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CHAPTER The Theory of Consumer Choice 21 W hen you walk into a store, you are confronted with thousands of goods that you might buy. Because your financial resources...

CHAPTER The Theory of Consumer Choice 21 W hen you walk into a store, you are confronted with thousands of goods that you might buy. Because your financial resources are limited, however, you cannot buy everything that you want. You therefore consider the prices of the various goods offered for sale and buy a bundle of goods that, given your resources, best suits your needs and desires. In this chapter, we develop a theory that describes how consumers make deci- sions about what to buy. Thus far in this book, we have summarized consumers’ decisions with the demand curve. As we have seen, the demand curve for a good 425 Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203 426 PART VII TOPICS FOR FURTHER STUDY reflects consumers’ willingness to pay for that good. When the price rises, con- sumers are willing to pay for fewer units, so the quantity demanded falls. We now look more deeply at the decisions that lie behind the demand curve. The theory of consumer choice presented in this chapter provides a more complete understand- ing of demand, just as the theory of the competitive firm in Chapter 14 provides a more complete understanding of supply. One of the Ten Principles of Economics discussed in Chapter 1 is that people face trade-offs. The theory of consumer choice examines the trade-offs that people face as consumers. When a consumer buys more of one good, she can afford less of other goods. When she spends more time enjoying leisure and less time work- ing, she has lower income and therefore lower consumption. When she spends more of her income in the present and saves less of it, she reduces the amount she will be able to consume in the future. The theory of consumer choice examines how consumers facing these trade-offs make decisions and how they respond to changes in their environment. After developing the basic theory of consumer choice, we apply it to three questions about household decisions. In particular, we ask: Do all demand curves slope downward? How do wages affect labor supply? How do interest rates affect household saving? At first, these questions might seem unrelated. But as we will see, we can use the theory of consumer choice to address each of them. 21-1 The Budget Constraint: What the Consumer Can Afford Most people would like to increase the quantity or quality of the goods they con- sume—to take longer vacations, drive fancier cars, or eat at better restaurants. People consume less than they desire because their spending is constrained, or lim- ited, by their income. We begin our study of consumer choice by examining this link between income and spending. To keep things simple, we examine the decision facing a consumer who buys only two goods: pizza and Pepsi. Of course, real people buy thousands of dif- ferent kinds of goods. Assuming there are only two goods greatly simplifies the problem without altering the basic insights about consumer choice. We first consider how the consumer ’s income constrains the amount she spends on pizza and Pepsi. Suppose the consumer has an income of $1,000 per month and spends her entire income on pizza and Pepsi. The price of a pizza is $10, and the price of a liter of Pepsi is $2. The table in Figure 1 shows some of the many combinations of pizza and Pepsi that the consumer can buy. The first row in the table shows that if the consumer spends all her income on pizza, she can eat 100 pizzas during the month, but she would not be able to buy any Pepsi at all. The second row shows another possible consumption bundle: 90 pizzas and 50 liters of Pepsi. And so on. Each consump- tion bundle in the table costs exactly $1,000. The graph in Figure 1 illustrates the consumption bundles that the consumer can choose. The vertical axis measures the number of liters of Pepsi, and the horizontal axis measures the number of pizzas. Three points are marked on this Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203  CHAPTER 21 THE THEORY OF CONSUMER CHOICE 427 The budget constraint shows the various bundles of goods that the consumer FIGURE 1 can buy for a given income. Here the consumer buys bundles of pizza and Pepsi. The table and graph show what the consumer can afford if her income The Consumer’s Budget Constraint is $1,000, the price of pizza is $10, and the price of Pepsi is $2. Quantity Number Liters Spending Spending Total of Pepsi of Pizzas of Pepsi on Pizza on Pepsi Spending B 100 0 $1,000 $ 0 $1,000 500 90 50 900 100 1,000 80 100 800 200 1,000 70 150 700 300 1,000 60 200 600 400 1,000 C 250 50 250 500 500 1,000 40 300 400 600 1,000 Consumer’s 30 350 300 700 1,000 budget constraint 20 400 200 800 1,000 10 450 100 900 1,000 A 0 500 0 1,000 1,000 0 50 100 Quantity of Pizza figure. At point A, the consumer buys no Pepsi and consumes 100 pizzas. At point B, the consumer buys no pizza and consumes 500 liters of Pepsi. At point C, the consumer buys 50 pizzas and 250 liters of Pepsi. Point C, which is exactly at the middle of the line from A to B, is the point at which the consumer spends an equal amount ($500) on pizza and Pepsi. These are only three of the many combinations of pizza and Pepsi that the consumer can choose. All the points on the line from A to B are possible. This line, called the budget constraint, shows the consumption budget constraint bundles that the consumer can afford. In this case, it shows the trade-off between the limit on the pizza and Pepsi that the consumer faces. consumption bundles The slope of the budget constraint measures the rate at which the consumer can that a consumer can trade one good for the other. Recall that the slope between two points is calculated afford as the change in the vertical distance divided by the change in the horizontal dis- tance (“rise over run”). From point A to point B, the vertical distance is 500 liters, and the horizontal distance is 100 pizzas. Thus, the slope is 5 liters per pizza. (Actually, because the budget constraint slopes downward, the slope is a negative number. But for our purposes we can ignore the minus sign.) Notice that the slope of the budget constraint equals the relative price of the two goods—the price of one good compared to the price of the other. A pizza costs five times as much as a liter of Pepsi, so the opportunity cost of a pizza is 5 liters of Pepsi. The budget constraint’s slope of 5 reflects the trade-off the market is offer- ing the consumer: 1 pizza for 5 liters of Pepsi. Draw the budget constraint for a person with income of $1,000 if the QuickQuiz price of Pepsi is $5 and the price of pizza is $10. What is the slope of this budget constraint? Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203 428 PART VII TOPICS FOR FURTHER STUDY 21-2 Preferences: What the Consumer Wants Our goal in this chapter is to understand how consumers make choices. The bud- get constraint is one piece of the analysis: It shows the combinations of goods the consumer can afford given her income and the prices of the goods. The consum- er’s choices, however, depend not only on her budget constraint but also on her preferences regarding the two goods. Therefore, the consumer’s preferences are the next piece of our analysis. 21-2a Representing Preferences with Indifference Curves The consumer’s preferences allow her to choose among different bundles of pizza and Pepsi. If you offer the consumer two different bundles, she chooses the bun- dle that best suits her tastes. If the two bundles suit her tastes equally well, we say that the consumer is indifferent between the two bundles. Just as we have represented the consumer’s budget constraint graphically, we can also represent her preferences graphically. We do this with indifference indifference curve curves. An indifference curve shows the various bundles of consumption that a curve that shows make the consumer equally happy. In this case, the indifference curves show the consumption bundles combinations of pizza and Pepsi with which the consumer is equally satisfied. that give the consumer Figure 2 shows two of the consumer’s many indifference curves. The consumer the same level of is indifferent among combinations A, B, and C because they are all on the same satisfaction curve. Not surprisingly, if the consumer’s consumption of pizza is reduced, say, from point A to point B, consumption of Pepsi must increase to keep her equally happy. If consumption of pizza is reduced again, from point B to point C, the amount of Pepsi consumed must increase yet again. The slope at any point on an indifference curve equals the rate at which the consumer is willing to substitute one good for the other. This rate is called the marginal rate of marginal rate of substitution (MRS). In this case, the marginal rate of substitution substitution measures how much Pepsi the consumer requires to be compensated for a one- the rate at which a con- unit reduction in pizza consumption. Notice that because the indifference curves sumer is willing to trade are not straight lines, the marginal rate of substitution is not the same at all one good for another points on a given indifference curve. The rate at which a consumer is willing to trade one good for the other depends on the amounts of the goods she is already consuming. In other words, the rate at which a consumer is willing to trade pizza FIGURE 2 Quantity of Pepsi The Consumer’s Preferences C The consumer’s preferences are repre- sented with indifference curves, which show the combinations of pizza and Pepsi that make the consumer equally satisfied. Because the consumer prefers more of B D a good, points on a higher indifference MRS I2 curve (I2) are preferred to points on a 1 lower indifference curve (I1). The mar- Indifference A ginal rate of substitution (MRS) shows curve, I1 the rate at which the consumer is willing 0 Quantity to trade Pepsi for pizza. It measures the of Pizza quantity of Pepsi the consumer must be given in exchange for 1 pizza. Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203  CHAPTER 21 THE THEORY OF CONSUMER CHOICE 429 for Pepsi depends on whether she is hungrier or thirstier, which in turn depends on her current consumption of pizza and Pepsi. The consumer is equally happy at all points on any given indifference curve, but she prefers some indifference curves to others. Because she prefers more consumption to less, higher indifference curves are preferred to lower ones. In Figure 2, any point on curve I2 is preferred to any point on curve I1. A consumer’s set of indifference curves gives a complete ranking of the consum- er’s preferences. That is, we can use the indifference curves to rank any two bundles of goods. For example, the indifference curves tell us that point D is preferred to point A because point D is on a higher indifference curve than point A. (That con- clusion may be obvious, however, because point D offers the consumer both more pizza and more Pepsi.) The indifference curves also tell us that point D is preferred to point C because point D is on a higher indifference curve. Even though point D has less Pepsi than point C, it has more than enough extra pizza to make the con- sumer prefer it. By seeing which point is on the higher indifference curve, we can use the set of indifference curves to rank any combination of pizza and Pepsi. 21-2b Four Properties of Indifference Curves Because indifference curves represent a consumer’s preferences, they have certain properties that reflect those preferences. Here we consider four properties that describe most indifference curves: Property 1: Higher indifference curves are preferred to lower ones. People usually prefer to consume more rather than less. This preference for greater quanti- ties is reflected in the indifference curves. As Figure 2 shows, higher indif- ference curves represent larger quantities of goods than lower indifference curves. Thus, the consumer prefers being on higher indifference curves. Property 2: Indifference curves are downward-sloping. The slope of an indiffer- ence curve reflects the rate at which the consumer is willing to substitute one good for the other. In most cases, the consumer likes both goods. Therefore, if the quantity of one good is reduced, the quantity of the other good must increase for the consumer to be equally happy. For this reason, most indiffer- ence curves slope downward. Property 3: Indifference curves do not cross. To see why this is true, suppose that two indifference curves did cross, as in Figure 3. Then, because point A Quantity FIGURE 3 of Pepsi The Impossibility of Intersecting C Indifference Curves A situation like this can never happen. According to these indifference curves, A the consumer would be equally satisfied at points A, B, and C, even though B point C has more of both goods than point A. 0 Quantity of Pizza Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203 430 PART VII TOPICS FOR FURTHER STUDY is on the same indifference curve as point B, the two points would make the consumer equally happy. In addition, because point B is on the same indif- ference curve as point C, these two points would make the consumer equally happy. But these conclusions imply that points A and C would also make the consumer equally happy, even though point C has more of both goods. This contradicts our assumption that the consumer always prefers more of both goods to less. Thus, indifference curves cannot cross. Property 4: Indifference curves are bowed inward. The slope of an indifference curve is the marginal rate of substitution—the rate at which the consumer is willing to trade off one good for the other. The marginal rate of substitu- tion (MRS) usually depends on the amount of each good the consumer is currently consuming. In particular, because people are more willing to trade away goods that they have in abundance and less willing to trade away goods of which they have little, the indifference curves are bowed inward toward the graph’s origin. As an example, consider Figure 4. At point A, because the consumer has a lot of Pepsi and only a little pizza, she is very hungry but not very thirsty. To induce the consumer to give up 1 pizza, she has to be given 6 liters of Pepsi: The MRS is 6 liters per pizza. By contrast, at point B, the consumer has little Pepsi and a lot of pizza, so she is very thirsty but not very hungry. At this point, she would be willing to give up 1 pizza to get 1 liter of Pepsi: The MRS is 1 liter per pizza. Thus, the bowed shape of the indifference curve reflects the consumer’s greater willingness to give up a good that she already has a lot of. 21-2c Two Extreme Examples of Indifference Curves The shape of an indifference curve reveals the consumer’s willingness to trade one good for the other. When the goods are easy to substitute for each other, the indifference curves are less bowed; when the goods are hard to substitute, the FIGURE 4 Quantity of Pepsi Bowed Indifference Curves 14 Indifference curves are usually bowed inward. This shape implies that the marginal rate of substitution (MRS) depends on the quantity of the two goods MRS = 6 the consumer is currently consuming. At point A, the consumer has little pizza and A much Pepsi, so she requires a lot of extra 8 1 Pepsi to induce her to give up one of the pizzas: The MRS is 6 liters of Pepsi per pizza. At point B, the consumer has much pizza and little Pepsi, so she requires 4 only a little extra Pepsi to induce her to MRS = 1 B 3 give up one of the pizzas: The MRS is 1 Indifference 1 liter of Pepsi per pizza. curve 0 2 3 6 7 Quantity of Pizza Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203  CHAPTER 21 THE THEORY OF CONSUMER CHOICE 431 indifference curves are very bowed. To see why this is true, let’s consider the extreme cases. Perfect Substitutes Suppose that someone offered you bundles of nickels and dimes. How would you rank the different bundles? Most likely, you would care only about the total monetary value of each bun- dle. If so, you would always be willing to trade 2 nickels for 1 dime. Your mar- ginal rate of substitution between nickels and dimes would be a fixed number: MRS = 2, regardless of the number of nickels and dimes in the bundle. We can represent your preferences for nickels and dimes with the indifference curves in panel (a) of Figure 5. Because the marginal rate of substitution is con- stant, the indifference curves are straight lines. In this extreme case of straight indifference curves, we say that the two goods are perfect substitutes. perfect substitutes two goods with straight- Perfect Complements Suppose now that someone offered you bundles of shoes. line indifference curves Some of the shoes fit your left foot, others your right foot. How would you rank these different bundles? In this case, you might care only about the number of pairs of shoes. In other words, you would judge a bundle based on the number of pairs you could assemble from it. A bundle of 5 left shoes and 7 right shoes yields only 5 pairs. Getting 1 more right shoe has no value if there is no left shoe to go with it. We can represent your preferences for right and left shoes with the indifference curves in panel (b) of Figure 5. In this case, a bundle with 5 left shoes and 5 right shoes is just as good as a bundle with 5 left shoes and 7 right shoes. It is also just as good as a bundle with 7 left shoes and 5 right shoes. The indifference curves, perfect complements therefore, are right angles. In this extreme case of right-angle indifference curves, two goods with right- we say that the two goods are perfect complements. angle indifference curves When two goods are easily substitutable, such as nickels and dimes, the indifference curves FIGURE 5 are straight lines, as shown in panel (a). When two goods are strongly complementary, such as left shoes and right shoes, the indifference curves are right angles, as shown in panel (b). Perfect Substitutes and Perfect Complements (a) Perfect Substitutes (b) Perfect Complements Nickels Left Shoes 6 4 I2 7 5 I1 2 I1 I2 I3 0 1 2 3 Dimes 0 5 7 Right Shoes Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203 432 PART VII TOPICS FOR FURTHER STUDY In the real world, of course, most goods are neither perfect substitutes (like nickels and dimes) nor perfect complements (like right shoes and left shoes). More typically, the indifference curves are bowed inward, but not so bowed that they become right angles. Draw some indifference curves for pizza and Pepsi. Explain the four prop- QuickQuiz erties of these indifference curves. 21-3 Optimization: What the Consumer Chooses The goal of this chapter is to understand how a consumer makes choices. We have the two pieces necessary for this analysis: the consumer’s budget constraint (how much she can afford to spend) and the consumer’s preferences (what she wants to spend it on). Now we put these two pieces together and consider the consumer’s decision about what to buy. 21-3a The Consumer’s Optimal Choices Once again, consider our pizza and Pepsi example. The consumer would like to end up with the best possible combination of pizza and Pepsi for her—that is, the combination on her highest possible indifference curve. But the consumer must also end up on or below her budget constraint, which measures the total resources available to her. Figure 6 shows the consumer ’s budget constraint and three of her many indifference curves. The highest indifference curve that the consumer can reach (I2 in the figure) is the one that just barely touches her budget constraint. The point at which this indifference curve and the budget constraint touch is called the optimum. The consumer would prefer point A, but she cannot afford that point because it lies above her budget constraint. The consumer can afford point B, but that point is on a lower indifference curve and, therefore, provides the consumer less satisfaction. The optimum represents the best combination of pizza and Pepsi available to the consumer. FIGURE 6 Quantity of Pepsi The Consumer’s Optimum The consumer chooses the point on her budget constraint that lies on the highest indifference Optimum curve. At this point, called the optimum, the B marginal rate of substitution equals the relative A price of the two goods. Here the highest indif- ference curve the consumer can reach is I2. I3 The consumer prefers point A, which lies on I2 indifference curve I3, but she cannot afford this I1 bundle of pizza and Pepsi. By contrast, point B is affordable, but because it lies on a lower indif- Budget constraint ference curve, the consumer does not prefer it. 0 Quantity of Pizza Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203  CHAPTER 21 THE THEORY OF CONSUMER CHOICE 433 Notice that, at the optimum, the slope of the indifference curve equals the slope of the budget constraint. We say that the indifference curve is tangent to the bud- get constraint. The slope of the indifference curve is the marginal rate of substitu- tion between pizza and Pepsi, and the slope of the budget constraint is the relative price of pizza and Pepsi. Thus, the consumer chooses consumption of the two goods so that the marginal rate of substitution equals the relative price. In Chapter 7, we saw how market prices reflect the marginal value that con- sumers place on goods. This analysis of consumer choice shows the same result in another way. In making her consumption choices, the consumer takes the relative price of the two goods as given and then chooses an optimum at which her mar- ginal rate of substitution equals this relative price. The relative price is the rate at which the market is willing to trade one good for the other, whereas the mar- ginal rate of substitution is the rate at which the consumer is willing to trade one good for the other. At the consumer’s optimum, the consumer’s valuation of the F YI Utility: An Alternative Way to Describe Preferences and Optimization W e have used indifference curves to represent the consumer’s pref- erences. Another common way to represent preferences is with the concept of utility. Utility is an abstract measure of the satisfaction or MRS = PX/PY. Because the marginal rate of substitution equals the happiness that a consumer receives from a bundle of goods. Economists ratio of marginal utilities, say that a consumer prefers one bundle of goods to another if one pro- we can write this condition vides more utility than the other. for optimization as Indifference curves and utility are closely related. Because the con- sumer prefers points on higher indifference curves, bundles of goods on MUX/MUY = PX/PY. higher indifference curves provide higher utility. Because the consumer is equally happy with all points on the same indifference curve, all these Now rearrange this expression to become bundles provide the same utility. You can think of an indifference curve MUX/PX = MUY/PY. as an “equal-utility” curve. The marginal utility of any good is the increase in utility that the This equation has a simple interpretation: At the optimum, the marginal consumer gets from an additional unit of that good. Most goods are utility per dollar spent on good X equals the marginal utility per dol- assumed to exhibit diminishing marginal utility : The more of the good lar spent on good Y. If this equality did not hold, the consumer could the consumer already has, the lower the marginal utility provided by an increase utility by spending less on the good that provided lower mar- extra unit of that good. ginal utility per dollar and more on the good that provided higher mar- The marginal rate of substitution between two goods depends on ginal utility per dollar. their marginal utilities. For example, if the marginal utility of good When economists discuss the theory of consumer choice, they X is twice the marginal utility of good Y, then a person would need sometimes express the theory using different words. One economist 2 units of good Y to compensate for losing 1 unit of good X, and the might say that the goal of the consumer is to maximize utility. Another MRS equals 2. More generally, the marginal rate of substitution (and economist might say that the goal of the consumer is to end up on the thus the slope of the indifference curve) equals the marginal utility highest possible indifference curve. The first economist would conclude of one good divided by the marginal utility of the other good. that at the consumer’s optimum, the marginal utility per dollar is Utility analysis provides another way to describe consumer optimi- the same for all goods, whereas the second would conclude that the zation. Recall that, at the consumer’s optimum, the marginal rate of indifference curve is tangent to the budget constraint. In essence, these substitution equals the ratio of prices. That is, are two ways of saying the same thing. Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203 434 PART VII TOPICS FOR FURTHER STUDY two goods (as measured by the marginal rate of substitution) equals the market’s valuation (as measured by the relative price). As a result of this consumer optimi- zation, market prices of different goods reflect the value that consumers place on those goods. 21-3b How Changes in Income Affect the Consumer’s Choices Now that we have seen how the consumer makes a consumption decision, let’s examine how this decision responds to changes in the consumer’s income. To be specific, suppose that income increases. With higher income, the consumer can afford more of both goods. The increase in income, therefore, shifts the budget constraint outward, as in Figure 7. Because the relative price of the two goods has not changed, the slope of the new budget constraint is the same as the slope of the initial budget constraint. That is, an increase in income leads to a parallel shift in the budget constraint. The expanded budget constraint allows the consumer to choose a better combination of pizza and Pepsi, one that is on a higher indifference curve. Given the shift in the budget constraint and the consumer’s preferences as represented by her indifference curves, the consumer’s optimum moves from the point labeled “initial optimum” to the point labeled “new optimum.” Notice that, in Figure 7, the consumer chooses to consume more Pepsi and more pizza. The logic of the model does not require increased consumption of both goods in response to increased income, but this situation is the most normal good common. As you may recall from Chapter 4, if a consumer wants more of a a good for which an good when her income rises, economists call it a normal good. The indifference increase in income raises curves in Figure 7 are drawn under the assumption that both pizza and Pepsi the quantity demanded are normal goods. FIGURE 7 Quantity of Pepsi New budget constraint An Increase in Income When the consumer’s income rises, the budget constraint 1. An increase in income shifts the shifts outward. If both goods budget constraint outward... are normal goods, the consumer responds to the increase in New optimum income by buying more of both of them. Here the consumer 3.... and buys more pizza and more raising Pepsi consumption. Initial Pepsi. optimum I2 Initial budget I1 constraint 0 Quantity of Pizza 2.... raising pizza consumption... Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203  CHAPTER 21 THE THEORY OF CONSUMER CHOICE 435 Quantity FIGURE 8 of Pepsi New budget constraint An Inferior Good A good is inferior if the consumer buys less of it when her income rises. Here Pepsi is an inferior good: When the consumer’s 1. When an increase in income shifts the income increases and the budget 3.... but budget constraint outward... Initial constraint shifts outward, the Pepsi optimum consumer buys more pizza but consumption falls, making less Pepsi. New optimum Pepsi an inferior good. Initial budget I1 I2 constraint 0 Quantity of Pizza 2.... pizza consumption rises, making pizza a normal good... Figure 8 shows an example in which an increase in income induces the consumer to buy more pizza but less Pepsi. If a consumer buys less of a good when her income rises, economists call it an inferior good. Figure 8 is drawn inferior good under the assumption that pizza is a normal good and Pepsi is an inferior good. a good for which an Although most goods in the world are normal goods, there are some inferior increase in income goods as well. An example is bus rides. As income increases, consumers are more reduces the quantity likely to own cars or take taxis and less likely to ride the bus. Bus rides, therefore, demanded are an inferior good. 21-3c How Changes in Prices Affect the Consumer’s Choices Let’s now use this model of consumer choice to consider how a change in the price of one of the goods alters the consumer’s choices. Suppose, in particular, that the price of Pepsi falls from $2 to $1 per liter. It is no surprise that the lower price expands the consumer’s set of buying opportunities. In other words, a fall in the price of any good shifts the budget constraint outward. Figure 9 considers more specifically how the fall in price affects the budget constraint. If the consumer spends her entire $1,000 income on pizza, then the price of Pepsi is irrelevant. Thus, point A in the figure stays the same. Yet if the consumer spends her entire income of $1,000 on Pepsi, she can now buy 1,000 liters rather than only 500. Thus, the endpoint of the budget constraint moves from point B to point D. Notice that in this case the outward shift in the budget constraint changes its slope. (This differs from what happened previously when prices stayed the same but the consumer’s income changed.) As we have discussed, the slope of the budget constraint reflects the relative price of pizza and Pepsi. Because the price of Pepsi has fallen to $1 from $2, while the price of pizza has remained $10, the consumer can now trade a pizza for 10 rather than 5 liters of Pepsi. As a result, the new budget constraint has a steeper slope. Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203 436 PART VII TOPICS FOR FURTHER STUDY FIGURE 9 Quantity of Pepsi A Change in Price D New budget constraint When the price of Pepsi falls, 1,000 the consumer’s budget con- straint shifts outward and changes slope. The consumer moves from the initial optimum to the new optimum, which New optimum changes her purchases of both B 1. A fall in the price of Pepsi rotates pizza and Pepsi. In this case, 500 the budget constraint outward... the quantity of Pepsi consumed 3.... and rises, and the quantity of pizza raising Pepsi Initial optimum consumed falls. consumption. Initial I2 budget I1 constraint A 0 100 Quantity of Pizza 2.... reducing pizza consumption... How such a change in the budget constraint alters the consumption of both goods depends on the consumer’s preferences. For the indifference curves drawn in this figure, the consumer buys more Pepsi and less pizza. 21-3d Income and Substitution Effects The impact of a change in the price of a good on consumption can be decomposed income effect into two effects: an income effect and a substitution effect. To see what these two the change in effects are, consider how our consumer might respond when she learns that the consumption that results price of Pepsi has fallen. She might reason in the following ways: when a price change moves the consumer “Great news! Now that Pepsi is cheaper, my income has greater purchasing to a higher or lower power. I am, in effect, richer than I was. Because I am richer, I can buy both indifference curve more pizza and more Pepsi.” (This is the income effect.) “Now that the price of Pepsi has fallen, I get more liters of Pepsi for every substitution effect pizza that I give up. Because pizza is now relatively more expensive, I should the change in buy less pizza and more Pepsi.” (This is the substitution effect.) consumption that results when a price change Which statement do you find more compelling? moves the consumer In fact, both of these statements make sense. The decrease in the price of Pepsi along a given indifference makes the consumer better off. If pizza and Pepsi are both normal goods, the curve to a point with consumer will want to spread this improvement in her purchasing power over a new marginal rate of both goods. This income effect tends to make the consumer buy more pizza and substitution more Pepsi. Yet at the same time, consumption of Pepsi has become less expensive relative to consumption of pizza. This substitution effect tends to make the consumer choose less pizza and more Pepsi. Now consider the result of these two effects working at the same time. The consumer certainly buys more Pepsi because the income and substitution effects both act to increase purchases of Pepsi. But for pizza, the income and substitution effects work in opposite directions. As a result, whether the consumer buys more Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203  CHAPTER 21 THE THEORY OF CONSUMER CHOICE 437 Good Income Effect Substitution Effect Total Effect TABLE 1 Pepsi Consumer is richer, Pepsi is relatively Income and substitution Income and Substitution so she buys more Pepsi. cheaper, so consumer effects act in the Effects When the Price of buys more Pepsi. same direction, Pepsi Falls so consumer buys more Pepsi. Pizza Consumer is richer, Pizza is relatively Income and substitution so she buys more pizza. more expensive, effects act in so consumer buys opposite directions, less pizza. so the total effect on pizza consumption is ambiguous. or less pizza is not clear. The outcome could go either way, depending on the sizes of the income and substitution effects. Table 1 summarizes these conclusions. We can interpret the income and substitution effects using indifference curves. The income effect is the change in consumption that results from the movement to a new indifference curve. The substitution effect is the change in consumption that results from moving to a new point on the same indifference curve with a different marginal rate of substitution. Figure 10 shows graphically how to decompose the change in the consumer’s decision into the income effect and the substitution effect. When the price of Pepsi falls, the consumer moves from the initial optimum, point A, to the new optimum, point C. We can view this change as occurring in two steps. First, the consumer moves along the initial indifference curve, I1, from point A to point B. The consumer Quantity FIGURE 10 of Pepsi Income and Substitution Effects New budget constraint The effect of a change in price can be broken down into an income effect and a substi- tution effect. The substitution effect—the movement along an indifference curve to a point with a different marginal rate of C New optimum substitution—is shown here as the change Income from point A to point B along indifference effect B curve I1. The income effect—the shift to a Initial optimum higher indifference curve—is shown here Substitution Initial budget as the change from point B on indifference effect curve I1 to point C on indifference curve I2. constraint A I2 I1 0 Quantity Substitution effect of Pizza Income effect Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203 438 PART VII TOPICS FOR FURTHER STUDY is equally happy at these two points, but at point B, the marginal rate of substitution reflects the new relative price. (The dashed line through point B is parallel to the new budget constraint and thus reflects the new relative price.) Next, the consumer shifts to the higher indifference curve, I2, by moving from point B to point C. Even though point B and point C are on different indifference curves, they have the same marginal rate of substitution. That is, the slope of the indifference curve I1 at point B equals the slope of the indifference curve I2 at point C. The consumer never actually chooses point B, but this hypothetical point is useful to clarify the two effects that determine the consumer’s decision. Notice that the change from point A to point B represents a pure change in the marginal rate of substitution without any change in the consumer’s welfare. Similarly, the change from point B to point C represents a pure change in welfare without any change in the marginal rate of substitution. Thus, the movement from A to B shows the substitution effect, and the movement from B to C shows the income effect. 21-3e Deriving the Demand Curve We have just seen how changes in the price of a good alter the consumer’s budget constraint and, therefore, the quantities of the two goods that she chooses to buy. The demand curve for any good reflects these consumption decisions. Recall that a demand curve shows the quantity demanded of a good for any given price. We can view a consumer’s demand curve as a summary of the optimal decisions that arise from her budget constraint and indifference curves. For example, Figure 11 considers the demand for Pepsi. Panel (a) shows that when the price of a liter falls from $2 to $1, the consumer’s budget constraint shifts outward. Because of both income and substitution effects, the consumer increases her purchases of Pepsi from 250 to 750 liters. Panel (b) shows the demand curve FIGURE 11 Panel (a) shows that when the price of Pepsi falls from $2 to $1, the consumer’s optimum moves from point A to point B, and the quantity of Pepsi consumed rises Deriving the Demand Curve from 250 to 750 liters. The demand curve in panel (b) reflects this relationship between the price and the quantity demanded. (a) The Consumer’s Optimum (b) The Demand Curve for Pepsi Quantity Price of of Pepsi Pepsi New budget constraint B A 750 $2 I2 B 1 A 250 Demand I1 0 Quantity 0 250 750 Quantity Initial budget of Pizza of Pepsi constraint Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203  CHAPTER 21 THE THEORY OF CONSUMER CHOICE 439 that results from this consumer’s decisions. In this way, the theory of consumer choice provides the theoretical foundation for the consumer’s demand curve. It may be comforting to know that the demand curve arises naturally from the theory of consumer choice, but this exercise by itself does not justify developing the theory. There is no need for a rigorous, analytic framework just to establish that people respond to changes in prices. The theory of consumer choice is, however, useful in studying various decisions that people make as they go about their lives, as we see in the next section. Draw a budget constraint and indifference curves for pizza and Pepsi. QuickQuiz Show what happens to the budget constraint and the consumer’s optimum when the price of pizza rises. In your diagram, decompose the change into an income effect and a substitution effect. 21-4 Three Applications Now that we have developed the basic theory of consumer choice, let’s use it to shed light on three questions about how the economy works. These three questions might at first seem unrelated. But because each question involves household decision making, we can address it with the model of consumer behavior we have just developed. 21-4a Do All Demand Curves Slope Downward? Normally, when the price of a good rises, people buy less of it. This typical behavior, called the law of demand, is reflected in the downward slope of the demand curve. As a matter of economic theory, however, demand curves can sometimes slope upward. In other words, consumers can sometimes violate the law of demand and buy more of a good when the price rises. To see how this can happen, consider Figure 12. In this example, the consumer buys two goods—meat and potatoes. Quantity of FIGURE 12 Potatoes Initial budget constraint B A Giffen Good In this example, when the price of potatoes rises, the consumer’s optimum shifts from point C to point E. In this case, the con- Optimum with high sumer responds to a higher price of potatoes price of potatoes by buying less meat and more potatoes. Optimum with low D price of potatoes E 2.... which 1. An increase in the price of increases C potatoes rotates the budget potato constraint inward... consumption if potatoes I1 are a Giffen New budget I2 good. constraint 0 A Quantity of Meat Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203 440 PART VII TOPICS FOR FURTHER STUDY Initially, the consumer’s budget constraint is the line from point A to point B. The optimum is point C. When the price of potatoes rises, the budget constraint shifts inward and is now the line from point A to point D. The optimum is now point E. Notice that a rise in the price of potatoes has led the consumer to buy a larger quantity of potatoes. Why is the consumer responding in this strange way? In this example, potatoes are a strongly inferior good; that is, potatoes are a good that a person buys a lot less of when her income rises and a lot more of when her income falls. In Figure 12, the increase in the price of potatoes makes the consumer poorer; that is, the higher price puts her on a lower indifference curve. Because she is poorer and potatoes are an inferior good, the income effect makes her want to buy less meat and more potatoes. At the same time, because the potatoes have become more expensive relative to meat, the substitution effect makes the consumer want to buy more meat and fewer potatoes. If the income effect is much larger than the substitution effect, as it is in this example, the consumer responds to the higher price of potatoes by buying less meat and more potatoes. Giffen good Economists use the term Giffen good to describe a good that violates the law a good for which an of demand. (The term is named for economist Robert Giffen, who first noted this increase in the price possibility.) In this example, potatoes are a Giffen good. Giffen goods are inferior raises the quantity goods for which the income effect dominates the substitution effect. Therefore, demanded they have demand curves that slope upward. THE SEARCH FOR GIFFEN GOODS CASE Have any actual Giffen goods ever been observed? Some historians STUDY suggest that potatoes were a Giffen good during the Irish potato famine of the 19th century. Potatoes were such a large part of people’s diet that when the price of potatoes rose, the change had a large income effect. People responded to their reduced living standard by cutting back on the luxury of meat and buying more of the staple food of potatoes. Thus, it is argued that a higher price of potatoes actually raised the quantity of potatoes demanded. A study by Robert Jensen and Nolan Miller, published in the American Economic Review in 2008, produced similar but more concrete evidence for the existence of Giffen goods. These two economists conducted a field experiment for five months in the Chinese province of Hunan. They gave randomly selected households vouchers that subsidized the purchase of rice, a staple in local diets, and used surveys to measure how consumption of rice responded to changes in the price. They found strong evidence that poor households exhibited Giffen behavior. Lowering the price of rice with the subsidy voucher caused households to reduce their consumption of rice, and removing the subsidy had the opposite effect. Jensen and Miller wrote, “To the best of our knowledge, this is the first rigorous empirical evidence of Giffen behavior.” Thus, the theory of consumer choice allows demand curves to slope upward, and sometimes that strange phenomenon actually occurs. As a result, the law of demand we first saw in Chapter 4 is not completely reliable. It is safe to say, however, that Giffen goods are very rare. 21-4b How Do Wages Affect Labor Supply? So far, we have used the theory of consumer choice to analyze how a person allocates income between two goods. We can apply the same theory to analyze how a person allocates time. People spend some of their time enjoying leisure and Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203  CHAPTER 21 THE THEORY OF CONSUMER CHOICE 441 some of it working so they can afford to buy consumption goods. The essence of the time-allocation problem is the trade-off between leisure and consumption. Consider the decision facing Kayla, a freelance software designer. Kayla is awake for 100 hours per week. She spends some of this time enjoying leisure— playing Minecraft, watching The Bachelor on television, and reading this textbook. She spends the rest of this time at her computer developing software. For every hour she works developing software, she earns $50, which she spends on consumption goods—food, clothing, and music downloads. Her hourly wage of $50 reflects the trade-off Kayla faces between leisure and consumption. For every hour of leisure she gives up, she works one more hour and gets $50 of consumption. Figure 13 shows Kayla’s budget constraint. If she spends all 100 hours enjoying leisure, she has no consumption. If she spends all 100 hours working, she earns a weekly consumption of $5,000 but has no time for leisure. If she works a 40-hour week, she enjoys 60 hours of leisure and has weekly consumption of $2,000. Figure 13 uses indifference curves to represent Kayla’s preferences for consumption and leisure. Here consumption and leisure are the two “goods” between which Kayla is choosing. Because Kayla always prefers more leisure and more consumption, she prefers points on higher indifference curves to points on lower ones. At a wage of $50 per hour, Kayla chooses a combination of consumption and leisure represented by the point labeled “optimum.” This is the point on the budget constraint that is on the highest possible indifference curve, I2. Now consider what happens when Kayla’s wage increases from $50 to $60 per hour. Figure 14 illustrates two possible outcomes. In each case, the budget constraint, shown in the left graphs, shifts outward from BC1 to BC2. In the process, the budget constraint becomes steeper, reflecting the change in relative price: At the higher wage, Kayla earns more consumption for every hour of leisure that she gives up. Kayla’s preferences, as represented by her indifference curves, determine how her choice regarding consumption and leisure responds to the higher wage. In both panels, consumption rises. Yet the response of leisure to the change in the Consumption FIGURE 13 $5,000 The Work-Leisure Decision This figure shows Kayla’s budget constraint for deciding how much to work, her indiffer- ence curves for consumption and leisure, and her optimum. Optimum I3 2,000 I2 I1 0 60 100 Hours of Leisure Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203 442 PART VII TOPICS FOR FURTHER STUDY FIGURE 14 The two panels of this figure show how a person might respond to an increase in the wage. The graphs on the left show the consumer’s initial budget constraint, BC1, and new budget An Increase in the Wage constraint, BC2, as well as the consumer’s optimal choices over consumption and leisure. The graphs on the right show the resulting labor-supply curve. Because hours worked equal total hours available minus hours of leisure, any change in leisure implies an opposite change in the quantity of labor supplied. In panel (a), when the wage rises, consumption rises and leisure falls, resulting in a labor-supply curve that slopes upward. In panel (b), when the wage rises, both consumption and leisure rise, resulting in a labor-supply curve that slopes backward. (a) For a person with these preferences...... the labor supply curve slopes upward. Consumption Wage Labor supply 1. When the wage rises... BC1 BC2 I2 I1 0 Hours of 0 Hours of Labor 2.... hours of leisure decrease... Leisure 3.... and hours of labor increase. Supplied (b) For a person with these preferences...... the labor supply curve slopes backward. Consumption Wage BC2 1. When the wage rises... Labor BC1 supply I2 I1 0 Hours of 0 Hours of Labor 2.... hours of leisure increase... Leisure 3.... and hours of labor decrease. Supplied wage is different in the two cases. In panel (a), Kayla responds to the higher wage by enjoying less leisure. In panel (b), Kayla responds by enjoying more leisure. Kayla’s decision between leisure and consumption determines her supply of labor because the more leisure she enjoys, the less time she has left to work. In each panel of Figure 14, the right graph shows the labor-supply curve implied by Kayla’s decision. In panel (a), a higher wage induces Kayla to enjoy less leisure Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203  CHAPTER 21 THE THEORY OF CONSUMER CHOICE 443 and work more, so the labor-supply curve slopes upward. In panel (b), a higher wage induces Kayla to enjoy more leisure and work less, so the labor-supply curve slopes “backward.” At first, the backward-sloping labor-supply curve is puzzling. Why would a person respond to a higher wage by working less? The answer comes from considering the income and substitution effects of a higher wage. Consider first the substitution effect. When Kayla’s wage rises, leisure becomes more expensive relative to consumption, and this encourages Kayla to substitute away from leisure and toward consumption. In other words, the substitution effect induces Kayla to work more in response to higher wages, which tends to make the labor-supply curve slope upward. Now consider the income effect. When Kayla’s wage rises, she moves to a higher indifference curve. She is now better off than she was. As long as consumption and leisure are both normal goods, she tends to want to use this increase in well-being to enjoy both higher consumption and greater leisure. In other words, the income effect induces her to work less, which tends to make the labor-supply curve slope backward. In the end, economic theory does not give a clear prediction about whether an increase in the wage induces Kayla to work more or less. If the substitution effect is greater than the income effect, she works more. If the income effect is greater than the substitution effect, she works less. The labor-supply curve, therefore, could be either upward- or backward-sloping. INCOME EFFECTS ON LABOR SUPPLY: HISTORICAL TRENDS, LOTTERY CASE WINNERS, AND THE CARNEGIE CONJECTURE STUDY The idea of a backward-sloping labor-supply curve might at first seem like a mere theoretical curiosity, but in fact it is not. Evidence indicates that the labor-supply curve, considered over long periods, does indeed slope backward. A hundred years ago, many people worked six days a week. Today, five-day workweeks are the norm. At the same time that the length of the workweek has been falling, the wage of the typical worker (adjusted for inflation) has been rising. Here is how economists explain this historical pattern: Over time, advances in technology raise workers’ productivity and, thereby, the demand for labor. This increase in labor demand raises equilibrium wages. As wages rise, so does the reward for working. Yet rather than responding to this increased incentive by working more, most workers choose to take part of their greater prosperity in the form of more leisure. In other words, the income effect of higher wages dominates the substitution effect. Further evidence that the income effect on labor supply is strong comes from a very different kind of data: winners of lotteries. Winners of large prizes in the lottery see large increases in their incomes and, as a result, large outward shifts in their budget constraints. Because the winners’ wages have not changed, however, GETTY IMAGES NEWS/GETTY IMAGES the slopes of their budget constraints remain the same. There is, therefore, no substitution effect. By examining the behavior of lottery winners, we can isolate the income effect on labor supply. The results from studies of lottery winners are striking. Of those winners who win more than $50,000, almost 25 percent quit working within a year and another 9 percent reduce the number of hours they work. Of those winners who win more than $1 million, almost 40 percent stop working. The income effect on labor supply of winning such a large prize is substantial. “No more 9 to 5 for me.” Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203 444 PART VII TOPICS FOR FURTHER STUDY Similar results were found in a 1993 study, published in the Quarterly Journal of Economics, of how receiving a bequest affects a person’s labor supply. The study found that a single person who inherits more than $150,000 is four times as likely to stop working as a single person who inherits less than $25,000. This finding would not have surprised the 19th-century industrialist Andrew Carnegie. Carnegie warned that “the parent who leaves his son enormous wealth generally deadens the talents and energies of the son, and tempts him to lead a less useful and less worthy life than he otherwise would.” That is, Carnegie viewed the income effect on labor supply to be substantial and, from his paternalistic perspective, regrettable. During his life and at his death, Carnegie gave much of his vast fortune to charity. 21-4c How Do Interest Rates Affect Household Saving? An important decision that every person faces is how much income to consume today and how much to save for the future. We can use the theory of consumer choice to analyze how people make this decision and how the amount they save depends on the interest rate their savings will earn. Consider the decision facing Saul, a worker planning for retirement. To keep things simple, let’s divide Saul’s life into two periods. In the first period, Saul is young and working. In the second period, he is old and retired. When young, Saul earns $100,000. He divides this income between current consumption and saving. When he is old, Saul will consume what he has saved, including the interest that his savings have earned. Suppose the interest rate is 10 percent. Then for every dollar that Saul saves when young, he can consume $1.10 when old. We can view “consumption when young” and “consumption when old” as the two goods that Saul must choose between. The interest rate determines the relative price of these two goods. Figure 15 shows Saul’s budget constraint. If he saves nothing, he consumes $100,000 when young and nothing when old. If he saves everything, he consumes nothing when young and $110,000 when old. The budget constraint shows these and all the intermediate possibilities. FIGURE 15 Consumption Budget When Old constraint The Consumption-Saving Decision $110,000 This figure shows the budget constraint for a person deciding how much to consume in the two periods of his life, the indifference curves representing his preferences, and the optimum. 55,000 Optimum I3 I2 I1 0 $50,000 100,000 Consumption When Young Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203  CHAPTER 21 THE THEORY OF CONSUMER CHOICE 445 Figure 15 uses indifference curves to represent Saul’s preferences for consumption in the two periods. Because Saul prefers more consumption in both periods, he prefers points on higher indifference curves to points on lower ones. Given his preferences, Saul chooses the optimal combination of consumption in both periods of life, which is the point on the budget constraint that is on the highest possible indifference curve. At this optimum, Saul consumes $50,000 when young and $55,000 when old. Now consider what happens when the interest rate increases from 10 to 20 percent. Figure 16 shows two possible outcomes. In both cases, the budget constraint shifts outward and becomes steeper. At the new, higher interest rate, Saul gets more consumption when old for every dollar of consumption that he gives up when young. The two panels show the results given different preferences by Saul. In both cases, consumption when old rises. Yet the response of consumption when young to the change in the interest rate is different in the two cases. In panel (a), Saul responds to the higher interest rate by consuming less when young. In panel (b), Saul responds by consuming more when young. Saul’s saving is his income when young minus the amount he consumes when young. In panel (a), an increase in the interest rate reduces consumption when young, so saving must rise. In panel (b), an increase in the interest rate induces Saul to consume more when young, so saving must fall. The case shown in panel (b) might at first seem odd: Saul responds to an increase in the return to saving by saving less. But this behavior is not as peculiar as it might seem. We can understand it by considering the income and substitution effects of a higher interest rate. In both panels, an increase in the interest rate shifts the budget constraint FIGURE 16 outward. In panel (a), consumption when young falls, and consumption when old rises. The result is an increase in saving when young. In panel (b), consumption in An Increase in the Interest Rate both periods rises. The result is a decrease in saving when young. (a) Higher Interest Rate Raises Saving (b) Higher Interest Rate Lowers Saving Consumption Consumption When Old BC 2 When Old BC 2 1. A higher interest rate rotates 1. A higher interest rate rotates the budget constraint outward... the budget constraint outward... BC 1 BC 1 I2 I2 I1 I1 0 Consumption 0 Consumption 2.... resulting in lower When Young 2.... resulting in higher When Young consumption when young consumption when young and, thus, higher saving. and, thus, lower saving. Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203 446 PART VII TOPICS FOR FURTHER STUDY Consider first the substitution effect. When the interest rate rises, consumption when old becomes less costly relative to consumption when young. Therefore, the substitution effect induces Saul to consume more when old and less when young. In other words, the substitution effect induces Saul to save more. Now consider the income effect. When the interest rate rises, Saul moves to a higher indifference curve. He is now better off than he was. As long as consumption in both periods consists of normal goods, he tends to want to use this increase in well-being to enjoy higher consumption in both periods. In other words, the income effect induces him to save less. The result depends on both the income and substitution effects. If the substitution effect of a higher interest rate is greater