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Lecture # 07-b The Theory of Demand Lecturer: Martin Paredes. Outline. Individual Demand Curves Income and Substitution Effects and the Slope of Demand Applications: the Work-Leisure Trade-off Consumer Surplus Constructing Aggregate Demand. Individual Demand Curves. - PowerPoint PPT Presentation
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Lecture # 07-bLecture # 07-b
The Theory of DemandThe Theory of Demand
Lecturer: Martin ParedesLecturer: Martin Paredes
2
1. Individual Demand Curves2. Income and Substitution Effects and
the Slope of Demand3. Applications: the Work-Leisure
Trade-off4. Consumer Surplus5. Constructing Aggregate Demand
3
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.
4
Y (units)
X (units)0PX = 4
XA=2
•10
PY = € 4I = € 40
20
5
Y (units)
X (units)0PX = 4 PX = 2
XA=2 XB=10
••
10
20
PY = € 4I = € 40
6
Y (units)
X (units)0PX = 4 PX = 2
PX = 1
XA=2 XB=10 XC=16
•• •
10
20
PY = € 4I = € 40
7
Y (units)
X (units)0PX = 4 PX = 2
PX = 1
XA=2 XB=10 XC=16
•• •
10
Price-consumption curve
20
PY = € 4I = € 40
8
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.
9X
PX
XA XB XC
Individual Demand CurveFor X
PX = 4
PX = 2PX = 1
••
•U increasing
10
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.
11
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
12X
PX Example: Demand Curve for an Interior Solution
QD = I/(2 PX)
13
Example: Suppose U(X,Y) = X + Y What is the price-consumption curve for good
X? What is the demand curve for good X?
14
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.
15
Example: Perfect Substitutes
X (units)
Y*=I/PY
PX>PY
0
Y (units)
•
IC
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Example: Perfect Substitutes
X (units)
Y*=I/PY
0
Y (units)
•
IC
PX=PY
17X (units)
Y*=I/PY
PX<PY
0
Y (units)
IC
Example: Perfect Substitutes
18X (units)
Y*=I/PY
0
Y (units)
IC
Example: Perfect Substitutes
•
Price-consumption curve
19
Demand curve for X:
0 when PX > PY
QDX = {0, I/P*} when PX = PY = P*
I/PX when PX < PY
20X
PX
0
PY
I/PY
I/PX
Demand curve for X
Example: Perfect Substitutes
21
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.
22X (units)
Y (units)
0 10
U1
I=40
23X (units)
Y (units)
0 10 18
U1 U2
I=68
I=40
24X (units)
Y (units)
0 10 18 24
U1 U2
U3
I=92
I=68
I=40
25X (units)
Y (units)
0 10 18 24
Income consumption curve
U1 U2
U3
I=92
I=68
I=40
26
Note: The points on the income-consumption
curve can be graphed as points on a shifting demand curve.
27
X (units)
Y (units)
0
PX
X (units)
$2
I=40
Income consumption curve
U1
I=40
10
10
28
X (units)
Y (units)
0
PX
X (units)
$2
I=68I=40
Income consumption curve
U1
U2
I=68
I=40
10 18
10 18
29
X (units)
Y (units)
0
10 18 24
PX
X (units)
10 18 24
$2I=92I=68I=40
Income consumption curve
U1
U2
U3
I=92
I=68
I=40
30
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.
31
X (units)0
I (€)
40
10
32
X (units)0
I (€)
68
40
10 18
33
X (units)0
I (€)
92
68
40
10 18 24
34
X (units)0
I (€)
92
68
40
10 18 24
Engel Curve
35
Note: When the slope of the income-
consumption curve is positive, then the slope of the Engel curve is also positive.
36
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.
37
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.
38
X (units)
Y (units)
0
I (€)
X (units)
U1
I=200
200
Example: Backward Bending Engel Curve
•
•
13
13
39
X (units)
Y (units)
0
I (€)
X (units)
U1U2
I=300
I=200
200
300
Example: Backward Bending Engel Curve
••
••
13 18
13 18
40
X (units)
Y (units)
0
I (€)
X (units)
U1U2
U3
I=400
I=300
I=200
200
300
400
Example: Backward Bending Engel Curve
•••
•
••
13 16 18
13 16 18
41
X (units)
Y (units)
0
I (€)
X (units)
13 16 18
U1U2
U3
I=400
I=300
I=200
200
300
400
Engel Curve
Example: Backward Bending Engel Curve
•••
•
••
13 16 18
Income consumption curve
