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

2. Outline Individual Demand Curves
Income and Substitution Effects and the Slope of Demand
Applications: the Work-Leisure Trade-off
Consumer Surplus
Constructing Aggregate Demand

3. Individual Demand Curves
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. The Price-Consumption Curve
Y (units)
The Price-Consumption Curve
PY = € 4
I = € 40 10 •
PX = 4
X (units)
XA=2 20

5. The Price-Consumption Curve
Y (units)
The Price-Consumption Curve
PY = € 4
I = € 40 10 • •
PX = 2
PX = 4
X (units)
XA=2
XB=10 20

6. The Price-Consumption Curve
Y (units)
The Price-Consumption Curve
PY = € 4
I = € 40 10 • • •
PX = 1
PX = 2
PX = 4
X (units)
XA=2
XB=10
XC=16 20

7. The Price-Consumption Curve
Y (units)
The Price-Consumption Curve
PY = € 4
I = € 40 10 •
Price-consumption curve • •
PX = 1
PX = 2
PX = 4
X (units)
XA=2
XB=10
XC=16 20

8. Individual Demand Curves
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.

9. Individual's Demand CurvePX
Individual Demand Curve
For X •
PX = 4 •
PX = 2 •
U increasing
PX = 1 X
XA XB XC

10. Individual Demand Curves
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. 1. MUX = MUY  Y = X  PY . Y = PX . X PX PY PX PY
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

12. PX
Example: Demand Curve for an Interior Solution
QD = I/(2 PX) X

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
Y (units)
Example: Perfect Substitutes •
Y*=I/PY
PX>PY IC
X (units)

16. Example: Perfect Substitutes
Y (units)
Example: Perfect Substitutes •
Y*=I/PY
PX=PY IC
X (units)

17. Example: Perfect Substitutes
Y (units)
Example: Perfect Substitutes
Y*=I/PY
PX<PY IC
X (units)

18. Example: Perfect Substitutes
Y (units)
Example: Perfect Substitutes •
Y*=I/PY
Price-consumption curve IC
X (units)

19. Demand curve for X:
0 when PX > PY
QDX = {0, I/P*} when PX = PY = P*
I/PX when PX < PY

20. Example: Perfect SubstitutesPX
Example: Perfect Substitutes PY
I/PX
Demand curve for X X
I/PY

21. Individual Demand when Income Changes
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.

22. Income-Consumption Curve
Y (units)
Income-Consumption Curve
I=40 U1 10
X (units)

23. Income-Consumption Curve
Y (units)
Income-Consumption Curve
I=68
I=40 U1 U2
10 18
X (units)

24. Income-Consumption Curve
Y (units)
Income-Consumption Curve
I=92
I=68 U3
I=40 U1 U2
X (units)

25. Income-Consumption Curve
Y (units)
Income-Consumption Curve
I=92
Income consumption curve
I=68 U3
I=40 U1 U2
X (units)

26. Individual Demand when Income Changes
Note:
The points on the income-consumption curve can be graphed as points on a shifting demand curve.

27. Income-Consumption Curve
Y (units)
Income-Consumption Curve
Income consumption curve
I=40 U1
X (units) 10 PX $2
I=40
X (units) 10

28. Income-Consumption Curve
Y (units)
Income-Consumption Curve
I=68
Income consumption curve
I=40 U2 U1
X (units) PX $2
I=40
I=68
X (units)

29. Income-Consumption Curve
Y (units)
Income-Consumption Curve
I=92
I=68 U3
Income consumption curve
I=40 U2 U1
X (units) PX $2
I=92
I=40
I=68
X (units)

30. The Engel Curve
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. I (€)
The Engel Curve 40
X (units) 10

32. I (€)
The Engel Curve 68 40
X (units)

33. I (€)
The Engel Curve 92 68 40
X (units)

34. I (€)
The Engel Curve
Engel Curve 92 68 40
X (units)

35. The Engel Curve
Note:
When the slope of the income-consumption curve is positive, then the slope of the Engel curve is also positive.

36. Definitions of Goods 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. Definitions of Goods 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. • • Example: Backward Bending Engel Curve Y (units) I=200 U1 X (units)
X (units) 13
I (€) •
200
X (units) 13

39. • • • • Example: Backward Bending Engel Curve Y (units) I=300 I=200 U2
X (units)
I (€) •
300 •
200
X (units)

40. • • • • • • Example: Backward Bending Engel Curve Y (units) I=400
X (units)
I (€) •
400 •
300 •
200
X (units)

41. • • • • • • Example: Backward Bending Engel Curve
Y (units)
I=400
Example: Backward Bending Engel Curve
I=300 U3 •
Income consumption curve
I=200 U2 U1 • •
X (units)
I (€) •
400 •
300
Engel Curve •
200
X (units)