1. Income and Substitution Effects
Engel Curves and the Slutsky Equation

2. Demand and income If your income is initially X1, you buy A1 apples
When your income rises to X2, you buy A2 apples.
To make the obvious point, demand is a function of income X2 X1 I2 I1 A1 A2

3. How demand rises with income
Lets plot the combinations of apples and income (X) from the previous graph. A2 A1 X1 X2

4. How demand rises with income
Lets plot the combinations of apples and income (X) from the previous graph.
Connecting all possible points, we get the Engel curve, giving demand as a function of income. A2 A1 X1 X2

5. The Shape of the Engel Curve
The shape of the Engel Curve gives us the income elasticity of demand for the good
If the Engel Curve is a straight line, the income elasticity is 1.0 X

6. The Shape of the Engel Curve
The shape of the Engel Curve gives us the income elasticity of demand for the good
If the Engel Curve has increasing slope the elasticity is greater than 1.0 X

7. The Shape of the Engel Curve
The shape of the Engel Curve gives us the income elasticity of demand for the good
If the Engel Curve has decreasing slope the elasticity is less than 1.0 X

8. The Shape of the Engel Curve
Of course the Engel Curve need not be so well behaved
This Engel Curve corresponds to a good that is both inferior and superior, depending on income X

9. Income and Substitution Effects
We know that both price and income influence demand.

10. Income and Substitution Effects
We know that both price and income influence demand.
A price change means an income change.

11. Income and Substitution Effects
We know that both price and income influence demand.
A price change, means an income change.
You are purchasing 10 apples at $1 each.
If the price falls to 50¢, you effectively get $5 more income

12. Income and Substitution Effects
Let’s draw the indifference curves between money and apples. $ Yo I1 A
Yo/pA

13. Income and Substitution Effects
Let’s draw the indifference curves between money and apples.
Your income is Yo; Apples initially cost pa $ Yo I1 A
Yo/pA

14. Income and Substitution Effects
Let’s draw the indifference curves between money and apples.
Your income is Yo; Apples initially cost pa
You are are on indifference curve I1. $ Yo I1 A
Yo/pA

15. Income and Substitution Effects
Suppose the price of apples drops to p*a $ Yo I2 I1 A
Yo/p*A
Yo/pA

16. Income and Substitution Effects
Suppose the price of apples drops to p*a
The budget line rotates out and you move to indifference curve I2. $ Yo I2 I1 A
Yo/p*A
Yo/pA

17. Income and Substitution Effects
Suppose the price of apples drops to p*a
The budget line rotates out and you move to indifference curve I2.
Two things have occurred: a price cut and an increase in income. $ Yo I2 I1 A
Yo/p*A
Yo/pA

18. Income and Substitution Effects
The substitution effect $ Yo I2 I1 A
Yo/p*A
Yo/pA

19. Income and Substitution Effects
The substitution effect
To isolate the effect of the lower price, imagine a budget line like the red line, reflecting the lower price but tangent to the old indifference curve. $ Yo I2 I1 A
Yo/p*A
Yo/pA

20. Income and Substitution Effects
The substitution effect
To isolate the effect of the lower price, imagine a budget line like the red line, reflecting the lower price but tangent to the old indifference curve.
The move to the red point on I1 shows the substitution effect. $ Yo I2 I1 A
Yo/p*A
Yo/pA

21. Income and Substitution Effects
The substitution effect is always negative
Diminishing MRS guarantees it $ Yo I2 I1 A
Yo/p*A
Yo/pA

22. Income and Substitution Effects
The substitution effect is always negative
The income effect
Of course, income has gone up as well, and the movement from the red point to the green point reflects that. $ Yo I2 I1 A
Yo/p*A
Yo/pA

23. Income and Substitution Effects
We effectively break the price change down into its two components.
The substitution effect
The income effect. $ Yo I2 I1 A
Yo/p*A
Yo/pA

24. Income and Substitution Effects
We effectively break the price change down into its two components.
The substitution effect
The income effect.
While the substitution effect is always negative, the income effect may or not be positive $ Yo I2 I1 A
Yo/p*A
Yo/pA

25. A Summary Table

26. The Slutsky Equation
These effects are often summarized in the Slutsky equation

27. The Slutsky Equation
These effects are often summarized in the Slutsky equation
The substitution effect shows the change in demand from a movement along the indifference curve.

28. The Slutsky Equation
These effects are often summarized in the Slutsky equation
The income effect shows the change in demand from the effective increase in income.

29. An Application

30. An Application

31. An Application

32. An Application

33. An Application
(Q/P) = 3/(-0.05) = - 60

34. An Application
(Q/P) = - 60
Q(Q/I) = 50 (1) = 50

35. -60  (Q/P)U=Constant –50
An Application
(Q/P) = - 60
Q(Q/I) = 50
-60  (Q/P)U=Constant –50

36. -60  (Q/P)U=Constant –50
An Application
-60  (Q/P)U=Constant –50
(Q/P)U=Constant = -10

37. A Caution
The version of the Slutsky equation we use is only an approximation.

38. A Caution
The version of the Slutsky equation we use is only an approximation.
We are assuming discrete changes in price and income; the correct equation assumes infinitesimal changes.

39. Why spend time on this topic?
Giffin Goods

40. Why spend time on this topic?
Giffin Goods
The Demand for Leisure

41. Why spend time on this topic?
Giffin Goods
The Demand for Leisure
As wage rates increase, the cost of an hour of leisure increases
Demand goes up because the income effect dominates the substitution effect.

42. Why spend time on this topic?
Giffin Goods
The Demand for Leisure
Different Slopes .

43. Why spend time on this topic?
Giffin Goods
The Demand for Leisure
Different Slopes
Changes in the price of one brand versus changes in the prices of all brands. .

44. Why spend time on this topic?
Giffin Goods
The Demand for Leisure
Different Slopes
Changes in the price of one brand versus changes in the prices of all brands.
Heavily purchased goods versus lightly purchased goods.

45. A Final Point

46. A Final Point
The slope of the Marshallian, or uncompensated demand function

47. A Final Point
The slope of the Marshallian, or uncompensated demand function
The slope of the Hicksian, or compensated demand function.
©2003 Charles W. Upton