Chapter 21: The Theory of Consumer Choice PDF

## Chapter 21: The Theory of Consumer Choice When 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...

## Chapter 21: The Theory of Consumer Choice When 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 decisions 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 reflects consumers' willingness to pay for it. When the price of a good rises, consumers 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 understanding of demand, just as the theory of the competitive firm in Chapter 14 provides a more complete understanding of supply. ### The Budget Constraint: What the Consumer Can Afford Most people would like to increase the quantity or quality of the goods they consume- to take longer vacations, drive fancier cars, or eat at better restaurants. People 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 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 different 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 she 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 consumption 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 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 bundles that the consumer can afford. **Figure 1:** The Consumer's Budget Constraint | Number of Pizzas | Liters of Pepsi | Spending on Pizza | Spending on Pepsi | Total Spending | Quantity of Pepsi | |---|---|---|---|---|---| | 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 | | 50 | 250 | $500 | $500 | $1,000 | 250 | | 40 | 300 | $400 | $600 | $1,000 | | 30 | 350 | $300 | $700 | $1,000 | | 20 | 400 | $200 | $800 | $1,000 | | 10 | 450 | $100 | $900 | $1,000 | | 0 | 500 | $0 | $1,000 | $1,000 | The slope of the budget constraint measures the rate at which the consumer can trade one good for the other. Recall that the slope between two points is calculated as the change in the vertical distance divided by the change in the horizontal distance ("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 offering the consumer: 1 pizza for 5 liters of Pepsi. **Quick Quiz:** 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? ### Preferences: What the Consumer Wants Our goal in this chapter is to see how consumers make choices. The budget 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 consumer'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. ### 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 bundle 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 curves. An indifference curve shows the various bundles of consumption that make the consumer equally happy. In this case, the indifference curves show the combinations of pizza and Pepsi with which the consumer is equally satisfied. **Figure 2:** The Consumer's Preferences Figure 2 shows two of the consumer's many indifference curves. The consumer 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 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 substitution (MRS). In this case, the marginal rate of substitution measures how much Pepsi the consumer requires to be compensated for a one-unit reduction in pizza consumption. Notice that because the indifference curves are not straight lines, the marginal rate of substitution is not the same at all 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. That is, the rate at which a consumer is willing to trade pizza for Pepsi depends on whether she is hungrier or thirstier, which in turn depends on how much pizza and Pepsi she is consuming. 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 consumer'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 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 combination of pizza and Pepsi. ### 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: 1. Higher indifference curves are preferred to lower ones. People usually prefer to consume more goods rather than less. This preference for greater quantities is reflected in the indifference curves. As Figure 2 shows, higher indifference curves represent larger quantities of goods than lower indifference curves. Thus, the consumer prefers being on higher indifference curves. 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 for the consumer to be equally happy. For this reason, most indifference curves slope downward. 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 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. 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 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 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 marginal rate of substitution 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 marginal rate of substitution 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 in large quantity. **Figure 3:** The Impossibility of Intersecting Indifference Curves **Figure 4:** Bowed Indifference Curves ### 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 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 bundle. If so, you would always be willing to trade 2 nickels for 1 dime, regardless of the number of nickels and dimes in the bundle. Your marginal rate of substitution between nickels and dimes would be a fixed number - 2. We can represent your preferences over nickels and dimes with the indifference curves in panel (a) of Figure 5. Because the marginal rate of substitution is constant, the indifference curves are straight lines. In this extreme case of straight indifference curves, we say that the two goods are perfect substitutes. **Perfect Complements:** 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 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, therefore, are right angles. In this extreme case of right-angle indifference curves, we say that the two goods are perfect complements. 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. **Figure 5:** Perfect Substitutes and Perfect Complements **Quick Quiz:** Draw some indifference curves for pizza and Pepsi. Explain the four properties of these indifference curves. ### 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. ### The Consumer's Optimal Choices Consider once again 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:** The Consumer's Optimum 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. 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 substitution 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. ### Utility: An Alternative Way to Describe Preferences and Optimization We have used indifference curves to represent the consumer's preferences. Another common way to represent preferences is with the concept of utility. Utility is an abstract measure of the satisfaction or happiness that a consumer receives from a bundle of goods. Economists say that a consumer prefers one bundle of goods to another if one provides more utility than the other. Indifference curves and utility are closely related. Because the consumer prefers points on higher indifference curves, bundles of goods on higher indifference curves provide higher utility. Because the consumer is equally happy with all points on the same indifference curve, all these bundles provide the same utility. You can think of an indifference curve as an "equal-utility" curve. The marginal utility of any good is the increase in utility that the consumer gets from an additional unit of that good. Most goods are assumed to exhibit diminishing marginal utility: The more of the good the consumer already has, the lower the marginal utility provided by an extra unit of that good. The marginal rate of substitution between two goods depends on their marginal utilities. For example, if the marginal utility of good X is twice the marginal utility of good Y, then a person would need 2 units of good Y to compensate for losing 1 unit of good X, and the marginal rate of substitution equals 2. More generally, the marginal rate of substitution (and thus the slope of the indifference curve) equals the marginal utility of one good divided by the marginal utility of the other good. Utility analysis provides another way to describe consumer optimization. Recall that, at the consumer's optimum, the marginal rate of substitution equals the ratio of prices. That is, $MRS = P_x / P_y$. Because the marginal rate of substitution equals the ratio of marginal utilities, we can write this condition for optimization as $MU_x / MU_y = P_x / P_y$. Now rearrange this expression to become $MU_x / P_x = MU_y / P_y$. This equation has a simple interpretation: At the optimum, the marginal utility per dollar spent on good X equals the marginal utility per dollar spent on good Y. (Why? If this equality did not hold, the consumer could increase utility by spending less on the good that provided lower marginal utility per dollar and more on the good that provided higher marginal utility per dollar.) When economists discuss the theory of consumer choice, they sometimes express the theory using different words. One economist might say that the goal of the consumer is to maximize utility. Another economist might say that the goal of the consumer is to end up on the highest possible indifference curve. The first economist would conclude that at the consumer's optimum, the marginal utility per dollar is the same for all goods, whereas the second would conclude that the indifference curve is tangent to the budget constraint. In essence, these are two ways of saying the same thing. ### 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:** A Change in Price 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 rather than only 500 liters. 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 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. 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. ### 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 effects are, consider how our consumer might respond when she learns that the price of Pepsi has fallen. She might reason in the following ways: - "Great news! Now that Pepsi is cheaper, my income has greater purchasing power. I am, in effect, richer than I was. Because I am richer, I can buy both 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 pizza that I give up. Because pizza is now relatively more expensive, I should buy less pizza and more Pepsi." (This is the substitution effect.) 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 pizza and Pepsi are both normal goods, the consumer will want to spread this improvement in her 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 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 it is ambiguous whether the consumer buys more pizza, because the income and substitution effects work in opposite directions. This conclusion is summarized in Table 1. **Figure 10:** Income and Substitution Effects **Table 1:** Income and Substitution Effects When the Price of Pepsi Falls 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 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 is equally happy at these two points, but at point B, the marginal rate of substitution is lower than it is at point C. The substitution effect from point A to point B is the change along indifference curve I₁. The income effect from point B to point C is the move to a higher indifference curve, I₂. The new optimum, point C, shows the change in consumption that occurs as a result of both effects working together. ### Inferior Goods 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 income increases and the budget constraint shifts outward, the consumer buys more pizza but less Pepsi. ### Conclusion The theory of consumer choice is a powerful tool for understanding how consumers make decisions about what to buy. This chapter has introduced the three key elements of this theory: the consumer's budget constraint, the consumer's preferences, and the consumer's optimization. These elements can be used to explain a wide range of consumer behavior, from the decisions that consumers make about their everyday purchases to the choices that they make about their savings and investment.