Lecture # 07-b
The Theory of Demand
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
2
Definition: The price-consumption curve of good X
is the set of optimal baskets for every possible
price of good X
 Assumes all other variables remain constant.
3
Y (units)
PY = € 4
I = € 40
10
•
PX = 4
0
XA=2
20
X (units)
4
Y (units)
PY = € 4
I = € 40
10
•
0
XA=2
•
PX = 4
XB=10
PX = 2
20
X (units)
5
Y (units)
PY = € 4
I = € 40
10
•
0
XA=2
•
PX = 4
XB=10
•
PX = 1
PX = 2
XC=16
20
X (units)
6
Y (units)
PY = € 4
I = € 40
10
•
0
XA=2
Price-consumption curve
•
PX = 4
XB=10
•
PX = 1
PX = 2
XC=16
20
X (units)
7
Note:
 The price-consumption curve for good X can be
written as the quantity consumed of good X for
any price of X.
 This is the individual’s demand curve for
good X.
8
PX
Individual Demand Curve
For X
PX = 4
•
PX = 2
PX = 1
XA
•
XB
•
XC
U increasing
X
9
Notes:
 The consumer is maximizing utility at every
point along the demand curve
 The marginal rate of substitution falls along the
demand curve as the price of X falls (if there
was an interior solution).
 As the price of X falls, utility increases along
the demand curve.
10
Example: Finding a Demand Curve with an Interior
Solution
 Suppose
U(X,Y) = XY
 The optimal conditions are:
1. MUX = MUY  Y = X  PY . Y = PX . X
PX
PY
PX
PY
2. PX . X + PY . Y = I  2 PX . X = I  X = I .
2 PX
11
PX
Example: Demand Curve for an Interior Solution
QD = I/(2 PX)
X
12
Example:
 Suppose
U(X,Y) = X + Y
 What is the price-consumption curve for good X?
 What is the demand curve for good X?
13
Price-consumption curve:
 When PX < PY, then X* = I/PX and Y* = 0
 When PX > PY, then X* = 0 and Y* = I/PY
 When PX = PY, the consumer chooses any point in
the budget line.
14
Y (units)
Example: Perfect Substitutes
Y*=I/PY
•
PX>PY
IC
0
X (units)
15
Y (units)
Example: Perfect Substitutes
Y*=I/PY
•
PX=PY
IC
0
X (units)
16
Y (units)
Example: Perfect Substitutes
Y*=I/PY
PX<PY
IC
0
X (units)
17
Y (units)
Example: Perfect Substitutes
Y*=I/PY
•
Price-consumption curve
IC
0
X (units)
18
Demand curve for X:
QDX =
0
when PX > PY
{0, I/P*}
when PX = PY = P*
I/PX
when PX < PY
19
PX
Example: Perfect Substitutes
PY
I/PX
Demand curve for X
0
I/PY
X
20
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.
21
Y (units)
I=40
U1
0
10
X (units)
22
Y (units)
I=68
I=40
U1
0
10
18
U2
X (units)
23
Y (units)
I=92
I=68
U3
I=40
U1
0
10
18
U2
24
X (units)
24
Y (units)
I=92
Income consumption curve
I=68
U3
I=40
U1
0
10
18
U2
24
X (units)
25
Note:
 The points on the income-consumption curve
can be graphed as points on a shifting demand
curve.
26
Y (units)
I=40
0
Income consumption curve
U1
10
X (units)
PX
$2
I=40
10
X (units)
27
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)
28
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)
29
 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.
30
I (€)
40
0
10
X (units)
31
I (€)
68
40
0
10
18
X (units)
32
I (€)
92
68
40
0
10
18
24
X (units)
33
I (€)
Engel Curve
92
68
40
0
10
18
24
X (units)
34
Note:
 When the slope of the income-consumption
curve is positive, then the slope of the Engel
curve is also positive.
35
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.
36
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.
37
Y (units)
Example: Backward Bending Engel Curve
I=200
0
U1
•
13
X (units)
I (€)
200
•
13
X (units)
38
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)
39
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)
40
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)
41