1. INTERMEDIATE MICROECONOMICS Topic 3 Consumer Choice These slides are copyright © 2010 by Tavis Barr. This work is licensed under a Creative Commons Attribution- ShareAlike 3.0 Unported License. See http://creativecommons.org/licenses/by-sa/3.0/ for further information.http://creativecommons.org/licenses/by-sa/3.0/

2. Topic Outline ● Preferences and Demand ● Ordinal Utility and Indifference Curves ● The Consumer's Budget and Choice Problem – Some problems and policy examples ● Working Backwards: Revealed Preference

3. Preferences and Demand ● Ordinal utility theory is based on preferences ● Ordinal utility is only strong enough to make statements about Pareto optimality ● The theory of demand is also based on preferences, so, similarly....

4. Preferences and Demand ● Two purposes of developing theories: – Positive statements predict how economic agents (e.g., consumers) are likely to behave – Normative statements tell us how agents ought to behave to achieve a good outcome ● So far we have mainly seen normative economics; we will begin looking at positive economics

5. Two-Good Bundles ● We usually consider economies with two goods available ● Screen is two-dimensional ● Works the same way for more goods but needs more dimensions

6. Recalling Assumptions 1.Completeness: The consumer can state whether she prefers any bundle to any other, or is indifferent between the two. 2.Transitivity: If A is preferred to B, and B is preferred to C, then A is preferred to C. 3.Continuity: If bundle A is preferred to bundle B, then any bundle sufficiently close to A is also preferred to B.

7. One More Assumption ● We will use Completeness, Transitivity, and Continuity ● We will need two more assumptions. The first: 2.Non-Satiation: All else equal, the consumer is strictly happier consuming a larger quantity of any good.

8. Indifference Curves ● A graphical tool that we use to describe and justify properties of consumer choice ● Properties of indifference curves can be derived from assumptions about preferences above

9. Indifference Point ● Suppose C>A (C is strictly preferred to A) ● We claim: There is a point D at the same level as C, such that D=A.

10. Indifference Point ● C>A; we claim that there is a point D=A – Because more is better, A>B and C>B

11. Indifference Point ● C>A; we claim that there is a point D=A – Because more is better, A>B and C>B – By continuity, there are points left of C strictly pref. to A.

12. Indifference Point ● C>A; we claim that there is a point D=A – Because more is better, A>B and C>B – By continuity, there are points left of C strictly pref. to A. – Let D be the upper bound of the points not strictly preferred

13. Indifference Point ● C>A; we claim that there is a point D=A – Let D be the upper bound of the points not strictly preferred – D cannot be strictly worse; otherwise continuity says so are points right of D

14. Indifference Point ● C>A; we claim that there is a point D=A – Let D be the upper bound of the points not strictly preferred – D cannot be strictly better; otherwise continuity says so are points left of D

15. Indifference Point ● C>A; we claim that there is a point D=A – Let D be the upper bound of the points not strictly preferred – D cannot be strictly better or worse – So D=A

16. Indifference Curve ● Imagine moving B and C up and down ● We can trace out a line of points indifferent to A – May have to move C further out or C may not exist ● This line is the indifference curve passing through A

17. Our Final Assumption ● Call the X axis good “X” and the Y axis good “Y” ● The marginal rate of substitution of X for Y is the amount of Y the consumer is willing to give up for a unit of X and still be equally well off

18. Our Final Assumption ● The marginal rate of substitution of X for Y is the amount of Y the consumer is willing to give up for a unit of X and still be equally well off ● In other words, it's just negative 1 times slope of the indifference curve

19. Our Final Assumption ● In other words, it's just negative 1 times the slope of the indifference curve:

20. Our Final Assumption ● Assumption U5: Diminishing MRS. The marginal rate of substitution decreases as we move down the indifference curve ● In other words,the curve becomes flatter ● This is called a convex curve

21. Our Final Assumption ● Assumption U5: Diminishing MRS. The marginal rate of substitution decreases as we move down the indifference curve ● In other words,the curve becomes flatter ● Implies we prefer mixtures of goods

22. Our Final Assumption ● Assumption U5: Diminishing MRS. The marginal rate of substitution decreases as we move down the indifference curve ● Implies we prefer mixtures of goods ● Violations: Addictions, small quantities, lifestyle changes

23. Features of Indifference Curves ● Feature 1: Indifference curves are downward sloping ● An upward-sloping or flat indifference curve would violate the “more is better” assumption

24. Features of Indifference Curves ● Feature 2: Indifference curves don't intersect – Suppose they did. Then B=C=A. – But more is better says B>A, strictly.

25. Features of Indifference Curves ● Feature 3: Indifference curves to the “Northeast” represent more preferred bundles – Because “more is better”

26. Features of Indifference Curves Some odd cases: ● Perfect Complements – Goods are ideally consumed in some given proportion – Outside of this proportion, an additional amount of just one good adds nothing to well- being – Violates non-satiation

27. Features of Indifference Curves Some odd cases: ● Perfect Substitutes – Amount a of one good always has the exact same effect on utility as amount b of the other good – Indifference curves are flat – Violates diminishing MRS

28. Features of Indifference Curves Utility functions and indifference curves: ● Example: Consider ● Indifference curve: U is constant ● Say, U = 2. Then, B = 4P ● Violates non-satiation

29. Features of Indifference Curves Utility functions and indifference curves: ● Example: Consider U = B + 2P ● Indifference curve: U is constant ● Say, U = 10. Then, B = 10 - 2P ● Violates diminishing MRS

30. The Budget Constraint ● Indifference curves are not so useful if all we want to do is find highest utility – It's just above and to the right, ad astra... ● Consumer wants to choose best bundle she can afford

31. The Budget Constraint ● Consumer wants to choose best bundle she can afford ● We assume she has a fixed income I ● She can only spend it on goods X and Y ● Price of good X is p X, price of good Y is p Y

32. The Budget Constraint ● We assume she has a fixed income I ● She can only spend it on goods X and Y ● Price of good X is p X, price of good Y is p Y ● Her constraint says she can't spend more than her income:

33. The Budget Constraint ● Her constraint says she can't spend more than her income: ● In practice, because “more is better” she never spends less:

34. The Budget Constraint ● In practice, the budget constraint is: ● We can re-arrange this:

35. The Budget Constraint ● In practice, the budget constraint is: ● We can re-arrange this:

36. The Budget Constraint ● We can rewrite the budget constraint as: ● This is a line with slope - p X /p Y and intercept I/p Y

37. The Budget Constraint ● This is a line with slope - p X /p Y and intercept I/p Y ● Intercept indicates amount consumer buys if she spends all income on that good ● Slope shows relative prices

38. The Budget Constraint ● Example: – Consumer has a budget of $50 – Meat costs $2 – Potatoes cost $5

39. The Budget Constraint Price and Income Changes ● Increase in p X – moves X-intercept in – makes line steeper – Y-intercept unchanged

40. The Budget Constraint Price and Income Changes ● Decrease in p X – moves X-intercept out – makes line flatter – Y-intercept unchanged

41. The Budget Constraint Price and Income Changes ● Decrease in p Y – moves Y-intercept out – makes line steeper – X-intercept unchanged

42. The Budget Constraint Price and Income Changes ● Increase in p Y – moves Y-intercept in – makes line flatter – X-intercept unchanged

43. The Budget Constraint Price and Income Changes ● Increase in I – Shifts line out in parallel – Slope does not change

44. The Budget Constraint Policy effects ● In-Kind Subsidy – Shifts budget line right – Beyond subsidy amount, relative prices haven't changed, so slope doesn't

45. The Budget Constraint Policy effects ● Tax on one good – Same as price increase ● Subsidy to one good – Same as price drop ● Matching grant for expenditures on one good – Same as price drop

46. The Consumer Choice Problem ● Consumer will choose most preferred bundle that she can afford ● In other words, she will try to get on the highest indifference curve that intersects her budget constraint

47. The Consumer Choice Problem ● Consumer tries for highest indifference curve that intersects her budget constraint – That curve won't cross it – Will intersect

48. The Consumer Choice Problem ● A line that intersects but does not cross a curve is called a tangent line ● At the point of intersection, curve and tangent line have the same slope

49. The Consumer Choice Problem ● At the point of intersection, curve and tangent line have the same slope ● Slope of budget line is constant ● So diminishing MRS implies unique choice

50. The Consumer Choice Problem ● Example: Tax Breaks for Teaching Supplies – Reimburses for money already spent – But also alters incentive to spend – Should we encourage teachers to spend?

51. The Consumer Choice Problem ● At the point of intersection, curve and tangent line have the same slope ● Slope of budget constraint: -p X /p Y ● Slope of indifference curve: -1 times MRS

52. The Consumer Choice Problem ● Slope of budget constraint: -p X /p Y ● Slope of indifference curve: -1 times MRS ● At chosen bundle,

53. The Consumer Choice Problem ● At chosen bundle,

54. The Consumer Choice Problem Implies substitution: ● When p X is high, budget line is steep ● Consume bundle with high MRS ● High MRS is above and left ● We use relatively less of expensive good

55. The Consumer Choice Problem Also implies value ● Smith, Ricardo, Marx: Labor Theory of Value – Social worth of a good is determined by how much labor it saves – Prices reflect this, and also dead labor (machinery) – Ricardo: Prices also reflect land rents

56. The Consumer Choice Problem Also implies value ● Neoclassical view: – All goods can be scarce, not just labor, land, capital – Relative price will reflect relative difficulty of obtaining more

57. The Consumer Choice Problem ● Same result can be expressed in terms of marginal utility ● The marginal utility of a good is the increase in utility from consuming one more unit of that good – At one crumpet and one cup of tea, marginal utility of crumpets is 5 and tea is 10

58. The Consumer Choice Problem We can show that MRS = -MU(X)/MU(Y) ● Move small amount along IC and slope and MU barely change ● Start at point A, bundle X,Y. Utility change from A to B is X × MU(X) + Y × MU(Y) ● But A and B have same utility, so X × MU(X) + Y × MU(Y) = 0 ● So MRS = -Y/X = MU(X)/MU(Y)

59. The Consumer Choice Problem We have shown: ● Anywhere along indifference curve: MRS =MU(Y)/MU(X) ● At chosen bundle of goods: MRS = p X /p Y ● This implies the Equal Marginal Principle: MU(X)/p X =MU(Y)/p Y at chosen bundle

60. The Consumer Choice Problem Equal Marginal Principle: MU(X)/p X = MU(Y)/p Y at the chosen bundle ● Says the “Bang for the buck” is the same for every good ● If it weren't, we should consume less of the good with the lower MU per dollar

61. The Consumer Choice Problem ● The exception: A corner solution ● Some goods don't interest us as much, relatively, as their price ratios would require ● We don't consume those goods

62. The Consumer Choice Problem ● Example: Food stamps – Designed to ensure stipends are spent on “good” things – May increase food expenditures above what people would prefer – May leave people in dissatisfied state since MRS < p X /p Y

63. Revealed Preference ● Ordinal utility functions can be derived from preferences if they are “well-behaved” ● We can make conclusions about utility (and also test assumptions about preference) by observing consumer choices ● Requires choice to be “well-behaved”

64. Revealed Preference ● We can draw conclusions about preferences if choice is “well-behaved” ● We require the Principle of Revealed Preference: Suppose that a consumer can afford both bundles A and B, but she chooses Bundle A. Then it must be the case that she prefers bundle A to bundle B.

65. Revealed Preference ● We require the Principle of Revealed Preference: Suppose that a consumer can afford both bundles A and B, but she chooses Bundle A. Then it must be the case that she prefers bundle A to bundle B. ● Says a chosen bundle is a (perhaps weakly) preferred bundle

66. Revealed Preference ● Revealed Preference says a chosen bundle is a (perhaps weakly) preferred bundle ● Example: – Period 1: Budget is $50, roses cost $1, and bread costs $2. – Emma chooses 20 loaves bread and 10 roses. – Period 1: Budget is $100, bread still costs $2, but roses now cost $4 – She now chooses 20 roses, 10 loaves bread.

67. Revealed Preference ● Example: Pd.Ip B p R q B q R 15021 2010 210024 1020 ● Can afford A in pd. 2? Yes: 2(20)+4(10)=80<100 ● Can afford B in pd. 1? Yes: 2(10)+1(20)=40<50

68. Revealed Preference ● Can afford A in pd. 2? Yes: 2(20)+4(10)=80<100 ● Can afford B in pd. 1? Yes: 2(10)+1(20)=40<50 ● Chooses A when she can afford B. Must prefer A to B. ● Chooses B when she can afford A. Must prefer B to A.

69. Revealed Preference ● Chooses A when she can afford B. Must prefer A to B. ● Chooses B when she can afford A. Must prefer B to A. ● Must be indifferent between A and B. ● But she can do better than B in period 1 and better than A in pd. 2.

70. Revealed Preference ● Must be indifferent between A and B. ● But she can do better than B in period 1 and better than A in pd. 2. ● Therefore either she does not follow revealed preference or her preferences are inconsistent.

71. Revealed Preference ● Therefore either she does not follow revealed preference or her preferences are inconsistent. ● The Weak Axiom of Revealed Preference says that if A is revealed preferred to B, then B will not be revealed preferred to A

72. Revealed Preference ● Another example: – Mario spends his income on magic mushrooms and sci-fi wasabe. – In period 1: ● Mushrooms cost $2 ● Wasabe costs $3 per jar ● Mario's budget is $40 ● He chooses 8 mushrooms & 8 jars wasabe

73. Revealed Preference ● Another example: – Mario spends his income on magic mushrooms and sci-fi wasabe. – In period 2: ● Mushrooms cost $5 ● Wasabe costs $4 per jar ● Mario's budget is $80 ● He chooses 4 mushrooms & 15 jars wasabe

74. Revealed Preference ● Recap: Pd.Ip M p W q M q W 14023 88 28054 415 ● Can afford A in pd. 2? Yes: 5(8)+4(8)=72<80 ● Can afford B in pd. 1? No: 2(4)+3(15)=53>40

75. Revealed Preference ● Can afford A in pd. 2? Yes: 5(8)+4(8)=72<80 ● Can afford B in pd. 1? No: 2(4)+3(15)=53>40 ● Chooses not to consume A in 2 even though he could ● Must like B better ● Was better off in period 2 than period 1.

76. Revealed Preference The general story: Could afford Period 1 bundle in Period 2? YesNo Could YesPreferencesBetter off affordInconsistentin Period 1 Period 2 bundle inNoBetter offNo Period 1?in Period 2Conclusion

77. Recovering Indifference Curves ● Suppose we know the consumer chose A, B, C, D,E ● Clearly, A is preferred to B, since B was affordable when A was chosen

78. Recovering Indifference Curves ● Clearly, A is preferred to B, since B was affordable when A was chosen ● Similarly: – B > C – C > D – D > E

79. Recovering Indifference Curves ● Revealed preference tells us: – A > B – B > C – C > D – D > E ● Transitivity then tells us: A > B > C > D > E

80. Recovering Indifference Curves ● We know: A>B>C>D>E ● Since B is preferred to C, so is anything better than B

81. Recovering Indifference Curves ● We know: A>B>C>D>E ● Since B is preferred to C, so is anything better than B ● And so is anything better than A

82. Recovering Indifference Curves ● We know: A>B>C>D>E ● Anything better than A or B is better than C ● By diminishing MRS, so is anything on or above the line between A and B

83. Recovering Indifference Curves ● We know: A>B>C>D>E ● Anything affordable when C was bought is worse than C

84. Recovering Indifference Curves ● We know: A>B>C>D>E ● Anything affordable when C was bought is worse than C ● And so is anything affordable when D or E was bought

85. Topic Summary Five assumptions ● Three original – Completeness – Transitivity – Continuity ● Two more – Non-satiation – Diminishing MRS Indifference Curves ● Do not cross ● Downward-sloping ● Convex with diminishing MRS ● “Northeast” is higher utility

86. Topic Summary Budget constraints ● Slope -p X /p Y Intercepts I/p X, I/p Y ● Steeper when p X goes up or p Y goes down ● Flatter when p X goes down or p Y goes up ● Income increase: Parallel shift out Consumer choice ● Consumer chooses bundle on indifference curve that touches, but does not cross, budget line ● If diminishing MRS, then bundle is unique

87. Topic Summary Properties of choice ● MRS = p X /p Y – Implies substitution – Prices reflect scarcity ● Equal Marginal Principle: MU X /p X = MU Y /p Y – “Bang for the buck” the same across goods Revealed Preference ● If cons. can afford both bundles in one period, but only one in the other, better off when she can afford both ● Both in both periods: Prefs Inconsistent ● Neither in other: No conclusion