1. Chapter 3 CONSUMER CHOICE

2. Chapter Outline 4-2 1. Preferences. 2. Utility. 3. Budget Constraint. 4. Constrained Consumer Choice. 5. Behavioral Economics.

3. Premises of Consumer Behavior 4-3 The model of consumer behavior is based on the following premises:  Individual preferences determine the amount of pleasure people derive from the goods and services they consume.  Consumers face constraints or limits on their choices.  Consumers maximize their well-being or pleasure from consumption, subject to the constraints they face.

4. Five Properties of Consumer Preferences 4-4  Completeness - when facing a choice between any two bundles of goods, a consumer can rank them so that one and only one of the following relationships is true: The consumer prefers the first bundle to the second, prefers the second to the first, or is indifferent between them.

5. Five Properties of Consumer Preferences 4-5  Transitivity – a consumer’s preferences over bundles is consistent in the sense that, if the consumer weakly prefers Bundle z to Bundle y (likes z at least as much as y) and weakly prefers Bundle y to Bundle x, the consumer also weakly prefers Bundle z to Bundle x.

6. Five Properties of Consumer Preferences 4-6  More Is Better - all else being the same, more of a commodity is better than less of it (always wanting more is known as nonsatiation).  Good - a commodity for which more is preferred to less, at least at some levels of consumption  Bad - something for which less is preferred to more, such as pollution Concentrate on goods

7. Five Properties of Consumer Preferences 4-7  Continuity- if a consumer prefers Bundle a to Bundle b, then the consumer prefers Bundle c to b is c is very close to a.  The purpose of this assumption is to rule out sudden preference reversals in response to small changes in the characteristics of a bundle

8. Five Properties of Consumer Preferences 4-8  Strict Convexity- means that consumers prefer averages to extremes, i.e. more balanced baskets that have some of each good.  For example if Bundle a and Bundle b are distinct bundles and the consumer prefers both of these bundles to Bundle c, then the consumer prefers a weighted average of a and b, β a+(1- β )b, to Bundle c.

9. Preference Maps 4-9  To summarize information about a consumer’s preferences is to create a graphical representation- a map-of them  Example: Each semester, Lisa, who lives for fast food, decides how many pizzas and burritos to eat.  The various bundles of pizzas and burritos she might consume are shown in panel a of Figure 3.1

10. 4-10 Figure 3.1 Bundles of Pizzas and Burritos Lisa Might Consume B, Bur r itos per semester (a) 302515 Z, Pizzas per semester 25 20 15 10 5 d a b e c f A B B, Bur r itos per semester (b) 302515 Z, Pizzas per semester 25 20 15 10 a b I 1 e c Which of these two bundles would be preferred by Lisa? Lisa prefers bundle e over bundle d, since e has more of both goods: Pizza and Burritos Lisa prefers bundle e to any bundle in area B Which of these two bundles would be preferred by Lisa? Lisa prefers bundle f over bundle e, since f has more of both goods: Pizza and Burritos Lisa prefers any bundle in area A over e If Lisa is indifferent between bundles e, a, and c ….. we can draw an indifferent curve over those three points

11. Indifference Curves  Indifference curve - the set of all bundles of goods that a consumer views as being equally desirable.  The figure shows indifference curves that are continuous (have no gaps).  Indifference map - a complete set of indifference curves that summarize a consumer’s tastes or preferences 4-11

12. Properties of Indifference Maps 4-12 1. Bundles on indifference curves farther from the origin are preferred to those on indifference curves closer to the origin. (more is better) 2. There is an indifference curve through every possible bundle. 3. Indifference curves cannot cross. 4. Indifference curves slope downward. 5. Indifference curves can not be thick.

13. Figure 3.1 Bundles of Pizzas and Burritos Lisa Might Consume 4-13 B, Bur r itos per semester (a) 302515 Z, Pizzas per semester 25 20 15 10 5 d a b e c f A B B, Bur r itos per semester (c) 302515 Z, Pizzas per semester 25 20 15 10 d a I 1 e c f we can draw an indifferent curve over those three points I2I2 I0I0

14. Fig 3.2 Impossible Indifference Curves 4-14  Lisa is indifferent between e and a, and also between e and b…  so by transitivity she should also be indifferent between a and b …  but this is impossible, since b must be preferred to a given it has more of both goods. ( More-is-better) B, Bur r itos per semester Z, Pizzas per semester I 1 I 0 a b e Indifference curves can not cross: A given bundle cannot be on two indifference curves

15. 15 ©2005 Pearson Education, Inc. Therefore, indifference curves must slope downward to the right  If they sloped upward, they would violate the assumption that more is preferred to less Some points that had more of both goods would be indifferent to a basket with less of both goods To consume more food, the consumer is willing to give up some units of clothing consumption and still get the same utility. In other words, if food consumption is decreased, the consumer needs to obtain more units of clothing to keep the same level of utility.

16. Impossible Indifference Curves 4-16  Lisa is indifferent between b and a since both points are in the same indifference curve…  But this contradicts the “more is better” assumption. Can you tell why?  Yes, b has more of both and hence it should be preferred over a. B, Bur r itos per semester Z, Pizzas per semester I a b

17. Impossible Indifference Curves 4-17

18. Solved Problem 3.1 4-18  Can indifference curves be thick?  Answer:  Draw an indifference curve that is at least two bundles thick, and show that a preference property is violated

19. Solved Problem 3.1 4-19  Consumer is indifferent between b and a since both points are in the same indifference curve…  But this contradicts the “more is better” assumption since b has more of both and hence it should be preferred over a. B, Bur r itos per semester a b Z, Pizzas per semester I

20. Utility 4-20  Utility - a set of numerical values that reflect the relative rankings of various bundles of goods.  utility function - the relationship between utility values and every possible bundle of goods. U(B, Z)

21. 21 ©2005 Pearson Education, Inc. Consumer Preferences  Utility  A numerical score representing the satisfaction that a consumer gets from a given market basket  If buying 3 copies of Microeconomics makes you happier than buying one shirt, then we say that the books give you more utility than the shirt

22. Utility Function: Example  Suppose that the utility Lisa gets from pizzas and burritos is  Question: Can we determine whether Lisa would be happier if she had Bundle x with 9 burritos and 16 pizzas or Bundle y with 13 of each?  Answer: The utility she gets from x is 12utils. The utility she gets from y is 13utils. Therefore, she prefers y to x. 4-22

23. 23 ©2005 Pearson Education, Inc. Utility  Although we numerically rank baskets and indifference curves, numbers are ONLY for ranking  A utility of 4 is not necessarily twice as good as a utility of 2  There are two types of rankings  Ordinal ranking  Cardinal ranking

24. Ordinal Preferences  If we know only consumers’ relative rankings of bundles, our measure of pleasure is ordinal rather than cardinal  An ordinal measure is one that tells us the relative ranking of two things but does not tell us how much more one rank is than another  A cardinal measure is one by which absolute comparisons between ranks may be made Utility measures are not unique 4-24

25. Willingness to Substitute between goods  Marginal Rate of Substitution- maximum amount of one good that a consumer will sacrifice (trade) to obtain one more unit of another good Slope of the indifference curve  Indifference curve is downward sloping, hence a negative MRS  We will use calculus to determine MRS at a point on Lisa’s indifference curve 4-25

26. Marginal Rate of Substitution 4-26 MRS at e = - slope of indifference curve at e = - dB/dP =-dq 2 /dq 1

27. 27 ©2005 Pearson Education, Inc. Utility - Example Food 10155 5 10 15 0 Clothing U 1 = 25 U 2 = 50 U 3 = 100 A B C BasketU = FC C25 = 2.5(10) A25 = 5(5) B25 = 10(2.5)

28. Marginal Utility  MRS depends on how much extra utility Lisa gets from a little more of each good  marginal utility - the extra utility that a consumer gets from consuming the last unit of a good.  the slope of the utility function as we hold the quantity of the other good constant.  Lisa’s utility function is: 4-28

29. 4-29 Utility and Marginal Utility  As Lisa consumes more pizza, holding her consumption of burritos constant at 10, her total utility, U, increases…  and her marginal utility of pizza, MU Z, decreases (though it remains positive).  Marginal utility is the slope of the utility function as we hold the quantity of the other good constant. MU Z, Marginal utility of pizza MU Z 10987654321 Z, Pizzas per semester 0 130 (b) Marginal Utility 20 U, Utils  U = 20 Utility function,U (10,Z)  Z = 1 10987654321 Z, Pizzas per semester 0 350 250 (a) Utility 230

30. (a) MRS along an Indifference curve 4-30  The MRS from bundle a to bundle b is -3.  This is the same as the slope of the indifference curve between those two points.  From b to c,  MRS = -2.  This is the same as the slope of the indifference curve between those two points. From bundle c to bundle d, Lisa is willing to give up 1 Burritos in exchange for 1 more Pizza… From bundle a to bundle b, Lisa is willing to give up 3 Burritos in exchange for 1 more Pizza… B, Bur r itos per semester Indifference Curve Convex to the Origin 5 3 8 1 1 1 2 0 -2 –3 3456 Z, Pizzas per semester a b c d I

31. 31 ©2005 Pearson Education, Inc. Marginal Rate of Substitution  Indifference curves are typically convex (bowed inward).  As more of one good is consumed, a consumer would prefer to give up fewer units of a second good to get additional units of the first one (property of diminishing MRS)  In other words, consumers generally prefer a balanced market basket

32. 32 ©2005 Pearson Education, Inc. Marginal Rate of Substitution  The MRS decreases as we move down the indifference curve  Along an indifference curve there is a diminishing marginal rate of substitution.  The MRS went from 3 to 2 to 1

33. 33 ©2005 Pearson Education, Inc. At point a, the consumer has many units of burritos and few units of pizza and therefore, it is reasonable to assume that s/he may value pizza relatively more than burritos: s/he would give up a lot of burritos (3 units) to obtain 1 additional unit of pizza and still be able to keep the same level of utility. However, at point c, s/he has few burritos and a lot of pizza. She’s only willing to give up a small amount of burritos for an additional unit of pizza, making the slope very flat. Therefore, it is reasonable to assume that MRS diminishes as we move down the indifference curve. Diminishing MRS along an Indifference curve 4-33 B, Bur r itos per semester Indifference Curve Convex to the Origin 5 3 8 1 1 1 2 0 -2 –3 3456 Z, Pizzas per semester a b c d I

34. (b) Marginal Rate of Substitution with concave indifference curves 4-34  From bundle a to bundle b, Lisa is willing to give up 2 Pizzas for 1 Burrito.  Nevertheless, from b to c she is willing to give up 3 Pizzas for 1 burrito.  This is very unlikely Could you think why? B, Bur r itos per semester (b) Indifference Curve Concave to the Origin 5 7 1 1 2 0 – 2 – 3 3456 Z, Pizzas per semester a b c I

35. Diminishing marginal rate of substitution 4-35  When we have CONVEX preferences (as in the normal case) The marginal rate of substitution approaches zero as we move down and to the right along an indifference curve.  Discussion: could you imagine a good that does not exhibit this property?

36. 36 ©2005 Pearson Education, Inc. Exercise: Suppose that utility function of a consumer is give by U(F,C)= FC.  Draw the indifference curve associated with a utility level of 12 and the indifference curve associated with the utility level of 24.  Show that the indifference curves are convex. Use indifference curve for utility level 12 as an example to show this.  Find the equation for the indifference curve for utility level equal to 12 and find the MRS at (F,C) = (3,4).  Find the MRS at point (F,C) = (2,3). You will have to derive the equation for indifference curve that goes through the point first, then find the MRS at that point.

37. Willingness to Substitute between goods Suppose more generally we have an indifference curve: Then once we select a value for q 1, then the point q 2 is determined by the equation of the indifference curve, so we can write q 2 as a function of q1, i.e. q 2 (q 1 ) (Example: U=FC; For utility=25, indifference curve is FC=25, or C=25/F) 4-37 Where U 1 is MU of good 1

38. 38 ©2005 Pearson Education, Inc. Marginal Utility and Consumer Choice  It must be the case along an indifference curve that No change in total utility along an indifference curve. Trade off of one good to the other leaves the consumer just as well off.

39. 39 ©2005 Pearson Education, Inc. Marginal Utility and Consumer Choice  Rearranging:

40. Solved Problem 3.2 Suppose that Jackie has what is known as a Cobb- Douglas utility function: where a is a positive constant, q1 is the number of CDs she buys a year and q2 is the number of movie DVDs she buys. What is her MRS? Answer: 4-40

41. Curvature of Indifference Curves. 4-41  Casual observation suggests that most people’s indifference curves are convex.  Exceptions:  Perfect substitutes - goods that a consumer is completely indifferent as to which to consume.  Perfect complements - goods that a consumer is interested in consuming only in fixed proportions

42. Figure 3.4a Perfect Substitutes 4-42  Bill views Coke and Pepsi as perfect substitutes: can you tell how his indifference curves would look like?  Straight, parallel lines with an MRS (slope) of − 1.  Bill is willing to exchange one can of Coke for one can of Pepsi. Co k e, Cans per w eek 1234 Pepsi, Cans perweek 1 0 2 3 4 I 1 I 2 I 3 I 4

43. Figure 3.4b Perfect Complements 4-43 Ice cream, Scoops per w eek 123 Pie, Slices perweek 1 2 3 0 I 1 I 2 I 3 a d e c b  If she has only one piece of pie, she gets as much pleasure from it and one scoop of ice cream, a,  as from it and two scoops, d,  or as from it and three scoops, e.

44. 44 ©2005 Pearson Education, Inc. EXERCISE  Suppose a consumer’s utility of consuming good-X and good-Y is given by U(X,Y) = min{X,2Y}  Where, X is the amount of good-X and Y is the amount of good-Y. The function “min” is a function that chooses the smallest value in the bracket. For example min{2,3} =2, min(3,2}=2, min{100,3} =3.

45. Figure 3.4c Imperfect Substitutes 4-45  The standard-shaped, convex indifference curve in panel lies between these two extreme examples.  Convex indifference curves show that a consumer views two goods as imperfect substitutes. B, Bur r itos per semester f Z, Pizzas per semester I

46. Application: Indifference Curves Between Food and Clothing 4-46 Research has shown that at low (subsistence) levels of income (I 1 ), there is little willingness to substitute between food and clothing.

47. 47 ©2005 Pearson Education, Inc. Consumer Preferences: An Application  An analysis of consumer preferences would help to determine where to spend more on changes in car design: performance or styling  Some consumers will prefer better styling and some will prefer better performance in their car

48. 48 ©2005 Pearson Education, Inc. Consumer Preferences: An Application These consumers place a greater value on performance than styling Styling Performance

49. 49 ©2005 Pearson Education, Inc. Consumer Preferences: An Application These consumers place a greater value on styling than performance Styling Performance

50. Problems: constructing indifference curves 4-50 1. Don is altruistic. Show the possible shape of his indifference curves between charity and all other goods. 2. Miguel considers tickets to the Houston Grand Opera and to Houston Astros baseball games to be perfect substitutes. Show his preference map. 3. If Joe views two candy bars and one piece of cake as perfect substitutes, what is his marginal rate of substitution between candy bars and cake?

51. Budget Constraint 4-51  budget line (or budget constraint) - the bundles of goods that can be bought if the entire budget is spent on those goods at given prices.  opportunity set - all the bundles a consumer can buy, including all the bundles inside the budget constraint and on the budget constraint

52. Budget Constraint 4-52  If Lisa spends all her budget, Y, on pizza and burritos, then p B B + p Z Z = Y  where p B B is the amount she spends on burritos and p Z Z is the amount she spends on pizzas.  This equation is her budget constraint. It shows that her expenditures on burritos and pizza use up her entire budget.

53. Budget Constraint (cont).  How many burritos can Lisa buy?  To answer solve budget constraint for B (quantity of burritos): 4-53

54. Budget Constraint (cont).  From previous slide we have:  If p Z = $1, p B = $2, and Y = $50, then: 4-54

55. 4-55 Figure 3.5 Budget Constraint  From previous slide we have that if: –p Z = $1, p B = $2, and Y = $50, then the budget constraint, L 1, is: B, Bur r itos per semester Opportunity set 50 = Y / p Z L 1 25 = Y/p B 20 10 030 Z, Pizzas per semester a b c d Amount of Burritos consumed if all income is allocated for Burritos. Amount of Pizza consumed if all income is allocated for Pizza.

56. 56 ©2005 Pearson Education, Inc. Budget Constraints: Budget Line  Letting x and y be the goods on the x- and y-axis respectively:  The vertical intercept, I/P y, illustrates the maximum amount of good y that can be purchased with income I  The horizontal intercept, I/P x, illustrates the maximum amount of x that can be purchased with income I  The slope of the line measures the relative cost of food and clothing; it’s the relative price of the good on the x- axis.  The slope is the negative of the ratio of the prices of the two goods; it’s –P x /P y

57. The Slope of the Budget Constraint  We have seen that the budget constraint for Lisa is given by the following equation:  The slope of the budget line is also called the marginal rate of transformation (MRT) rate at which Lisa can trade burritos for pizza in the marketplace 4-57 Slope =  B/  Z = MRT

58. Table: Allocations of a $50 Budget Between Burritos and Pizza 4-58

59. (a) Changes in the Budget Constraint: An increase in the Price of Pizzas. 4-59 B, Bur r itos per semester Loss 50 L 1 (p Z = $1) L 2 (p Z = $2) 25 0 Z, Pizzas per semester B = Y PBPB - P Z = $1 PBPB Z If the price of Pizza doubles, (increases from $1 to $2) the slope of the budget line increases This area represents the bundles she can no longer afford!!! $2 Slope = -$1/$2 = -0.5 Slope = -$2/$2 = -1

60. (b) Changes in the Budget Constraint: Increase in Income ( Y ) 4-60 Gain L 3 (Y = $100) L 1 (Y = $50) 0 B = $50 PBPB - PZPZ PBPB Z If Lisa’s income increases by $50 the budget line shifts to the right (with the same slope!) $100 This area represents the new consumption bundles she can now afford!!! 10050 Z, Pizzas per semester B, Burritos per semester 50 25

61. Solved Problem 4-61  A government rations water, setting a quota on how much a consumer can purchase. If a consumer can afford to buy 12 thousand gallons a month but the government restricts purchases to no more than 10 thousand gallons a month, how does the consumer’s opportunity set change?

62. Solved Problem 4-62

63. 4-63 Figure 3.6 (a) Consumer Maximization: Interior Solution  Would Lisa be able to consume any bundle along I 3 (i.e. bundle f)?  No! Lisa does not have enough income to afford any bundle along I 3 B, Bur r itos per semester 10 20 25 5030100 Z, Pizzas per semester I1I1 I2I2 I 3 d f c e a A B  Would Lisa be able to consume any bundle along I 1 ?  Yes; she could afford bundles d, c, and a.  Bundle e is called a consumer’s optimum.  If Lisa is consuming this bundle, she has no incentive to change her behavior by substituting one good for another.

64. 4-64 Consumer Maximization: Interior Solution  The budget constraint and the indifference curve have the same slope at the point e where they touch.  Therefore, at point e: Slope of I 2 B, Bur r itos per semester 25 500 Z, Pizzas per semester I2I2 e Slope of BL

65. Figure 3.6 (b) Consumer Maximization: Corner Solution 4-65 B, Bur r itos per semester Budget line 25 50 Z, Pizzas per semester I 1 I 2 I 3 e

66. Solved Problem 3.3 4-66  Nigel, a Brit, and Bob, a Yank, have the same tastes, and both are indifferent between a sports utility vehicle (SUV) and a luxury sedan. Each has a budget that will allow him to buy and operate one vehicle for a decade. For Nigel, the price of owning and operating an SUV is greater than that for the car. For Bob, an SUV is a relative bargain because he benefits from lower gas prices and can qualify for an SUV tax break. Use an indifference curve–budget line analysis to explain why Nigel buys and operates a car while Bob chooses an SUV.

67. Solved Problem 3.3 4-67

68. Figure 3.7 Optimal Bundles on Convex Sections of Indifference Curves 4-68

69. Maximizing utility subject to a constraint using calculus  Lisa’s objective is to maximize her utility, U(q 1, q 2 ), subject to (s.t.) her budget constraint:  Here the control variables are q 1 and q 2.  Lisa has no control over the prices she faces, p 1 and p 2, or her income, Y.  Two methods of solving the problem. We’ll focus on the substitution method only. 4-69

70. Substitution  First, we can substitute the budget constraint into the utility function. Using algebra we can rewrite the budget constraint as q 1 = (Y-p 2 q 2 )/p 1 and substitute this expression for q 1 in the utility function  Using standard maximization techniques we can solve this problem. (i.e. take the first derivative of the utility function with respect to q 2 and set it equal to zero) 4-70

71. Substitution  By rearranging terms in the above equation, we get the same condition for an optimum that we obtained using a graphical approach.  When we combine the MRS=MRT condition with the budget constraint we have two equations in two unknowns, q 1 and q 2. So we can solve for the optimal q 1 and q 2 as function of prices, p 1 and p 2, and income 4-71

72. Minimizing Expenditure  We have shown how Lisa chooses quantities of goods so as to maximize her utility subject to a budget constraint.  There is a related or dual constrained maximization problem where she finds the combination of goods that achieve a particular level of utility for the least expenditure.  Earlier we showed that Lisa maximized her utility by picking a bundle of q 1 = 30 and q 2 = 10 at the indifference curve I 2  Now we see: How can Lisa make the lowest possible expenditure to maintain her utility at a particular level which corresponds to indifference curve I 2 ? 4-72

73. Fig. 3.8 Minimizing Expenditure 4-73 The figure shows three possible budget lines corresponding to budgets or expenditures E 1, E 2 and E 3. E 1 lies below I 2. E 2 and E 3 both cross I 2. However the BL with E 2 is the least expensive way for her to stay on I 2. The rule for minimizing expenditure while achieving a given level of utility is to choose the lowest expenditure such that the budget line touches-is tangent to-the relevant indifference curve

74. Minimizing Expenditure  Solving either of the two problems yields the same optimal values.  More useful to use the expenditure minimizing approach  We can use calculus to solve the expenditure minimizing problem  The solution of this problem gives us the expenditure function: the relationship showing the minimal expenditures necessary to achieve a specific utility level for a given set of prices. 4-74

75. Food Stamps 4-75  Nearly 11% of U.S. households worry about having enough money to buy food and 3.3% report that they suffer from inadequate food (Sullivan and Choi, 2002).  Households that meet income, asset, and employment eligibility requirements receive coupons that can be used to purchase food from retail stores.

76. Food Stamps (cont). 4-76  The Food Stamps Program is one of the nation’s largest social welfare programs with expenditures of $33.1 billion for nearly 29.1 million people in 2006.  Would a switch to a comparable cash subsidy increase the well-being of food stamp recipients?  Would the recipients spend less on food and more on other goods?

77. 4-77 Food Stamps Versus Cash All other goods per month YY + 100 Y 0100 Food per month Budget line with food stamps Budget line with cash Original budget line A B f d e Y C I 1 I 2 I 3

78. Behavioral Economics 4-78  behavioral economics - by adding insights from psychology and empirical research on human cognition and emotional biases to the rational economic model, economists try to better predict economic decision making