Chapter Four Consumer Choice

Consumer Choice In this chapter, we examine four main topics. Preferences Utility Budget constraint Constrained consumer choice © 2007 Pearson Addison-Wesley. All rights reserved.

Preferences To explain consumer behavior, economists assume that consumers have a set of tastes or preferences that they use to guide them in choosing between goods. These tastes differ substantially among individuals. © 2007 Pearson Addison-Wesley. All rights reserved.

Properties of Consumer Preferences Economists make three critical assumptions about the properties of consumers’ preferences. For brevity, these properties are referred to as completeness, transitivity, and more is better. © 2007 Pearson Addison-Wesley. All rights reserved.

Completeness The completeness property holds that, 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. © 2007 Pearson Addison-Wesley. All rights reserved.

Transitivity The transitivity (or what some people refer to as rationality) property is that a consumer’s preferences over bundles is consistent in the sense that, if the consumer weakly prefers Bundle to Bundle (like at least as much as ) and weakly prefers Bundle to Bundle , the consumer also weakly prefers Bundle to Bundle . © 2007 Pearson Addison-Wesley. All rights reserved.

More is Better The more-is-better property holds that, all else the same, more of a commodity is better than less of it (always wanting more is known as nonsatiation). © 2007 Pearson Addison-Wesley. All rights reserved.

Properties of Consumer Preferences 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 © 2007 Pearson Addison-Wesley. All rights reserved.

Preference Maps One of the simplest ways to summarize information about a consumer’s preferences is to create a graphical interpretation—a map—of them. © 2007 Pearson Addison-Wesley. All rights reserved.

Preference Maps indifference curve the set of all bundles of goods that a consumer views as being equally desirable indifference map (or preference map) a complete set of indifference curves that summarize a consumer’s tastes or preferences © 2007 Pearson Addison-Wesley. All rights reserved.

Indifference Curves All indifference curve maps must have four important properties: Bundles on indifference curves farther from the origin are preferred to those on indifference curves closer to the origin. There is an indifference curve through every possible bundle. Indifference curve cannot cross. Indifference curves slope downward. © 2007 Pearson Addison-Wesley. All rights reserved.

Figure 4.1 Bundles of Pizzas and Burritos Lisa Might Consume 25 25 f 20 20 f e 15 15 e a a d d 10 b 10 b I 1 5 B 15 25 30 15 25 30 Z , Pizzas per semester Z , Pizzas per semester © 2007 Pearson Addison-Wesley. All rights reserved.

Figure 4.1 Bundles of Pizzas and Burritos Lisa Might Consume (cont’d) 25 f 20 2 e I 15 d 10 I 1 I 15 25 30 Z , Pizzas per semester © 2007 Pearson Addison-Wesley. All rights reserved.

Figure 4.2 Impossible Indifference Curves (a) Crossing (b) Upward Sloping b a e b I I 1 a I Z , Pizzas per semester Z , Pizzas per semester © 2007 Pearson Addison-Wesley. All rights reserved.

Figure 4.2 Impossible Indifference Curves (cont’d) (c) Thick b a I Z , Pizzas per semester © 2007 Pearson Addison-Wesley. All rights reserved.

Willingness to Substitute Between Goods Marginal Rate of Substitution (MRS) the maximum amount of one good a consumer will sacrifice to obtain one more unit of another good © 2007 Pearson Addison-Wesley. All rights reserved.

Willingness to Substitute Between Goods The marginal rate of substitution of burritos for pizza is where is the number of pizzas Lisa will give up to get more burritos or vice versa and pizza (Z) is on the horizontal axis. The marginal rate of substitution is the slope of the indifference curve. © 2007 Pearson Addison-Wesley. All rights reserved.

Curvature of Indifference Curves An indifference curve doesn’t have to be convex, but casual observation suggests that most people’s indifference curves are convex. When people have a lot of one good, they are willing to give up a relatively large amount of it to get a good of which they have relatively little. However, after that first trade, they are willing to give up less of the first good to get the same amount more of the second good. © 2007 Pearson Addison-Wesley. All rights reserved.

Curvature of Indifference Curves This willingness to trade fewer burritos for one more pizza as we move down and to the right along the indifference curve reflects a diminishing marginal rate of substitution: The marginal rate of substitution approaches zero as we move down and to the right along an indifference curve. © 2007 Pearson Addison-Wesley. All rights reserved.

Figure 4.3 Marginal Rate of Substitution (a) Indifference Curve Convex to the Origin (b) Indifference Curve Concave to the Origin a 8 a 7 – 3 – 2 b b 5 5 1 1 – 2 c – 3 3 1 d c – 1 2 2 1 1 I I 3 4 5 6 3 4 5 6 Z , Pizzas per semester Z , Pizzas per semester © 2007 Pearson Addison-Wesley. All rights reserved.

Curvature of Indifference Curves 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 © 2007 Pearson Addison-Wesley. All rights reserved.

Figure 4.4 Perfect Substitutes, Perfect Complements, Imperfect Substitutes (a) Perfect Substitutes (b) Perfect Complements 4 e c 3 3 I 3 d b 2 2 I 2 a 1 1 I 1 I 1 I 2 I 3 I 4 1 2 3 4 1 2 3 Pepsi, Cans per week Pie, Slices per week © 2007 Pearson Addison-Wesley. All rights reserved.

Figure 4.4 Perfect Substitutes, Perfect Complements, Imperfect Substitutes (cont’d) (c) Imperfect Substitutes I Z , Pizzas per semester © 2007 Pearson Addison-Wesley. All rights reserved.

Application (Page 83) Indifference Curves Between Food and Clothing 4 I 3 I 2 I 1 Clothing per year © 2007 Pearson Addison-Wesley. All rights reserved.

Utility Utility Utility Function 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 © 2007 Pearson Addison-Wesley. All rights reserved.

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 not how much more one rank is than another. Because utility is an ordinal measure, we should not put any weight on the absolute differences between the utility associated with one bundle and another. We care only about the relative utility or ranking of the two bundles. © 2007 Pearson Addison-Wesley. All rights reserved.

Utility and Marginal Utility the extra utility that a consumer gets from consuming the last unit of a good Thus marginal utility is the slope of the utility function © 2007 Pearson Addison-Wesley. All rights reserved.

Figure 4.5 Utility and Marginal Utility (a) Utility 350 Utility function, U (10, Z ) 250 D U = 20 230 D Z = 1 1 2 3 4 5 6 7 8 9 10 Z , Pizzas per semester (b) Marginal Utility 130 20 MU Z 1 2 3 4 5 6 7 8 9 10 © 2007 Pearson Addison-Wesley. All rights reserved. Z , Pizzas per semester

Utility and Marginal Rates of Substitution The marginal rate of substitution (MRS) is the slope of the indifference curve. The marginal rate of substitution can also be expressed in terms of marginal utilities. The marginal rate of substitution can be written as (4.1) © 2007 Pearson Addison-Wesley. All rights reserved.

Budget Constraint Consumers maximize their well-being subject to constraints. The most important constraint most of us face in deciding what to consume is our personal budget constraint. For simplicity, we assume that each consumer has a fixed amount of money to spend now, so we can use the terms budget and income interchangeably. © 2007 Pearson Addison-Wesley. All rights reserved.

Budget Constraint If Lisa spends all her budget, Y, on pizza and burritos, then (4.2) where is the amount she spends on burritos and is the amount she spends on pizzas. © 2007 Pearson Addison-Wesley. All rights reserved.

Budget Constraint Budget Line (or Budget Constraint) Opportunity Set 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 © 2007 Pearson Addison-Wesley. All rights reserved.

Slope of the Budget Constraint Marginal Rate of Transformation (MRT) the trade-off the market imposes on the consumer in terms of the amount of one good the consumer must give up to obtain more of the other good The marginal rate of transformation is the rate at which Lisa can trade burritos for pizza in the marketplace: (4.5) © 2007 Pearson Addison-Wesley. All rights reserved.

Table 4.1 Allocations of a $50 Budget Between Burritos and Pizza © 2007 Pearson Addison-Wesley. All rights reserved.

Figure 4.6 Budget Constraint 25 = Y / p B b 20 L 1 ( p = $1, Y = $50) Z c 10 Opportunity set d 10 30 50 = Y / p Z Z , Pizzas per semester © 2007 Pearson Addison-Wesley. All rights reserved.

Effect of A Change in Price on Consumption If the price of pizza doubles but the price of burritos is unchanged, the budget constraint swings in toward the origin in panel a of Figure 4.7. © 2007 Pearson Addison-Wesley. All rights reserved.

Figure 4.7 Changes in the Budget Constraint (a) Price of Pizza Doubles (b) Income Doubles 25 50 L 3 ( Y = $100) L 1 ( p Z = $1) 25 Loss Gain L 2 ( p = $2) L 1 ( Y = $50) Z 25 50 50 100 Z , Pizzas per semester Z , Pizzas per semester © 2007 Pearson Addison-Wesley. All rights reserved.

Effect of a Change in Income on Consumption If the consumer’s income increases, the consumer can buy more of all goods. The budget constraint shifts outward—away from the origin—and is parallel to the origin constraint in panel b of Figure 4.7. A change in income affects only the position and not the slope of the budget line. The slope is determined solely by the relative prices of pizza and burritos. © 2007 Pearson Addison-Wesley. All rights reserved.

Page 91 Solved Problem 4.2 Quota Budget line A B 10 12 10 12 Water, Thousand gallons per month © 2007 Pearson Addison-Wesley. All rights reserved.

The Consumer’s Optimal Bundle The optimal bundle must be on the budget constraint. Bundles that lie on indifference curves above the constraint, such as those on I3, are not in the opportunity set. For any bundle inside the constraint (such as d on I1), there is another bundle on the constraint with more of at least one of the two goods, and hence she prefers that bundle. Therefore, the optimal bundle must lie on the budget constraint. © 2007 Pearson Addison-Wesley. All rights reserved.

The Consumer’s Optimal Bundle Bundles that lie on indifference curves that cross the budget constraint (such as I1, which crosses the constraint at and ) are less desirable than certain other bundles on the constraint. Thus the optimal bundle must lie on the budget constraint and be on an indifference curve that does not cross it. Such a bundle is the consumer’s optimum. The optimal bundle must lie on an indifference curve that touches the budget constraint but does not cross it. © 2007 Pearson Addison-Wesley. All rights reserved.

Figure 4.8 Consumer Maximization (a) Interior Solution Budget line g 25 c f 20 B e 10 I 3 d a I A 2 I 1 10 30 50 Z , Pizzas per semester (b) Corner Solution e 25 I 3 I 2 Budget line I 1 50 © 2007 Pearson Addison-Wesley. All rights reserved. Z , Pizzas per semester

Interior Solution Rearranging terms, this condition is equivalent to For the indifference curve I2 to touch the budget constraint but not cross it, it must be tangent to the budget constraint: The budget constraint and the indifference curve have the same slope at the point where they touch. Rearranging terms, this condition is equivalent to (4.6) © 2007 Pearson Addison-Wesley. All rights reserved.

Page 95 Solved Problem 4.3 Corner Solution 1 N l L B L N e B 1 SUVs per decade © 2007 Pearson Addison-Wesley. All rights reserved.

Figure 4.9 Optimal Bundles on Convex Sections of Indifference Curves (a) Strictly Concave Indifference Curves (b) Concave and Convex Indifference Curves e Budget Budget line line d d e I 2 I 1 I 2 I 3 I 1 Z , Pizzas per semester Z , Pizzas per semester © 2007 Pearson Addison-Wesley. All rights reserved.

Buying Where More is Better If both goods are consumed in positive quantities and their prices are positive, more of either good must be preferred to less. In summary, we do not observe consumer optima at bundles where indifference curves are concave or consumers are satiated. Thus we can safely assume that indifference curves are convex and that consumers prefer more to less in the ranges of goods that we actually observe. © 2007 Pearson Addison-Wesley. All rights reserved.

Page 98 Solved Problem 4.4 L L f a I I American meals per year F A 2 1 © 2007 Pearson Addison-Wesley. All rights reserved.

Food Stamps Cash preferred to food stamps Poor people who receive cash have more choices than those who receive a comparable amount of food stamps. © 2007 Pearson Addison-Wesley. All rights reserved.

Figure 4.10 Food Stamps Versus Cash Budget line with cash Y + 100 f C e Y I 3 d I 2 I 1 B Budget line with food stamps A Original budget line 100 Y Y + 100 Food per month © 2007 Pearson Addison-Wesley. All rights reserved.