Income and Substitution Effects

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

2. Demand and income X • 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 A2 A1

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

36. 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