Lecture # 07-b The Theory of Demand Lecturer: Martin Paredes

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.

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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)

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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.

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Example: Perfect Substitutes

X (units)

Y*=I/PY

PX>PY

0

Y (units)

•

IC

16

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.

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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.

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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