1. Consumer behaviour: Ordinal approach Now, we go to the ordinal approach. Ordinalist cares only about ranking. It doesn’t matter if we say U(A) = 20, U(B) = 10, or U(A) = 25, U(B) = 12. Because in both cases, the U(A) > U(B). Any methods of “renaming” the utility figure is valid, provided that the order of the figures are retained. (monotonic transformation)

2. Consumer behaviour: Ordinal approach To take out all the intensity implication of utility, ordinalist proposes to use “indifference curves”. Suppose you need only two goods X and Y. U(X, Y) = U(20, 30) = 8. But you will be equally satisfied if you have more X but fewer Y. U(40, 20) = 8. Joining all the consumption combinations that give you the same utility level → indifference curve on the (X, Y)-space.

3. Consumer behaviour: Ordinal approach Indifferent between B, A, & D E is preferred to U 1 U 1 is preferred to H & G X 10 20 30 40 10203040 Y 50 U1U1 G D A E H B

4. Consumer behaviour: Ordinal approach Properties of IC: (1) Points on an IC gives the same utility to an consumer. The proof is trivial coz this is true by definition.

5. Consumer behaviour: Ordinal approach Properties of IC (cont’d): (2) IC of two “goods” can never be upward-sloping (mostly likely downward-sloping): At point A, you have more X and more Y than at point B, by “more is better”, U(A) > U(B). Good Y 34 Good X A B 6 4

6. Consumer behaviour: Ordinal approach Properties of IC (cont’d): (3) A higher IC represents a higher utility level: For a higher IC, it contains a point (such as A) that must be better than a point (such as B) for a lower IC. By “more is better”, A is better than B. Good Y 46 Good X A B 5 4

7. Consumer behaviour: Ordinal approach Properties of IC (cont’d): (4) Two ICs never cross: U(A) > U(B) (more is better. U(A) = U(C) and U(B) = U(C) by the definition of IC. By transitivity, U(A) = U(B). Inconsistent.

8. Consumer behaviour: Ordinal approach Food Clothing U(A)≠U(B) (two ICs) U(C)=U(A) & U(C)=U(B) (same IC) U(A)=U(B) (transitivity) Inconsistent. U1U1 U1U1 U2U2 U2U2 C A B U(A)>U(B) (more is better) U(C)=U(A) & U(C)=U(B) (same IC) U(A)=U(B) (transitivity) Inconsistent.

9. Consumer behaviour: Ordinal approach The 4 properties of ICs are all derived from the 3 basic preference postulates. The set of ICs that reflects your preference is like a map: indifference map.

10. Indifference Map U2U2 U3U3 X Y U1U1 A B D

11. Consumer behaviour: Ordinal approach In cardinal approach, we said we need one more information in addition to the 3 basic postulates: diminishing MU. In ordinal approach, we can’t use the concept of MU: We don’t know the 8 th bottle you consume generates fewer additional satisfaction than the 1 st bottle or not.

12. Consumer behaviour: Ordinal approach Instead, ordinalist believes preference is governed by another law: law of diminishing marginal rate of substitution (MRS). MRS: How much more of a good (e.g. Y) you would require to compensate for the loss of a unit of another good (e.g. X) so that you are equally well off?

13. X 23451 Y 2 4 6 8 10 12 14 16 A B D E G MRS = 6 MRS: the slope of an IC, -∆Y/∆X. Why? Because along the IC, utility is the same. Reducing certain amount of X, utility is lowered. Increasing the quantity of Y, utility is increased. Along the IC, the gain and loss just offset. +∆Y can just compensate the utility loss due to -∆X. Each unit of reduction in X must be given an increase in Y by -∆Y/∆X to compensate the loss.

14. X 23451 Y 2 4 6 8 10 12 14 16 A B D E G +6 +4 +2 +1 MRS = 6 MRS = 2 Diminishing MRS: the slope (absolute value) of IC is decreasing; it becomes flatter and flatter. Implication: when you have a lot of X, you need fewer Y to compensate for giving up a unit of X. IC with decreasing slope is called “convex” (to origin).

15. X 23451 Y 2 4 6 8 10 12 14 16 A B D E G +6 +4 +2 +1 MRS = 6 MRS = 2 Diminishing MU provides a reason for diminishing MRS. When we have a lot of X, MU X is smaller, required compensation (∆Y) is smaller. But MU X is high when X is small, required compensation (∆Y) is large.

16. Consumer behaviour: Ordinal approach Diminishing MRS also reflects people’s tendency to become fed up with a good when consuming more and more of it. But “MU” (a concept of cardinal U) is not needed (only changes in X and Y, no change in U). Alternatively, convex IC also means people prefer a balanced consumption combination to an unbalanced combination.

17. Convexity in IC U2U2 C X 408020 Y 30 40 0 U1U1 A B Balanced bundle: C Unbalanced bundle: A, B Along the line, X+Y is the same.

18. Consumer behaviour: Ordinal approach With a convex IC, we can “solve” the consumer problem as the cardinal approach does. Budget constraint I = P X X + P Y Y is a straight line (budget line) on the (X, Y)-space: -BL cuts vertical axis at I/P Y. -BL cuts horizontal axis at I/P X.

19. Budget Line 10 20 A B D E G ( I/P Y ) = 40 X 4060 80 = ( I/P X ) 20 10 20 30 0 Y

20. Consumer behaviour: Ordinal approach What will happen to BL if income increases? -Two end-points (I/P Y, I/P X ) What will happen to BL if P X falls? What will happen to BL if P Y falls?

21. Budget Line: Income Change A increase in income shifts the budget line outward X Y 80=80/P X 160=160/P X 40 20 160/P Y =80 0 ( I = $160) L2L2 ( I = $80) L1L1 L3L3 ( I = $40) A decrease in income shifts the budget line inward 80/P Y =40

22. Budget Line: Price Change ( P X = 1) L1L1 An increase in the price of X to $2.00 changes the slope of the budget line and rotates it inward. L3L3 ( P X = 2) ( P X ’= 1/2) L2L2 A decrease in the price of X to $.50 changes the slope of the budget line and rotates it outward. 40 X Y 80=I/P X 160=I/P X ’ 40 I=80

23. U3U3 D U2U2 C X 408020 Y 30 40 0 U1U1 A B Slope of IC = Slope of BL MRS = -ΔY/ΔX = P X /P Y A point on BL I = P X X + P Y Y Put BL and ICs together. At which point you can achieve the highest level of utility? The point where IC is tangent to BL. Some points above BL are not attainable. Some points below BL give you lower utility.

24. Consumer behaviour: Ordinal approach This result is equivalent to the result in cardinal approach MU X /P X = MU Y /P Y. Why? The slope of BL is - P X /P Y. (Because I/P Y  I/P X = P X /P Y )

25. Consumer behaviour: Ordinal approach The slope of IC is MU X /MU Y. -A movement along IC: ∆X and ∆Y. -This brings about utility change of MU X ∆X + MU Y ∆Y. -Utility does not change along IC: MU X ∆X + MU Y ∆Y = 0 -Hence, the slope of IC: ∆Y/∆X = MRS = - MU X /MU Y.

26. Consumer behaviour: Ordinal approach At the point where BC is tangent to IC: MRS = MU X /MU Y = P X /P Y Rearrange, this is exactly the result in cardinal approach MU X /P X = MU Y /P Y. Another condition is the budget constraint (I = P X X + P Y Y) – the best point must be on the budget line. Ordinal approach and cardinal approach is equivalent but ordinal approach doesn’t use MU and the controversial concept of cardinal utility.

27. Consumer behaviour: Ordinal approach Another advantage of IC approach is: it can show up the relationship between two goods more clearly. Examples: Perfect substitutes, perfect complements.

28. Orange Juice (glasses) Apple Juice (glasses) 2341 1 2 3 4 0 Perfect substitutes: willing to trade X for Y at a fixed rate (not necessarily 1:1)

29. Right Shoes Left Shoes 2341 1 2 3 4 0 Perfect complements: Can’t consume two goods at different ratios.

30. Relative Preference between Goods These consumers place a greater value on X than Y Y X

31. Relative Preference between Goods These consumers place a greater value on Y than X Y X

32. Consumer behaviour: Ordinal approach Other issues about IC analysis: Trade-off between one good and one “bad”: -When both X and Y are “goods”, IC is downward-sloping. -But when one of them is “bad”, it is upward- sloping. -More X reduces utility, need more Y to compensate.

33. IC for a Good and a Bad Working Hours, L Consumption, X Longer working time, higher value of consumption, constant utility U1U1 U2U2 U3U3

34. Consumer behaviour: Ordinal approach Trade-off between one good and one “bad” (cont’d): -You won’t pay to purchase more “bad”. Rather, usually you are “paid” to induce you to accept more “bad”. E.g. you receive wage to accept a longer hours of work. -Upward-sloping BL. P X X = wL. -Consumer’s choice.

35. Optimal Choice of a Good and a Bad X Budget Line P X X = wL U2U2 U1U1 U3U3 L X* L*

36. Consumer behaviour: Ordinal approach Corner solutions: -When consumer’s preference is “extreme”, e.g. prefer X strongly, the tangency point of IC and BL may not be the best choice. -The best point is located at the corner. -Our previous principle for best choice is no longer valid: MRS ≠P X /P Y.

37. Corner Solution Ice Cream (cup/month) Frozen Yogurt (cups monthly) B A U2U2 U3U3 U1U1 A corner solution exists at point B.

38. Orange Juice (glasses) Apple Juice (glasses) 2341 1 2 3 4 0 U1U1 U4U4 U3U3 U2U2 BL Other examples of corner solutions: For perfect substitutes, optimal point is also at the corner. Why consume only one good?

39. P Q Food ($) Other Consumption ($) U2U2 A U1U1 B Old budget: PQ A free gift of food PB New budget PBC B is corner solution MRS ≠ P F /P OC C Other examples of corner solutions: Kinked budget line: You are given a free gift (food) of certain amount. But you can pay more to consume more (both food and other consumption).

40. Corner Solution: Price Change Ice Cream (cup/month) Frozen Yogurt (cups monthly) B A U2U2 U3U3 U1U1 A corner solution exists at point B, even though price of Yogurt is different (AB, CB). Consumption changes only when price changes a lot (DB). C D

41. Interior Solution: Price Change U3U3 D U2U2 C Food (units per week) 408020 Clothing (units per week) 20 30 40 0 U1U1 A B

42. Consumer behaviour: Ordinal approach Summary: -Cardinal approach and ordinal approach can derive the same results for consumer behaviour. -Cardinal approach is more intuitive. -Ordinal approach sets aside the controversy about measurement of utility. Thus, this approach is preferred by economists. -In what follows, ordinal approach is used (you are required to be familiar with ordinal approach).