CHAPTER 3 CONSUMER CHOICE Chapter Outline 4 2

CHAPTER 3 CONSUMER CHOICE

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

4 -3 Premises of Consumer Behavior 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.

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.

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.

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

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

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, βa+(1 -β)b, to Bundle c.

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

Figure 3. 1 Bundles of Pizzas and Burritos Lisa Might Consume 25 Lisa prefers any bundle in area A (b) over e A f 20 15 e d 10 5 a b B 15 25 30 Z, Pizzas per semester 4 -10 If Lisa prefers is indifferent bundle e bundles between to any e, a, bundle and c …. . in area B B, Burritos per semester (a) Which of of these two bundles would be be preferred c preferred by by Lisa? c 25 20 Lisa prefers bundle feover 15 bundle e, d, since fe has more of both 10 goods: Pizza and Burritos e a b 15 25 I 1 30 Z, Pizzas per semester we can draw an indifferent curve over those three points

Indifference Curves 4 -11 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

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

Figure 3. 1 Bundles of Pizzas and Burritos Lisa Might Consume 4 -13 (c) A c 25 f 20 15 e d 10 5 a b B, Burritos per semester (a) 25 c f 20 I 2 e 15 a 10 d I 1 I 0 B 15 25 30 Z, Pizzas per semester we can draw an indifferent curve over those three points

B, Burritos per semester 4 -14 Fig 3. 2 Impossible Indifference Curves 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) Indifference curves can not cross: A given bundle cannot be on two indifference curves e b a I 1 I 0 Z, Pizzas per semester

Therefore, indifference curves must slope downward to the right © 2005 Pearson Education, Inc. 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. 15

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, Burritos per semester Impossible Indifference Curves b a I Z, Pizzas per semester

Impossible Indifference Curves 4 -17

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

Solved Problem 3. 1 B, Burritos per semester 4 -19 b a Consumer is indifferent between b and a since both points are in the same indifference curve… I Z, Pizzas per semester But this contradicts the “more is better” assumption since b has more of both and hence it should be preferred over a.

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)

Consumer Preferences © 2005 Pearson Education, Inc. 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 21

Utility Function: Example 4 -22 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 12 utils. The utility she gets from y is 13 utils. Therefore, she prefers y to x.

Utility © 2005 Pearson Education, Inc. 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 23

Ordinal Preferences 4 -24 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 -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

Marginal Rate of Substitution 4 -26 MRS at e = - slope of indifference curve at e = - d. B/d. P =-dq 2/dq 1

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

Marginal Utility 4 -28 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:

As Lisa consumes more pizza, holding her consumption of burritos constant at 10, her total utility, U, increases… 4 -29 and her marginal utility of pizza, MUZ, decreases (though it remains positive). Marginal utility is the slope of the utility function as we hold the quantity of the other good constant. 350 Utility function, U (10, Z ) 250 230 0 DU = 20 DZ = 1 1 2 3 4 5 6 7 8 9 10 Z, Pizzas per semester (b) Marginal Utility MU Z, Marginal utility of pizza U, Utils Utility and Marginal Utility (a) Utility 130 20 0 MU Z 1 2 3 4 5 6 7 8 9 10 Z, Pizzas per semester

(a) MRS along an Indifference curve Indifference Curve Convex to the Origin B, Burritos per semester 4 -30 8 5 3 2 0 The MRS from bundle a to bundle b is -3. From bundle a to bundle b, Lisa is a This is the same as the slope of the indifference willing to give up 3 curve between those two Burritos in exchange – 3 points. for 1 more Pizza… b From bundle c 1 From b to c, to bundle d, Lisa -2 c is willing to give MRS = -2. 1 d up 1 Burritos in -1 This is the same as the exchange for 1 1 slope of the indifference I more Pizza… curve between those two 3 4 5 6 points. Z, Pizzas per semester

Marginal Rate of Substitution © 2005 Pearson Education, Inc. 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 31

Marginal Rate of Substitution © 2005 Pearson Education, Inc. 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 32

Diminishing MRS along an Indifference curve Indifference Curve Convex to the Origin At point a, the consumer has many B, Burritos per semester 4 -33 © 2005 Pearson Education, Inc. 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. a 8 – 3 b 5 1 -2 3 c 1 -1 2 0 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. d Therefore, it is reasonable to assume that MRS diminishes as we move down the indifference curve. 1 3 4 5 I 6 Z, Pizzas per semester 33

(b) Marginal Rate of Substitution with concave indifference curves 4 -34 B, Burritos per semester (b) Indifference Curve Concave to the Origin a 7 Nevertheless, from b to c she is willing to give up 3 Pizzas for 1 burrito. This is very unlikely – 2 b 5 1 – 3 c 2 1 I 0 From bundle a to bundle b, Lisa is willing to give up 2 Pizzas for 1 Burrito. 3 4 5 6 Z, Pizzas per semester Could you think why?

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?

Exercise: © 2005 Pearson Education, Inc. 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. 36

Willingness to Substitute between goods 4 -37 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 q 1, i. e. q 2(q 1) (Example: U=FC; For utility=25, indifference curve is FC=25, or C=25/F) Where U 1 is MU of good 1

© 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. 38

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

Solved Problem 3. 2 4 -40 Suppose that Jackie has what is known as a Cobb-Douglas utility function: where a is a positive constant, q 1 is the number of CDs she buys a year and q 2 is the number of movie DVDs she buys. What is her MRS? Answer:

4 -41 Curvature of Indifference Curves. 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

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

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

EXERCISE © 2005 Pearson Education, Inc. Suppose a consumer’s utility of consuming good-X and good-Y is given by U(X, Y) = min{X, 2 Y} 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. 44

f B, Burritos per semester 4 -45 Figure 3. 4 c Imperfect Substitutes The standardshaped, convex indifference curve in panel lies between these two extreme examples. I Z, Pizzas per semester Convex indifference curves show that a consumer views two goods as imperfect substitutes.

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.

Consumer Preferences: An Application © 2005 Pearson Education, Inc. 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 47

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

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

Problems: constructing indifference curves 4 -50 1. 2. 3. Don is altruistic. Show the possible shape of his indifference curves between charity and all other goods. Miguel considers tickets to the Houston Grand Opera and to Houston Astros baseball games to be perfect substitutes. Show his preference map. 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?

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

Budget Constraint 4 -52 If Lisa spends all her budget, Y, on pizza and burritos, then p. BB + p. ZZ = Y where p. BB is the amount she spends on burritos and p. ZZ 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.

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

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

Figure 3. 5 Budget Constraint From previous slide we have that if: B, Burritos per semester Amount of Burritos consumed if all income is allocated for Burritos. 25 = Y/p. B 20 – p. Z = $1, p. B = $2, and Y = $50, then the budget constraint, L 1, is: a b L 1 c 10 Amount of Pizza consumed if all income is allocated for Pizza. Opportunity set d 0 4 -55 10 30 50 = Y /p. Z Z, Pizzas per semester

Budget Constraints: Budget Line © 2005 Pearson Education, Inc. Letting x and y be the goods on the x- and y-axis respectively: The vertical intercept, I/Py, illustrates the maximum amount of good y that can be purchased with income I The horizontal intercept, I/Px, 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 –Px/Py 56

The Slope of the Budget Constraint 4 -57 We have seen that the budget constraint for Lisa is given by the following equation: Slope = DB/DZ = MRT 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

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

(a) Changes in the Budget Constraint: An increase in the Price of Pizzas. B, Burritos per semester 4 -59 Slope = -$1/$2 = -0. 5 25 L 1 (p. Z = $1) $2 Y - PZ = $1 PB PB B= If the price of Pizza doubles, (increases from $1 to $2) the slope of the budget line increases Loss L 2 (p. Z = $2) 0 Slope = -$2/$2 = -1 Z 25 50 Z, Pizzas per semester This area represents the bundles she can no longer afford!!!

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

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?

Solved Problem 4 -62

Figure 3. 6 (a) Consumer Maximization: Interior Solution B, Burritos per semester 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 Bundle e is called a consumer’s optimum. w If Lisa is consuming this bundle, she has no incentive to change her behavior by substituting one good for another. § 25 c 20 e d A 0 f B 10 4 -63 § 10 Would Lisa be able to consume any bundle along I 1 ? w Yes; she could afford bundles d, c, and a. a 30 I 3 I 2 I 1 50 Z, Pizzas per semester

B, Burritos per semester Consumer Maximization: Interior Solution § The budget constraint and the indifference curve have the same slope at the point e where they touch. w Therefore, at point e: 25 Slope of I 2 e I 2 0 4 -64 50 Z, Pizzas per semester Slope of BL

Figure 3. 6 (b) Consumer Maximization: Corner Solution B, Burritos per semester 4 -65 25 e I 3 I 2 Budget line I 1 50 Z, Pizzas per semester

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.

Solved Problem 3. 3 4 -67

Figure 3. 7 Optimal Bundles on Convex Sections of Indifference Curves 4 -68

Maximizing utility subject to a constraint using calculus 4 -69 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.

Substitution 4 -70 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)

Substitution 4 -71 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

Minimizing Expenditure 4 -72 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?

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

Minimizing Expenditure 4 -74 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.

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.

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?

All other goods per month Food Stamps Versus Cash Budget line with cash Y + 100 Y f C e I 3 d I 2 I 1 B Budget line with food stamps A 0 4 -77 Original budget line 100 Y Y + 100 Food per month

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