y
Example: Inferior Good: Income and Substitution Effects
•
C
A
•
U2
BL2 has slope
-PX2/PY
U1
0
XA
XC
X
35
Y
Example: Inferior Good: Income and Substitution Effects
•
C
A
•
•
B
0
XA
XC
XB
U2
BLd has slope
-PX2/PY
U1
X
36
Y
Example: Inferior Good: Income and Substitution Effects
Substitution Effect: XB-XA
•
C
A
•
•
B
0
XA
XC
XB
U2
U1
X
37
Y
Example: Inferior Good: Income and Substitution Effects
Substitution Effect: XB-XA
Income Effect:
XC-XB
•
C
A
•
•
B
0
XA
XC
XB
U2
U1
X
38
Y
Example: Inferior Good: Income and Substitution Effects
Substitution Effect: XB-XA
Income Effect:
XC-XB
Overall Effect:
XC-XA
•
C
A
•
•
B
0
XA
XC
XB
U2
U1
X
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 Theoretically, it is possible that, for an inferior
good, the income effect dominates the
substitution effect
 A Giffen good is a good that is so inferior, that
the net effect of a decrease in the price of that
good, all else constant, is a decrease in
consumption of that good.
40
Y
Example: Giffen Good: Income and Substitution Effects
BL1 has slope
-PX1/PY
A
•
U1
0
XA
X
41
Y
Example: Giffen Good: Income and Substitution Effects
•
C
U2
BL2 has slope
-PX2/PY
A
•
U1
0
XC XA
X
42
Y
Example: Giffen Good: Income and Substitution Effects
•
C
U2
A
•
•
BLd has slope
-PX2/PY
B
0
XC XA
XB
U1
X
43
Y
Example: Giffen Good: Income and Substitution Effects
•
C
Substitution Effect: XB-XA
Income Effect:
XC-XB
Overall Effect:
XC-XA
U2
A
•
•
B
0
XC XA
XB
U1
X
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Notes:
 For Giffen goods, demand does not slope
down.
 For the income effect to be large enough to
offset the substitution effect, the good would
have to represent a very large proportion of the
budget.
45
Example: Finding Income and Substitution Effects
Suppose a Quasilinear Utility:
U(X,Y) = 2X0.5 + Y
=>
MUX = 1/X0.5
PY = € 1
I = € 10
MUY = 1
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1. Suppose PX = € 0.50
• Tangency condition:
MUX = PX  _1_ = 0.5  XA = 4
MUY PY
X0.5
• Budget constraint:
PX . X + PY . Y = I  YA = 8
• Utility level:
U* = 2 (4)0.5 + 8 = 12
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2. Suppose PX = € 0.20
• Tangency condition:
MUX = PX  _1_ = 0.2  XC = 25
MUY PY
X0.5
• Budget constraint:
PX . X + PY . Y = I  YC = 5
• Utility level:
U* = 2 (25)0.5 + 5 = 15
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3. What are the substitution and income effects that result
from the decline in PX?
• Find the basket B that gives a utility level of U = 12
at prices PX = € 0.20 and PY = € 1
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Y
Substitution Effect: XB-XA
Income Effect:
XC-XB
Overall Effect:
XC-XA
A
•
C
•
B
0
XA=4
XB
•
U2=15
U1=12
XC=25
X
50
• Tangency condition:
MUX = PX  _1_ = 0.2  XB = 25
MUY PY
X0.5
• Utility constraint:
U* = 2 (25)0.5 + Y = 12  YB = 2
• Then:
• Substitution Effect:
• Income Effect:
XB - XA = 25 - 4 = 21
XC - XB = 25 - 25 = 0
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 The individual’s demand curve can be
interpreted as the maximum amount such
individual is willing to pay for a good
 In turn, the market price determines the
amount the individual actually pays for all the
units consumed.
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Definition:
 The consumer surplus is the net economic
benefit to the consumer due to a purchase of a
good
 It is measured by the difference between the
maximum amount the consumer is willing to
pay and the actual amount he pays for it.
 The area under the ordinary demand curve and
above the market price provides a measure of
consumer surplus.
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Example: Consumer Surplus
• Consider a Demand function:
• Suppose PX = € 3
Q = 40 - 4PX
• What is the consumer surplus?
• First, at price PX = € 3
=> Q = 28
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PX
Example: Consumer Surplus
10
X = 40 - 4PX ... Demand
40
X
55
PX
Example: Consumer Surplus
10
3
28
40
X
56
Example: Consumer Surplus
PX
10
Area = (0.5) (10-3) (28) = 98
G
3
28
40
X
57
PX
10
Example: Consumer Surplus
What if PX = € 2?
Area = (0.5) (10-2) (32) = 128
3
2
28
32
40
X
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Definition: The market demand function is the
horizontal sum of the demands of the
individual consumers.
 In other words, the market demand is obtained
by adding the quantities demanded by the
individuals at each price and plotting this total
quantity for all possible prices.
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Example: Suppose we have two consumers, as
shown below:
P
10
P
Q = 10 - p
P
Q = 20 - 5p
4
Consumer 1
Q
Consumer 2
Q
Q
Market demand
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1. Individual ordinary (uncompensated) demands
are derived from the utility maximization
problem of the consumer.
2. The optimal consumption basket for a utility
maximizing consumer changes as prices
change due to both income and substitution
effects.
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3. If income effects are strong enough, a price rise
may result in increased consumption for an
optimizing consumer.
4. Consumer surplus measures the net economic
benefit of a purchase.
5. Market demand is the horizontal sum of the
individual consumer demands for a particular
good.
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