Consumer Choice PDF

IN THIS CHAPTER YOU WILL... See how a budget...

IN THIS CHAPTER YOU WILL... See how a budget constraint represents the choices a consumer can af ford Learn how indif ference curves can be used to represent a consumer’s preferences Analyze how a consumer’s optimal choices are determined See how a consumer THE THEORY OF responds to changes in income CONSUMER CHOICE and changes in prices When you walk into a store, you are confronted with thousands of goods that you Decompose the might buy. Of course, because your financial resources are limited, you cannot buy impact of a price everything that you want. You therefore consider the prices of the various goods change into an being offered for sale and buy a bundle of goods that, given your resources, best income ef fect and a suits your needs and desires. substitution ef fect In this chapter we develop the theory that describes how consumers make de- cisions about what to buy. So far throughout this book, we have summarized con- sumers’ decisions with the demand curve. As we discussed in Chapters 4 through 7, the demand curve for a good reflects consumers’ willingness to pay for it. When Apply the theory of the price of a good rises, consumers are willing to pay for fewer units, so the quan- consumer choice to tity demanded falls. We now look more deeply at the decisions that lie behind the four questions demand curve. The theory of consumer choice presented in this chapter provides about household behavior 463 464 PA R T S E V E N A D VA N C E D T O P I C a more complete understanding 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 tradeoffs. The theory of consumer choice examines the tradeoffs that people face in their role as consumers. When a consumer buys more of one good, he can afford less of other goods. When he spends more time enjoying leisure and less time working, he has lower income and can afford less consumption. When he spends more of his income in the present and saves less of it, he must accept a lower level of consumption in the future. The theory of consumer choice examines how con- sumers facing these tradeoffs make decisions and how they respond to changes in their environment. After developing the basic theory of consumer choice, we apply it to several 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? ◆ Do the poor prefer to receive cash or in-kind transfers? 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. THE BUDGET CONSTRAINT : W H AT T H E C O N S U M E R C A N A F F O R D 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. Peo- ple consume less than they desire because their spending is constrained, or limited, by their income. We begin our study of consumer choice by examining this link be- tween income and spending. To keep things simple, we examine the decision facing a consumer who buys only two goods: Pepsi and pizza. Of course, real people buy thousands of different kinds of goods. Yet assuming there are only two goods greatly simplifies the prob- lem without altering the basic insights about consumer choice. We first consider how the consumer’s income constrains the amount he spends on Pepsi and pizza. Suppose that the consumer has an income of $1,000 per month and that he spends his entire income each month on Pepsi and pizza. The price of a pint of Pepsi is $2, and the price of a pizza is $10. Table 21-1 shows some of the many combinations of Pepsi and pizza that the consumer can buy. The first line in the table shows that if the consumer spends all his income on pizza, he can eat 100 pizzas during the month, but he would not be able to buy any Pepsi at all. The second line shows another possible consumption bundle: 90 pizzas and 50 pints of Pepsi. And so on. Each consumption bundle in the table costs exactly $1,000. Figure 21-1 graphs the consumption bundles that the consumer can choose. The vertical axis measures the number of pints of Pepsi, and the horizontal axis  CHAPTER 21 THE THEORY OF CONSUMER CHOICE 465 Ta b l e 2 1 - 1 NUMBER SPENDING SPENDING TOTAL PINTS OF PEPSI PIZZAS OF ON PEPSI ON PIZZA SPENDING T HE C ONSUMER ’ S O PPORTUNITIES. This table 0 100 $ 0 $1,000 $1,000 shows what the consumer can 50 90 100 900 1,000 afford if his income is $1,000, the 100 80 200 800 1,000 price of Pepsi is $2, and the price 150 70 300 700 1,000 of pizza is $10. 200 60 400 600 1,000 250 50 500 500 1,000 300 40 600 400 1,000 350 30 700 300 1,000 400 20 800 200 1,000 450 10 900 100 1,000 500 0 1,000 0 1,000 Figure 21-1 Quantity T HE C ONSUMER ’ S B UDGET of Pepsi C ONSTRAINT. The budget B constraint shows the various 500 bundles of goods that the consumer can afford for a given income. Here the consumer buys bundles of Pepsi and pizza. The more Pepsi he buys, the less C pizza he can afford. 250 Consumer’s budget constraint A 0 50 100 Quantity of Pizza measures the number of pizzas. Three points are marked on this figure. At point A, the consumer buys no Pepsi and consumes 100 pizzas. At point B, the consumer buys no pizza and consumes 500 pints of Pepsi. At point C, the consumer buys 50 pizzas and 250 pints 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 Pepsi and pizza. Of course, these are only three of the many combinations of Pepsi and pizza 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 bundles budget constraint that the consumer can afford. In this case, it shows the tradeoff between Pepsi and the limit on the consumption pizza that the consumer faces. bundles that a consumer can afford 466 PA R T S E V E N A D VA N C E D T O P I C The slope of the budget constraint measures the rate at which the consumer can trade one good for the other. Recall from the appendix to Chapter 2 that the slope between two points is calculated as the change in the vertical distance di- vided by the change in the horizontal distance (“rise over run”). From point A to point B, the vertical distance is 500 pints, and the horizontal distance is 100 pizzas. Thus, the slope is 5 pints 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 5 times as much as a pint of Pepsi, so the opportunity cost of a pizza is 5 pints of Pepsi. The budget constraint’s slope of 5 reflects the tradeoff the market is offering the consumer: 1 pizza for 5 pints of Pepsi. Q U I C K Q U I Z : Draw the budget constraint for a person with income of $1,000 if the price of Pepsi is $5 and the price of pizza is $10. What is the slope of this budget constraint? P R E F E R E N C E S : W H AT T H E C O N S U M E R WA N T S Our goal in this chapter is to see how consumers make choices. The budget con- straint is one piece of the analysis: It shows what combination of goods the con- sumer can afford given his income and the prices of the goods. The consumer’s choices, however, depend not only on his budget constraint but also on his prefer- ences regarding the two goods. Therefore, the consumer’s preferences are the next piece of our analysis. REPRESENTING PREFERENCES WITH INDIFFERENCE CURVES The consumer’s preferences allow him to choose among different bundles of Pepsi and pizza. If you offer the consumer two different bundles, he chooses the bundle that best suits his tastes. If the two bundles suit his 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 his preferences graphically. We do this with indifference curves. indif ference curve An indifference curve shows the bundles of consumption that make the consumer a curve that shows consumption equally happy. In this case, the indifference curves show the combinations of Pepsi bundles that give the consumer the and pizza with which the consumer is equally satisfied. same level of satisfaction Figure 21-2 shows two of the consumer’s many indifference curves. The con- sumer is indifferent among combinations A, B, and C, because they are all on the same 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 him equally happy. If consumption of pizza is reduced again, from point B to point C, the amount of Pepsi consumed must increase yet again.  CHAPTER 21 THE THEORY OF CONSUMER CHOICE 467 Figure 21-2 Quantity T HE C ONSUMER ’ S P REFERENCES. of Pepsi The consumer’s preferences are represented with indifference C curves, which show the combinations of Pepsi and pizza that make the consumer equally satisfied. Because the consumer prefers more of a good, points on a higher indifference curve B D (I2 here) are preferred to points on MRS a lower indifference curve (I1). I2 1 The marginal rate of substitution (MRS) shows the rate at which A Indifference curve, I 1 the consumer is willing to trade Pepsi for pizza. 0 Quantity of Pizza 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 substitution (MRS). In this case, the marginal rate of substitution marginal rate of measures how much Pepsi the consumer requires in order to be compensated for substitution a one-unit reduction in pizza consumption. Notice that because the indifference the rate at which a consumer is curves are not straight lines, the marginal rate of substitution is not the same at all willing to trade 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 he is already consuming. That is, the rate at which a consumer is willing to trade pizza for Pepsi depends on whether he is more hungry or more thirsty, which in turn depends on how much pizza and Pepsi he has. The consumer is equally happy at all points on any given indifference curve, but he prefers some indifference curves to others. Because he prefers more con- sumption to less, higher indifference curves are preferred to lower ones. In Fig- ure 21-2, 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 con- sumer’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 pre- ferred to point A because point D is on a higher indifference curve than point A. (That conclusion 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 consumer prefer it. By seeing which point is on the higher indifference curve, we can use the set of indifference curves to rank any combinations of Pepsi and pizza. 468 PA R T S E V E N A D VA N C E D T O P I C 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 de- scribe most indifference curves: ◆ Property 1: Higher indifference curves are preferred to lower ones. Consumers usually prefer more of something to less of it. (That is why we call this something a “good” rather than a “bad.”) This preference for greater quantities is reflected in the indifference curves. As Figure 21-2 shows, higher indifference 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 indifference 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 in order for the consumer to be equally happy. For this reason, most indifference 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 21-3. Then, because point A 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 indifference 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. Figure 21-3 T HE I MPOSSIBILITY OF Quantity I NTERSECTING I NDIFFERENCE of Pepsi C URVES. A situation like this can never happen. According to these indifference curves, the C consumer would be equally satisfied at points A, B, and C, A even though point C has more of both goods than point A. B 0 Quantity of Pizza  CHAPTER 21 THE THEORY OF CONSUMER CHOICE 469 Figure 21-4 Quantity B OWED I NDIFFERENCE C URVES. of Pepsi Indifference curves are usually bowed inward. This shape 14 implies that the marginal rate of substitution (MRS) depends on MRS = 6 the quantity of the two goods the consumer is consuming. At point A A, the consumer has little pizza 8 1 and much Pepsi, so he requires a lot of extra Pepsi to induce him to give up one of the pizzas: The 4 B marginal rate of substitution is MRS = 1 3 6 pints of Pepsi per pizza. At 1 Indifference curve point B, the consumer has much pizza and little Pepsi, so he 0 2 3 6 7 Quantity requires only a little extra Pepsi of Pizza to induce him to give up one of the pizzas: The marginal rate of substitution is 1 pint of Pepsi per pizza. ◆ 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 substitution (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. As an example, consider Figure 21-4. At point A, because the consumer has a lot of Pepsi and only a little pizza, he is very hungry but not very thirsty. To induce the consumer to give up 1 pizza, the consumer has to be given 6 pints of Pepsi: The marginal rate of substitution is 6 pints per pizza. By contrast, at point B, the consumer has little Pepsi and a lot of pizza, so he is very thirsty but not very hungry. At this point, he would be willing to give up 1 pizza to get 1 pint of Pepsi: The marginal rate of substitution is 1 pint per pizza. Thus, the bowed shape of the indifference curve reflects the consumer’s greater willingness to give up a good that he already has in large quantity. TWO EXTREME EXAMPLES OF INDIFFERENCE CURVES The shape of an indifference curve tells us about 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 indifference curves are very bowed. To see why this is true, let’s consider the ex- treme cases. Per fect Substitutes Suppose that someone offered you bundles of nick- els and dimes. How would you rank the different bundles? 470 PA R T S E V E N A D VA N C E D T O P I C (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 P ERFECT S UBSTITUTES AND P ERFECT C OMPLEMENTS. When two goods are easily Figure 21-5 substitutable, such as nickels and dimes, the indifference curves 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). Most likely, you would care only about the total monetary value of each bun- dle. If so, you would judge a bundle based on the number of nickels plus twice the number of dimes. In other words, you would always be willing to trade 1 dime for 2 nickels, regardless of the number of nickels and dimes in the bundle. Your mar- ginal rate of substitution between nickels and dimes would be a fixed number—2. We can represent your preferences over nickels and dimes with the indiffer- ence curves in panel (a) of Figure 21-5. Because the marginal rate of substitution is constant, the indifference curves are straight lines. In this extreme case of straight per fect substitutes indifference curves, we say that the two goods are perfect substitutes. two goods with straight-line indifference curves P e r f e c t C o m p l e m e n t s Suppose now that someone offered you bundles of shoes. 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 assem- ble 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 indiffer- ence curves in panel (b) of Figure 21-5. 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, therefore, are right angles. In this extreme case of right-angle indifference per fect complements curves, we say that the two goods are perfect complements. two goods with right-angle In the real world, of course, most goods are neither perfect substitutes (like indifference curves nickels and dimes) nor perfect complements (like right shoes and left shoes). More  CHAPTER 21 THE THEORY OF CONSUMER CHOICE 471 FYI Utility: An We have used indifference curves, bundles of goods on higher indifference curves pro- Alternative curves to represent the con- vide higher utility. Because the consumer is equally happy Way to sumer’s preferences. Another with all points on the same indifference curve, all these Represent a common way to represent pref- bundles provide the same utility. Indeed, you can think of an Consumer’s erences is with the concept of indifference curve as an “equal-utility” curve. The slope of Preferences utility. Utility is an abstract mea- the indifference curve (the marginal rate of substitution) re- sure of the satisfaction or happi- flects the marginal utility generated by one good compared ness that a consumer receives to the marginal utility generated by the other good. from a bundle of goods. Econo- When economists discuss the theory of consumer mists say that a consumer choice, they might express the theory using different words. prefers one bundle of goods to One economist might say that the goal of the consumer is to another if the first provides maximize utility. Another might say that the goal of the con- more utility than the second. sumer is to end up on the highest possible indifference Indifference curves and utility are closely related. Be- curve. In essence, these are two ways of saying the same cause the consumer prefers points on higher indifference thing. typically, the indifference curves are bowed inward, but not so bowed as to be- come right angles. Q U I C K Q U I Z : Draw some indifference curves for Pepsi and pizza. Explain the four properties of these indifference curves. O P T I M I Z AT I O N : W H AT T H E C O N S U M E R C H O O S E S 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 and the consumer’s preferences. Now we put these two pieces together and consider the consumer’s decision about what to buy. THE CONSUMER’S OPTIMAL CHOICES Consider once again our Pepsi and pizza example. The consumer would like to end up with the best possible combination of Pepsi and pizza—that is, the combi- nation on the highest possible indifference curve. But the consumer must also end up on or below his budget constraint, which measures the total resources available to him. Figure 21-6 shows the consumer’s budget constraint and three of his many in- difference curves. The highest indifference curve that the consumer can reach (I2 in the figure) is the one that just barely touches the budget constraint. The point at which this indifference curve and the budget constraint touch is called the opti- mum. The consumer would prefer point A, but he cannot afford that point because 472 PA R T S E V E N A D VA N C E D T O P I C Figure 21-6 T HE C ONSUMER ’ S O PTIMUM. Quantity The consumer chooses the point of Pepsi on his budget constraint that lies on the highest indifference curve. At this point, called the optimum, the marginal rate of substitution Optimum equals the relative price of the two goods. Here the highest B A indifference curve the consumer can reach is I2. The consumer prefers point A, which lies on I3 indifference curve I3 , but the consumer cannot afford this I2 bundle of Pepsi and pizza. By I1 contrast, point B is affordable, but because it lies on a lower Budget constraint indifference curve, the consumer 0 Quantity does not prefer it. of Pizza it lies above his budget constraint. The consumer can afford point B, but that point is on a lower indifference curve and, therefore, provides the consumer less satis- faction. The optimum represents the best combination of consumption of Pepsi and pizza available to the consumer. 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 budget constraint. The slope of the indifference curve is the marginal rate of sub- stitution between Pepsi and pizza, and the slope of the budget constraint is the relative price of Pepsi and pizza. 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 his consumption choices, the consumer takes as given the relative price of the two goods and then chooses an optimum at which his 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 marginal 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 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 optimization, mar- ket prices of different goods reflect the value that consumers place on those goods. HOW CHANGES IN INCOME AFFECT THE CONSUMER’S CHOICES Now that we have seen how the consumer makes the consumption decision, let’s examine how consumption responds to changes in income. To be specific, suppose  CHAPTER 21 THE THEORY OF CONSUMER CHOICE 473 Figure 21-7 Quantity A N I NCREASE IN I NCOME. of Pepsi New budget constraint When the consumer’s income rises, the budget constraint shifts out. If both goods are normal 1. An increase in income shifts the goods, the consumer responds to budget constraint outward... the increase in income by buying New optimum more of both of them. Here the consumer buys more pizza and 3.... and more Pepsi. Pepsi consumption. Initial optimum I2 Initial budget constraint I1 0 Quantity of Pizza 2.... raising pizza consumption... 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 21-7. 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 com- bination of Pepsi and pizza. In other words, the consumer can now reach a higher indifference curve. Given the shift in the budget constraint and the consumer’s preferences as represented by his indifference curves, the consumer’s optimum moves from the point labeled “initial optimum” to the point labeled “new opti- mum.” Notice that, in Figure 21-7, the consumer chooses to consume more Pepsi and more pizza. Although the logic of the model does not require increased consump- tion of both goods in response to increased income, this situation is the most com- mon one. As you may recall from Chapter 4, if a consumer wants more of a good when his income rises, economists call it a normal good. The indifference curves normal good in Figure 21-7 are drawn under the assumption that both Pepsi and pizza are nor- a good for which an increase in mal goods. income raises the quantity demanded Figure 21-8 shows an example in which an increase in income induces the con- sumer to buy more pizza but less Pepsi. If a consumer buys less of a good when his income rises, economists call it an inferior good. Figure 21-8 is drawn under the inferior good assumption that pizza is a normal good and Pepsi is an inferior good. a good for which an increase in Although most goods are normal goods, there are some inferior goods in the income reduces the quantity world. One example is bus rides. High-income consumers are more likely to own demanded cars and less likely to ride the bus than low-income consumers. Bus rides, there- fore, are an inferior good. 474 PA R T S E V E N A D VA N C E D T O P I C Figure 21-8 Quantity A N I NFERIOR G OOD. A good is of Pepsi New budget constraint an inferior good if the consumer buys less of it when his income rises. Here Pepsi is an inferior good: When the consumer’s income increases and the budget constraint shifts outward, the 1. When an increase in income shifts the 3.... but budget constraint outward... consumer buys more pizza but Pepsi Initial less Pepsi. optimum consumption falls, making New optimum Pepsi an inferior good. Initial budget I1 I2 constraint 0 Quantity of Pizza 2.... pizza consumption rises, making pizza a normal good... 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 a pint. It is no surprise that the lower price ex- pands the consumer’s set of buying opportunities. In other words, a fall in the price of any good shifts the budget constraint outward. Figure 21-9 considers more specifically how the fall in price affects the budget constraint. If the consumer spends his 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 con- sumer spends his entire income of $1,000 on Pepsi, he can now buy 1,000 rather than only 500 pints. Thus, the end point 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 bud- get constraint reflects the relative price of Pepsi and pizza. Because the price of Pepsi has fallen to $1 from $2, while the price of pizza has remained $10, the con- sumer can now trade a pizza for 10 rather than 5 pints of Pepsi. As a result, the new budget constraint is more steeply sloped. 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.  CHAPTER 21 THE THEORY OF CONSUMER CHOICE 475 Figure 21-9 Quantity of Pepsi A C HANGE IN P RICE. When the price of Pepsi falls, the D New budget constraint consumer’s budget constraint 1,000 shifts outward and changes slope. The consumer moves from the initial optimum to the new optimum, which changes his New optimum purchases of both Pepsi and 1. A fall in the price of Pepsi rotates pizza. In this case, the quantity of 500 B the budget constraint outward... Pepsi consumed rises, and the 3.... and quantity of pizza consumed falls. raising Pepsi Initial optimum consumption. Initial I2 budget I1 constraint A 0 100 Quantity of Pizza 2.... reducing pizza consumption... INCOME AND SUBSTITUTION EFFECTS The impact of a change in the price of a good on consumption can be decomposed into two effects: an income effect and a substitution effect. To see what these two income ef fect effects are, consider how our consumer might respond when he learns that the the change in consumption that price of Pepsi has fallen. He might reason in the following ways: results when a price change moves the consumer to a higher or lower ◆ “Great news! Now that Pepsi is cheaper, my income has greater purchasing indifference curve power. I am, in effect, richer than I was. Because I am richer, I can buy both substitution ef fect more Pepsi and more pizza.” (This is the income effect.) the change in consumption that ◆ “Now that the price of Pepsi has fallen, I get more pints of Pepsi for every results when a price change moves pizza that I give up. Because pizza is now relatively more expensive, I should the consumer along a given buy less pizza and more Pepsi.” (This is the substitution effect.) indifference curve to a point with a new marginal rate of substitution Which statement do you find more compelling? In fact, both of these statements make sense. The decrease in the price of Pepsi makes the consumer better off. If Pepsi and pizza are both normal goods, the con- sumer will want to spread this improvement in his purchasing power over both goods. This income effect tends to make the consumer buy more pizza and more Pepsi. Yet, at the same time, consumption of Pepsi has become less expensive rela- tive to consumption of pizza. This substitution effect tends to make the consumer choose more Pepsi and less pizza. Now consider the end result of these two effects. The consumer certainly buys more Pepsi, because the income and substitution effects both act to raise purchases of Pepsi. But it is ambiguous whether the consumer buys more pizza, because the 476 PA R T S E V E N A D VA N C E D T O P I C income and substitution effects work in opposite directions. This conclusion is summarized in Table 21-2. 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 higher indifference curve. The substitution effect is the change in consumption that results from being at a point on an indifference curve with a different marginal rate of substitution. Figure 21-10 shows graphically how to decompose the change in the con- sumer’s decision into the income effect and the substitution effect. When the price GOOD INCOME EFFECT SUBSTITUTION EFFECT TOTAL EFFECT Pepsi Consumer is richer, Pepsi is relatively cheaper, so Income and substitution effects act in so he buys more Pepsi. consumer buys more Pepsi. same direction, so consumer buys more Pepsi. Pizza Consumer is richer, Pizza is relatively more Income and substitution effects act in so he buys more pizza. expensive, so consumer opposite directions, so the total effect buys less pizza. on pizza consumption is ambiguous. I NCOME AND S UBSTITUTION E FFECTS W HEN THE P RICE OF P EPSI FALLS Ta b l e 2 1 - 2 Figure 21-10 I NCOME AND S UBSTITUTION Quantity of Pepsi E FFECTS. The effect of a change in price can be broken down into New budget constraint an income effect and a substitu- tion 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 Income the change from point A to effect B Initial optimum point B along indifference Initial Substitution curve I1. The income effect—the budget effect shift to a higher indifference constraint A curve—is shown here as the I2 change from point B on indifference curve I1 to point C on I1 indifference curve I2. 0 Quantity Substitution effect of Pizza Income effect  CHAPTER 21 THE THEORY OF CONSUMER CHOICE 477 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 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 reflects the new relative price by being parallel to the new budget constraint.) 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 indiffer- ence 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. Although the consumer never actually chooses point B, 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. 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 he 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 his budget constraint and indifference curves. For example, Figure 21-11 considers the demand for Pepsi. Panel (a) shows that when the price of a pint falls from $2 to $1, the consumer’s budget constraint shifts outward. Because of both income and substitution effects, the consumer in- creases his purchases of Pepsi from 50 to 150 pints. Panel (b) shows the demand curve that results from this consumer’s decisions. In this way, the theory of con- sumer choice provides the theoretical foundation for the consumer’s demand curve, which we first introduced in Chapter 4. Although it is comforting to know that the demand curve arises naturally from the theory of consumer choice, this exercise by itself does not justify devel- oping the theory. There is no need for a rigorous, analytic framework just to estab- lish that people respond to changes in prices. The theory of consumer choice is, however, very useful. As we see in the next section, we can use the theory to delve more deeply into the determinants of household behavior. Q U I C K Q U I Z : Draw a budget constraint and indifference curves for Pepsi and pizza. 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. 478 PA R T S E V E N A D VA N C E D T O P I C (a) The Consumer’s Optimum (b) The Demand Curve for Pepsi Quantity Price of of Pepsi Pepsi New budget constraint B A 150 $2 I2 B 1 A 50 Demand I1 0 Initial budget Quantity 0 50 150 Quantity constraint of Pizza of Pepsi D ERIVING THE D EMAND C URVE. Panel (a) shows that when the price of Pepsi falls from Figure 21-11 $2 to $1, the consumer’s optimum moves from point A to point B, and the quantity of Pepsi consumed rises from 50 to 150 pints. The demand curve in panel (b) reflects this relationship between the price and the quantity demanded. F O U R A P P L I C AT I O N S Now that we have developed the basic theory of consumer choice, let’s use it to shed light on four questions about how the economy works. These four questions might at first seem unrelated. But because each question involves household decisionmaking, we can address it with the model of consumer behavior we have just developed. D O A L L D E M A N D C U R V E S S L O P E D O W N WA R D ? Normally, when the price of a good rises, people buy less of it. Chapter 4 called this usual behavior the law of demand. This law 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 Fig- ure 21-12. In this example, the consumer buys two goods—meat and potatoes. Ini- tially, 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.  CHAPTER 21 THE THEORY OF CONSUMER CHOICE 479 Figure 21-12 Quantity of A G IFFEN G OOD. In this Potatoes Initial budget constraint example, when the price of B potatoes rises, the consumer’s optimum shifts from point C to point E. In this case, the consumer responds to a higher Optimum with high price of potatoes by buying less price of potatoes 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 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 a seemingly perverse way? The reason is that potatoes here are a strongly inferior good. When the price of potatoes rises, the consumer is poorer. The income effect makes the consumer 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 less potatoes. In this particular case, however, the income ef- fect is so strong that it exceeds the substitution effect. In the end, the consumer re- sponds to the higher price of potatoes by buying less meat and more potatoes. Economists use the term Giffen good to describe a good that violates the law Gif fen good of demand. (The term is named for economist Robert Giffen, who first noted this a good for which an increase in the possibility.) In this example, potatoes are a Giffen good. Giffen goods are inferior price raises the quantity demanded goods for which the income effect dominates the substitution effect. Therefore, they have demand curves that slope upward. Economists disagree about whether any Giffen good has ever been discovered. Some historians suggest that potatoes were in fact a Giffen good during the Irish potato famine of the nineteenth century. Potatoes were such a large part of peo- ple’s diet that when the price of potatoes rose, it 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. Whether or not this historical account is true, it is safe to say that Giffen goods are very rare. The theory of consumer choice does allow demand curves to slope upward. Yet such occurrences are so unusual that the law of demand is as reliable a law as any in economics. 480 PA R T S E V E N A D VA N C E D T O P I C Figure 21-13 T HE W ORK -L EISURE D ECISION. Consumption This figure shows Sally’s budget constraint for deciding how $5,000 much to work, her indifference curves for consumption and leisure, and her optimum. Optimum I3 2,000 I2 I1 0 60 100 Hours of Leisure H O W D O WA G E S A F F E C T L A B O R S U P P LY ? So far we have used the theory of consumer choice to analyze how a person de- cides how to allocate his income between two goods. We can use the same theory to analyze how a person decides to allocate his time between work and leisure. Consider the decision facing Sally, a freelance software designer. Sally is awake for 100 hours per week. She spends some of this time enjoying leisure—rid- ing her bike, watching television, studying economics, and so on. She spends the rest of this time at her computer developing software. For every hour she spends developing software, she earns $50, which she spends on consumption goods. Thus, her wage ($50) reflects the tradeoff Sally faces between leisure and con- sumption. For every hour of leisure she gives up, she works one more hour and gets $50 of consumption. Figure 21-13 shows Sally’s budget constraint. If she spends all 100 hours en- joying 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 normal 40-hour week, she enjoys 60 hours of leisure and has weekly consumption of $2,000. Figure 21-13 uses indifference curves to represent Sally’s preferences for con- sumption and leisure. Here consumption and leisure are the two “goods” between which Sally is choosing. Because Sally always prefers more leisure and more con- sumption, she prefers points on higher indifference curves to points on lower ones. At a wage of $50 per hour, Sally chooses a combination of consumption and leisure represented by the point labeled “optimum.” This is the point on the budget con- straint that is on the highest possible indifference curve, which is curve I2. Now consider what happens when Sally’s wage increases from $50 to $60 per hour. Figure 21-14 shows two possible outcomes. In each case, the budget con- straint, shown in the left-hand graph, shifts outward from BC1 to BC2. In the process, the budget constraint becomes steeper, reflecting the change in relative  CHAPTER 21 THE THEORY OF CONSUMER CHOICE 481 (a) For a person with these preferences...... the labor supply curve slopes upward. Consumption Wage Labor supply 1. When the wage rises... BC1 BC2 I 2 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 A N I NCREASE IN THE WAGE. The two panels of this figure show how a person might Figure 21-14 respond to an increase in the wage. The graphs on the left show the consumer’s initial budget constraint BC1 and new budget 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. price: At the higher wage, Sally gets more consumption for every hour of leisure that she gives up. Sally’s preferences, as represented by her indifference curves, determine the resulting responses of consumption and leisure to the higher wage. In both panels, 482 PA R T S E V E N A D VA N C E D T O P I C consumption rises. Yet the response of leisure to the change in the wage is differ- ent in the two cases. In panel (a), Sally responds to the higher wage by enjoying less leisure. In panel (b), Sally responds by enjoying more leisure. Sally’s decision between leisure and consumption determines her supply of labor, for the more leisure she enjoys the less time she has left to work. In each panel, the right-hand graph in Figure 21-14 shows the labor supply curve implied by Sally’s decision. In panel (a), a higher wage induces Sally to enjoy less leisure and work more, so the labor supply curve slopes upward. In panel (b), a higher wage induces Sally 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 con- sidering the income and substitution effects of a higher wage. Consider first the substitution effect. When Sally’s wage rises, leisure becomes more costly relative to consumption, and this encourages Sally to substitute con- sumption for leisure. In other words, the substitution effect induces Sally to work harder in response to higher wages, which tends to make the labor supply curve slope upward. Now consider the income effect. When Sally’s wage rises, she moves to a higher indifference curve. She is now better off than she was. As long as con- sumption 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 Sally to work more or less. If the substitution effect is greater than the income effect for Sally, she works more. If the income effect is greater than the substitution effect, she works less. The labor supply curve, there- fore, could be either upward or backward sloping. CASE STUDY INCOME EFFECTS ON LABOR SUPPLY: HISTORICAL TRENDS, LOTTERY WINNERS, AND THE CARNEGIE CONJECTURE 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 of time, does in fact slope backward. A hun- dred 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. The increase in labor demand raises equilibrium wages. As wages rise, so does the reward for working. Yet rather than responding to this increased incentive “NO MORE 9-TO-5 FOR ME.” 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  CHAPTER 21 THE THEORY OF CONSUMER CHOICE 483 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, the slopes of their budget constraints remain the same. There is, therefore, no substitution effect. By examining the behavior of lottery win- ners, 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. Similar results were found in a study, published in the May 1993 issue of the Quarterly Journal of Economics, of how receiving a bequest affects a person’s la- bor 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 nineteenth-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 sub- stantial and, from his paternalistic perspective, regrettable. During his life and at his death, Carnegie gave much of his vast fortune to charity. H O W D O I N T E R E S T R AT E S A F F E C T H O U S E H O L D S AV I N G ? An important decision that every person faces is how much income to consume to- day 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 Sam, a worker planning ahead for retirement. To keep things simple, let’s divide Sam’s life into two periods. In the first period, Sam is young and working. In the second period, he is old and retired. When young, Sam earns a total of $100,000. He divides this income between current consump- tion and saving. When he is old, Sam will consume what he has saved, including the interest that his savings have earned. Suppose that the interest rate is 10 percent. Then for every dollar that Sam 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 Sam must choose between. The interest rate determines the relative price of these two goods. Figure 21-15 shows Sam’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 21-15 uses indifference curves to represent Sam’s preferences for con- sumption in the two periods. Because Sam prefers more consumption in both pe- riods, he prefers points on higher indifference curves to points on lower ones. Given his preferences, Sam chooses the optimal combination of consumption in both periods of life, which is the point on the budget constraint that is on the high- est possible indifference curve. At this optimum, Sam consumes $50,000 when young and $55,000 when old. 484 PA R T S E V E N A D VA N C E D T O P I C Figure 21-15 T HE C ONSUMPTION -S AVING Consumption Budget D ECISION. This figure shows when Old constraint the budget constraint for a person $110,000 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 Now consider what happens when the interest rate increases from 10 percent to 20 percent. Figure 21-16 shows two possible outcomes. In both cases, the budget constraint shifts outward and becomes steeper. At the new higher interest rate, Sam gets more consumption when old for every dollar of consumption that he gives up when young. The two panels show different preferences for Sam and the resulting response to the higher interest rate. In both cases, consumption when old rises. Yet the re- sponse of consumption when young to the change in the interest rate is different in the two cases. In panel (a), Sam responds to the higher interest rate by con- suming less when young. In panel (b), Sam responds by consuming more when young. Sam’s saving, of course, is his income when young minus the amount he con- sumes when young. In panel (a), consumption when young falls when the interest rate rises, so saving must rise. In panel (b), Sam consumes more when young, so saving must fall. The case shown in panel (b) might at first seem odd: Sam responds to an in- crease in the return to saving by saving less. Yet 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. 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 Sam to consume more when old and less when young. In other words, the substitution effect induces Sam to save more. Now consider the income effect. When the interest rate rises, Sam moves to a higher indifference curve. He is now better off than he was. As long as consump- tion 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 in- come effect induces him to save less.  CHAPTER 21 THE THEORY OF CONSUMER CHOICE 485 (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 I1 I2 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. A N I NCREASE IN THE I NTEREST R ATE. In both panels, an increase in the interest rate Figure 21-16 shifts the budget constraint 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 both periods rises. The result is a decrease in saving when young. The end result, of course, depends on both the income and substitution effects. If the substitution effect of a higher interest rate is greater than the income effect, Sam saves more. If the income effect is greater than the substitution effect, Sam saves less. Thus, the theory of consumer choice says that an increase in the interest rate could either encourage or discourage saving. Although this ambiguous result is interesting from the standpoint of economic theory, it is disappointing from the standpoint of economic policy. It turns out that an important issue in tax policy hinges in part on how saving responds to interest rates. Some economists have advocated reducing the taxation of interest and other capital income, arguing that such a policy change would raise the after-tax interest rate that savers can earn and would thereby encourage people to save more. Other economists have argued that because of offsetting income and substitution effects, such a tax change might not increase saving and could even reduce it. Unfortu- nately, research has not led to a consensus about how interest rates affect saving. As a result, there remains disagreement among economists about whether changes in tax policy aimed to encourage saving would, in fact, have the intended effect. DO THE POOR PREFER TO RECEIVE CASH OR IN-KIND TRANSFERS? Paul is a pauper. Because of his low income, he has a meager standard of liv- ing. The government wants to help. It can either give Paul $1,000 worth of food 486 PA R T S E V E N A D VA N C E D T O P I C (a) The Constraint Is Not Binding Cash Transfer In-Kind Transfer Food Food BC 2 (with $1,000 cash) BC 2 (with $1,000 food stamps) BC 1 BC 1 B B I2 I2 $1,000 $1,000 A A I1 I1 0 Nonfood 0 Nonfood Consumption Consumption (b) The Constraint Is Binding Cash Transfer In-Kind Transfer Food Food BC 2 (with $1,000 cash) BC 2 (with $1,000 food stamps) BC 1 BC 1 C $1,000 $1,000 B B A A I1 I2 I2 I1 I3 0 Nonfood 0 Nonfood Consumption Consumption C ASH VERSUS I N -K IND T RANSFERS. Both panels compare a cash transfer and a similar Figure 21-17 in-kind transfer of food. In panel (a), the in-kind transfer does not impose a binding constraint, and the consumer ends up on the same indifference curve under the two policies. In panel (b), the in-kind transfer imposes a binding constraint, and the consumer ends up on a lower indifference curve with the in-kind transfer than with the cash transfer. (perhaps by issuing him food stamps) or simply give him $1,000 in cash. What does the theory of consumer choice have to say about the comparison between these two policy options? Figure 21-17 shows how the two options might work. If the government gives Paul cash, then the budget constraint shifts outward. He can divide the extra cash  CHAPTER 21 THE THEORY OF CONSUMER CHOICE 487 between food and nonfood consumption however he pleases. By contrast, if the government gives Paul an in-kind transfer of food, then his new budget constraint is more complicated. The budget constraint has again shifted out. But now the budget constraint has a kink at $1,000 of food, for Paul must consume at least that amount in food. That is, even if Paul spends all his money on nonfood consump- tion, he still consumes $1,000 in food. The ultimate comparison between the cash transfer and in-kind transfer d