Mircoeconimics Ch. 5

DEMAND AND CONSUMER SURPLUS In Chapter 1, Thinking Like an Economist, we first encountered the concept of economic surplus, which in a buyer's case is the difference between the most she would have been willing to pay for a product and the amount she actually pays for it. The economic surplus received by buyers is often referred to as consumer surplus. The term consumer surplus sometimes refers to the surplus received by a single buyer in a transaction. On other occasions, it's used to denote the total surplus received by all buyers in a market or collection of markets.

CALCULATING CONSUMER SURPLUS For performing cost-benefit analysis, it's often important to be able to measure the total consumer surplus received by all buyers who participate in a given market. For example, a road linking a mountain village and a port city would create a new market for fresh fish in the mountain village; in deciding whether the road should be built, analysts would want to count as one of its benefits the gains that would be reaped by buyers in this new market. To illustrate how economists actually measure consumer surplus, we'll consider a hypothetical market for a good with 11 potential buyers, each of whom can buy a maximum of one unit of the good each day. The first potential buyer's reservation price for the product is $11; the second buyer's reservation price is $10; the third buyer's reservation price is $9; and so on. The demand curve for this market will have the staircase shape shown in Figure 5.9. We can think of this curve as the digital counterpart of traditional analog demand curves. (If the units shown on the horizontal axis were fine enough, this digital curve would be visually indistinguishable from its analog counterparts.) FIGURE 5.9 A Market with a "Digital" Demand Curve. When a product can be sold only in whole-number amounts, its demand curve has the stair-step shape shown. Suppose the good whose demand curve is shown in Figure 5.9 were available at a price of $6 per unit. How much total consumer surplus would buyers in this market reap? At a price of $6, six units per day would be sold in this market. The buyer of the sixth unit would receive no economic surplus since his reservation price for that unit was exactly $6, the same as its selling price. But the first five buyers would reap a surplus for their purchases. The buyer of the first unit, for example, would have been willing to pay as much as $11 for it, but since she'd pay only $6, she'd receive a surplus of exactly $5. The buyer of the second unit, who would have been willing to pay as much as $10, would receive a surplus of $4. The surplus would be $3 for the buyer of the third unit, $2 for the buyer of the fourth unit, and $1 for the buyer of the fifth unit. If we add all the buyers' surpluses together, we get a total of $15 of consumer surplus each day. That surplus corresponds to the shaded area shown in Figure 5.10. FIGURE 5.10 Consumer Surplus. Consumer surplus (shaded region) is the cumulative difference between the most that buyers are willing to pay for each unit and the price they actually pay. Page 131 CONCEPT CHECK 5.4 Calculate consumer surplus for a demand curve like the one just described except that the buyers' reservation prices for each unit are $2 higher than before, as shown in the graph below. Now suppose we want to calculate consumer surplus in a market with a conventional straight-line demand curve. As the following example illustrates, this task is a simple extension of the method used for digital demand curves.

Why do the wealthy in Manhattan live in smaller houses than the wealthy in Seattle? Microsoft cofounder Bill Gates lives in a 45,000-square-foot house in Seattle, Washington. His house is large even by the standards of Seattle, many of whose wealthy residents live in houses with more than 10,000 square feet of floor space. By contrast, persons of similar wealth in Manhattan rarely live in houses larger than 5,000 square feet. Why this difference? For people trying to decide how large a house to buy, the most obvious difference between Manhattan and Seattle is the huge difference in housing prices. The cost of land alone is several times higher in Manhattan than in Seattle, and construction costs are also much higher. Although plenty of New Yorkers could afford to build a 45,000-square-foot mansion, Manhattan housing prices are so high that they simply choose to live in smaller houses and spend what they save in other ways—on lavish summer homes in eastern Long Island, for instance. New Yorkers also eat out and go to the theater more often than their wealthy counterparts in other U.S. cities.

An especially vivid illustration of substitution occurred during the late 1970s, when fuel shortages brought on by interruptions in the supply of oil from the Middle East led to sharp increases in the price of gasoline and other fuels. In a variety of ways—some straightforward, others remarkably ingenious—consumers changed their behavior to economize on the use of energy. They formed car pools; switched to public transportation; bought four-cylinder cars; moved closer to work; took fewer trips; turned down their thermostats; installed insulation, storm windows, and solar heaters; and bought more efficient appliances. Many people even moved farther south to escape high winter heating bills. As the next example points out, consumers not only abandon a good in favor of substitutes when it gets more expensive, but they also return to that good when prices return to their original levels.

CONCEPT CHECK 5.3 The buyers' side of the market for movie tickets consists of two consumers whose demands are as shown in the diagram below. Graph the market demand curve for this market.

Figure 5.8 illustrates the special case in which each of 1,000 consumers in the market has the same demand curve (a). To get the market demand curve (b) in this case, we simply multiply each quantity on the representative individual demand curve by 1,000. FIGURE 5.8 The Individual and Market Demand Curves When All Buyers Have Identical Demand Curves. When individual demand curves are identical, we get the market demand curve (b) by multiplying each quantity on the individual demand curve (a) by the number of consumers in the market

Why did people turn to four-cylinder cars in the 1970s, only to shift back to six- and eight-cylinder cars in the 1990s? In 1973, the price of gasoline was 38 cents per gallon. The following year the price shot up to 52 cents per gallon in the wake of a major disruption of oil supplies. A second disruption in 1979 drove the 1980 price to $1.19 per gallon. These sharp increases in the price of gasoline led to big increases in the demand for cars with four-cylinder engines, which delivered much better fuel economy than the six- and eight-cylinder cars most people had owned. After 1980, however, fuel supplies stabilized, and prices rose only slowly, reaching $1.40 per gallon by 1999. Yet despite the continued rise in the price of gasoline, the switch to smaller engines did not continue. By the late 1980s, the proportion of cars sold with six- and eight-cylinder engines began rising again. Why this reversal? The key to explaining these patterns is to focus on changes in the real price of gasoline. When someone decides how big an automobile engine to choose, what matters is not the nominal price of gasoline, but the price of gasoline relative to all other goods. After all, for a consumer faced with a decision of whether to spend $1.40 for a gallon of gasoline, the important question is how much utility she could get from other things she could purchase with the same money. Even though the price of gasoline continued to rise slowly in nominal, or dollar, terms through the 1980s and 1990s, it declined sharply relative to the price of other goods. Indeed, in terms of real purchasing power, the 1999 price was actually slightly lower than the 1973 price. (That is, in 1999 $1.40 bought slightly fewer goods and services than 38 cents bought in 1973.) It is this decline in the real price of gasoline that accounts for the reversal of the trend toward smaller engines.

A sharp decline in the real price of gasoline also helps account for the explosive growth in sport utility vehicles in the 1990s. Almost 4 million SUVs were sold in the United States in 2001, up from only 750,000 in 1990. Some of them—like the Ford Excursion—weigh more than 7,500 pounds (three times as much as a Honda Civic) and get less than 10 miles per gallon on city streets. Vehicles like these would have been dismal failures during the 1970s, but they were by far the hottest sellers in the cheap-energy environment of 2001. In 2004, gasoline prices yet again began to rise sharply in real terms, and by the summer of 2008 had reached almost $5 per gallon in some parts of the country. Just as expected, the patterns of vehicle purchases began to shift almost immediately. Large SUVs, in high demand just months earlier, began selling at deep discounts. And with long waiting lists for fuel-efficient hybrids such as the Toyota Prius, buyers not only seldom received discounts, but they frequently paid even more than the sticker price. Here's another closely related example of the influence of price on spending decisions.

Consumer surplus is the area of the shaded triangle ($2,000/day). (1/2)($4,000 gallons/days)($1/gallon)= ($2,000/day). A useful way of thinking about consumer surplus is to ask what is the highest price consumers would pay, in the aggregate, for the right to continue participating in this milk market. The answer is $2,000 per day, since that's the amount by which their combined benefits exceed their combined costs.

As discussed in Chapter 3, Supply and Demand, the demand curve for a good can be interpreted either horizontally or vertically. The horizontal interpretation tells us, for each price, the total quantity that consumers wish to buy at that price. The vertical interpretation tells us, for each quantity, the most a buyer would be willing to pay for the good at that quantity. For the purpose of computing consumer surplus, we rely on the vertical interpretation of the demand curve. The value on the vertical axis that corresponds to each point along the demand curve corresponds to the marginal buyer's reservation price for the good. Consumer surplus is the cumulative sum of the differences between these reservation prices and the market price. It is the area bounded above by the demand curve and bounded below by the market price.

Is Sarah maximizing her utility from consuming chocolate and vanilla ice cream? Chocolate ice cream sells for $2 per pint and vanilla sells for $1. Sarah has a budget of $400 per year to spend on ice cream, and her marginal utility from consuming each type varies with the amount consumed, as shown in Figure 5.3. If she is currently buying 200 pints of vanilla and 100 pints of chocolate each year, is she maximizing her utility?

At Sarah's current consumption levels, her marginal utility of chocolate ice cream is 25 percent higher than her marginal utility of vanilla. But chocolate is twice as expensive as vanilla. Note first that with 200 pints per year of vanilla and 100 pints of chocolate, Sarah is spending $200 per year on each type of ice cream, for a total expenditure of $400 per year on ice cream, exactly the amount in her budget. By spending her money in this fashion, is she getting as much utility as possible? Note in Figure 5.3(b) that her marginal utility from chocolate ice cream is 16 utils per pint. Since chocolate costs $2 per pint, her current spending on chocolate is yielding additional utility at the rate of (16 utils/pint)/($2/pint) = 8 utils per dollar. Similarly, note in Figure 5.3(a) that Sarah's marginal utility for vanilla is 12 utils per pint. And since vanilla costs only $1 per pint, her current spending on vanilla is yielding (12 utils/pint)/($1/pint) = 12 utils per dollar. In other words, at her current rates of consumption of the two flavors, her spending yields higher marginal utility per dollar for vanilla than for chocolate. And this means that Sarah cannot possibly be maximizing her total utility. To see why, note that if she spent $2 less on chocolate (that is, if she bought one pint less than before), she would lose about 16 utils;1 but with the same $2, she could buy two additional pints of vanilla, which would boost her utility by about 24 utils,2 for a net gain of about 8 utils. Under Sarah's current budget allocation, she is thus spending too little on vanilla and too much on chocolate. In the next example, we'll see what happens if Sarah spends $100 per year less on chocolate and $100 per year more on vanilla.

Response to a Price Reduction How should Sarah respond to a reduction in the price of chocolate ice cream? Suppose that Sarah's total ice cream budget is still $400 per year and the prices of the two flavors are again $2 per pint for chocolate and $1 per pint for vanilla. Her marginal utility from consuming each type varies with the amounts consumed, as shown in Figure 5.6. As we showed in the previous example, she is currently buying 250 pints of vanilla and 75 pints of chocolate each year, which is the optimal combination for her at these prices. How should she reallocate her spending among the two flavors if the price of chocolate ice cream falls to $1 per pint?

At the current combination of flavors, marginal utility per dollar is the same for each flavor. When the price of chocolate falls, marginal utility per dollar becomes higher for chocolate than for vanilla. To redress this imbalance, Sarah should buy more chocolate and less vanilla. Because the quantities shown in Figure 5.6 constitute the optimal combination of the two flavors for Sarah at the original prices, they must exactly satisfy the rational spending rule: MUcPc = (20 utils/pints)($2/pints)=10 utils/dollars = MUvPv = (10 utils/pints)($1/pints) When the price of chocolate falls to $1 per pint, the original quantities will no longer satisfy the rational spending rule because the marginal utility per dollar for chocolate will suddenly be twice what it was before: MUcPc = (20 utils/pints)($1/pints)= 20 utils/dollars = MUvPv = 10 utils/dollars To redress this imbalance, Sarah must rearrange her spending on the two flavors in such a way as to increase the marginal utility per dollar for vanilla relative to the marginal utility per dollar for chocolate. And as we see in Figure 5.6, that will happen if she buys a larger quantity than before of chocolate and a smaller quantity than before of vanilla.

If C and V denote the quantities of chocolate and vanilla, respectively, the budget constraint must satisfy the following equation: PcC +PvV= M which says simply that the consumer's yearly expenditure on chocolate (PCC) plus her yearly expenditure on vanilla (PVV) must add up to her yearly income (M). To express the budget constraint in the manner conventionally used to represent the formula for a straight line, we solve Equation 5A.1 for V in terms of C, which yields V= M/Pv - (Pc/Pv)C Equation 5A.2 provides another way of seeing that the vertical intercept of the budget constraint is given by M/PV, and its slope by -(PC/PV). The equation for the budget constraint in Figure 5A.2 is V = 10 - (1/2)C.

BUDGET SHIFTS DUE TO INCOME OR PRICE CHANGES Price Changes The slope and position of the budget constraint are fully determined by the consumer's income and the prices of the respective goods. Change any one of these and we have a new budget constraint. Figure 5A.3 shows the effect of an increase in the price of chocolate from PC1 = $5 per pint to PC2 = $10 per pint. Since both her budget and the price of vanilla are unchanged, the vertical intercept of the consumer's budget constraint stays the same. The rise in the price of chocolate rotates the budget constraint inward about this intercept, as shown in the diagram.

ONCEPT CHECK 5A.4 Show the effect on the budget constraint B1 in Figure 5A.3 of an increase in income from $100 per year to $120 per year. Concept Check 5A.4 illustrates that an increase in income shifts the budget constraint parallel outwards. As in the case of an income reduction, the slope of the budget constraint remains the same.

BUDGETS INVOLVING MORE THAN TWO GOODS The examples discussed so far have all been ones in which the consumer is faced with the opportunity to buy only two different goods. Needless to say, not many consumers have such narrow options. In its most general form, the consumer budgeting problem can be posed as a choice between not two but N different goods, where N can be an indefinitely large number. With only two goods (N = 2), the budget constraint is a straight line, as we have just seen. With three goods (N = 3), it is a plane. When we have more than three goods, the budget constraint becomes what mathematicians call a hyperplane, or multidimensional plane. The only real difficulty is in representing this multidimensional case geometrically. We are just not very good at visualizing surfaces that have more than three dimensions. The nineteenth-century economist Alfred Marshall proposed a disarmingly simple solution to this problem. It is to view the consumer's choice as being one between a particular good—call it X—and an amalgam of other goods denoted Y. This amalgam is called the composite good. We may think of the composite good as the amount of income the consumer has left over after buying the good X. To illustrate how this concept is used, suppose the consumer has an income level of $M per year, and the price of X is given by PX. The consumer's budget constraint may then be represented as a straight line in the X,Y plane, as shown in Figure 5A.5. For simplicity, the price of a unit of the composite good is taken to be one, so that if the consumer devotes none of his income to X, he will be able to buy M units of the composite good. All this means is that he will have $M available to spend on other goods if he buys no X. Alternatively, if he spends all his income on X, he will be able to purchase the bundle (M/PX, 0). Since the price of Y is assumed to be one, the slope of the budget constraint is simply -PX. The vertical axis measures the amount of money spent each month on all goods other than X. As before, the budget constraint summarizes the various combinations of bundles that are affordable. For example, the consumer can have X1 units of X and Y1 units of the composite good in Figure 5A.5, or X2 and Y2, or any other combination that lies on the budget constraint. Summing up briefly, the budget constraint or opportunity set summarizes the combinations of bundles that the consumer is able to buy. Its position is determined jointly by income and prices. From the set of feasible bundles, the consumer's task is to pick the particular one she likes best. To identify this bundle, we need some means of summarizing the consumer's preferences over all possible bundles she might consume. To this task we now turn.

When chocolate goes up in price, the vertical intercept of the budget constraint remains the same. The original budget constraint rotates inward about this intercept. Note in Figure 5A.3 that even though the price of vanilla has not changed, the new budget constraint, B2, curtails not only the amount of chocolate the consumer can buy but also the amount of vanilla. CONCEPT CHECK 5A.1 Show the effect on the budget constraint B1 in Figure 5A.3 of a fall in the price of chocolate from $5 per pint to $4 per pint. In Concept Check 5A.1, you saw that a fall in the price of vanilla again leaves the vertical intercept of the budget constraint unchanged. This time the budget constraint rotates outward. Note also in Concept Check 5A.1 that although the price of vanilla remains unchanged, the new budget constraint enables the consumer to buy bundles that contain not only more chocolate but also more vanilla than she could afford on the original budget constrain

CONCEPT CHECK 5A.2 Show the effect on the budget constraint B1 in Figure 5A.3 of a rise in the price of vanilla from $10 per pint to $20 per pint. Concept Check 5A.2 demonstrates that when the price of vanilla changes, the budget constraint rotates about its horizontal intercept. Note also that even though income and the price of chocolate remain the same, the new budget constraint curtails not only the amount of vanilla he can buy but also the amount of chocolate. When we change the price of only one good, we necessarily change the slope of the budget constraint, -PC/PV. The same is true if we change both prices by different proportions. But as Concept Check 5A.3 will illustrate, changing both prices by exactly the same proportion gives rise to a new budget constraint with the same slope as before.

MEASURING WANTS: THE CONCEPT OF UTILITY

Economists use the concept of utility to represent the satisfaction people derive from their consumption activities. The assumption is that people try to allocate their incomes so as to maximize their satisfaction, a goal that is referred to as utility maximization. Early economists imagined that the utility associated with different activities might someday be subject to precise measurement. The nineteenth-century British economist Jeremy Bentham, for example, wrote of a "utilometer," a device that could be used to measure the amount of utility provided by different consumption activities. Although no such device existed in Bentham's day, contemporary neuropsychologists now have equipment that can generate at least crude measures of satisfaction. The accompanying photo, for example, shows a subject who is connected to an apparatus that measures the intensity of electrical waves emanating from different parts of his brain. University of Wisconsin psychologist Richard Davidson and his colleagues documented that subjects with relatively heavy brain-wave measures emanating from the left prefrontal cortex tend to be happier (as assessed by a variety of other measures) than subjects with relatively heavy brain-wave measures emanating from the right prefrontal cortex. Jeremy Bentham would have been thrilled to learn that a device like the one pictured here might exist some day. His ideal utilometer would measure utility in utils, much as a thermometer measures temperature in degrees Fahrenheit or Celsius. It would assign a numerical utility value to every activity—watching a movie, eating a cheeseburger, and so on. Unfortunately, even sophisticated devices are far from capable of such fine-grained assessments. For Bentham's intellectual enterprise, however, the absence of a real utilometer was of no practical significance. Even without such a machine, he could continue to envision the consumer as someone whose goal was to maximize the total utility she obtained from the goods she consumed. Bentham's "utility maximization model," as we'll see, affords important insights about how a rational consumer ought to spend her income. To explore how the model works, we begin with a very simple problem, the one facing a consumer who reaches the front of the line at a free ice cream stand. How many cones of ice cream should this person, whom we'll call Sarah, ask for? Table 5.1 shows the relationship between the total number of ice cream cones Sarah eats per hour and the total utility, measured in utils per hour, she derives from them. Note that the measurements in the table are stated in terms of cones per hour and utils per hour. Why "per hour"? Because without an explicit time dimension, we would have no idea whether a given quantity was a lot or a little. Five ice cream cones in a lifetime isn't much, but five in an hour would be more than most of us would care to eat

USING INDIFFERENCE CURVES TO DESCRIBE PREFERENCES To get a feel for how indifference maps describe a consumer's preferences, it is helpful to work through a simple example. Suppose that Tom and Mary like both chocolate and vanilla ice cream but that Tom's favorite flavor is chocolate while Mary's favorite is vanilla. This difference in their preferences is captured by the differing slopes of their indifference curves in Figure 5A.12. Note in the left panel, which shows Tom's indifference map, that he would be willing to exchange three pints of vanilla for one pint of chocolate at the bundle A. But at the corresponding bundle in the right panel, which shows Mary's indifference map, we see that Mary would trade three pints of chocolate to get another pint of vanilla. Their difference in preferences shows up clearly in this difference in their marginal rates of substitution of vanilla for chocolate.

FIGURE 5A.12 People with Different Tastes. Relatively speaking, Tom is a chocolate lover, Mary a vanilla lover. This difference shows up in the fact that at any given bundle, Tom's marginal rate of substitution of vanilla for chocolate is greater than Mary's. At bundle A, for example, Tom would give up three pints of vanilla to get another pint of chocolate, whereas Mary would give up three pints of chocolate to get another pint of vanilla.

As the entries in Table 5.1 show, Sarah's total utility increases with each cone she eats, up to the fifth cone. Eating five cones per hour makes her happier than eating four, which makes her happier than eating three, and so on. But beyond five cones per hour, consuming more ice cream actually makes Sarah less happy. Thus, the sixth cone reduces her total utility from 150 utils per hour to 140 utils per hour. We can display the utility information in Table 5.1 graphically, as in Figure 5.1. Note in the graph that the more cones per hour Sarah eats, the more utils she gets—but again only up to the fifth cone. Once she moves beyond five, her total utility begins to decline. Sarah's happiness reaches a maximum of 150 utils when she eats five cones per hour. At that point she has no incentive to eat the sixth cone, even though it's absolutely free. Eating it would actually make her worse off.

For most goods, utility rises at a diminishing rate with additional consumption. Table 5.1 and Figure 5.1 illustrate another important aspect of the relationship between utility and consumption—namely, that the additional utility from additional units of consumption declines as total consumption increases. Thus, whereas one cone per hour is a lot better—by 50 utils—than zero, five cones per hour is just a little better than four (just 10 utils' worth). The term marginal utility denotes the amount by which total utility changes when consumption changes by one unit. In Table 5.2, the third column shows the marginal utility values that correspond to changes in Sarah's level of ice cream consumption. For example, the second entry in that column represents the increase in total utility (measured in utils per cone) when Sarah's consumption rises from one cone per hour to two. Note that the marginal utility entries in the third column are placed midway between the rows of the preceding columns. We do this to indicate that marginal utility corresponds to the movement from one consumption quantity to the next. Thus, we'd say that the marginal utility of moving from one to two cones per hour is 40 utils per cone.

The rational consumer allocates income among different goods so that the marginal utility gained from the last dollar spent on each good is the same. This rational spending rule gives rise to the law of demand, which states that people do less of what they want to do as the cost of doing it rises. Here, "cost" refers to the sum of all monetary and nonmonetary sacrifices—explicit and implicit—that must be made in order to engage in the activity. (LO1, LO2) The ability to substitute one good for another is an important factor behind the law of demand. Because virtually every good or service has at least some substitutes, economists prefer to speak in terms of wants rather than needs. We face choices, and describing our demands as needs is misleading because it suggests we have no options. (LO3)

For normal goods, the income effect is a second important reason that demand curves slope downward. When the price of such a good falls, not only does it become more attractive relative to its substitutes, but the consumer also acquires more real purchasing power, and this, too, augments the quantity demanded. (LO3) The demand curve is a schedule that shows the amounts of a good people want to buy at various prices. Demand curves can be used to summarize the price-quantity relationship for a single individual, but more commonly we employ them to summarize that relationship for an entire market. At any quantity along a demand curve, the corresponding price represents the amount by which the consumer (or consumers) would benefit from having an additional unit of the product. For this reason, the demand curve is sometimes described as a summary of the benefit side of the market. (LO4) Consumer surplus is a quantitative measure of the amount by which buyers benefit as a result of their ability to purchase goods at the market price. It is the area between the demand curve and the market price. (LO5)

Measuring Consumer Surplus How much do buyers benefit from their participation in the market for milk? Consider the market for milk whose demand and supply curves are shown in Figure 5.11, which has an equilibrium price of $2 per gallon and an equilibrium quantity of 4,000 gallons per day. How much consumer surplus do the buyers in this market reap?

For the supply and demand curves shown, the equilibrium price of milk is $2 per gallon and the equilibrium quantity is 4,000 gallons per day. In Figure 5.11, note first that, as in Figure 5.10, the last unit exchanged each day generates no consumer surplus at all. Note also that for all milk sold up to 4,000 gallons per day, buyers receive consumer surplus, just as in Figure 5.10. For these buyers, consumer surplus is the cumulative difference between the most they'd be willing to pay for milk (as measured on the demand curve) and the price they actually pay. Total consumer surplus received by buyers in the milk market is thus the shaded triangle between the demand curve and the market price in Figure 5.12. Note that this area is a right triangle whose vertical arm is h = $1/gallon and whose horizontal arm is b = 4,000 gallons/day. And because the area of any triangle is equal to (1/2)bh, consumer surplus in this market is equal to

INDIVIDUAL AND MARKET DEMAND CURVES If we know what each individual's demand curve for a good looks like, how can we use that information to construct the market demand curve for the good? We must add the individual demand curves together, a process that is straightforward but requires care.

HORIZONTAL ADDITION Suppose that there are only two buyers—Smith and Jones—in the market for canned tuna and that their demand curves are as shown in Figure 5.7(a) and (b). To construct the market demand curve for canned tuna, we simply announce a sequence of prices and then add the quantity demanded by each buyer at each price. For example, at a price of 40 cents per can, Smith demands six cans per week (a) and Jones demands two cans per week (b), for a market demand of eight cans per week (c). The quantity demanded at any price on the market demand curve (c) is the sum of the individual quantities demanded at that price, (a) and (b). The process of adding individual demand curves to get the market demand curve is known as horizontal addition, a term used to emphasize that we are adding quantities, which are measured on the horizontal axes of individual demand curves.

THE ORIGINS OF DEMAND

How much are you willing to pay for the latest Beyoncé album? The answer will clearly depend on how you feel about her music. To her diehard fans, buying the new release might seem absolutely essential; they'd pay a steep price indeed. But those who don't like her music may be unwilling to buy it at any price. Wants (also called "preferences" or "tastes") are clearly an important determinant of a consumer's reservation price for a good. But that raises the question of where wants come from. Many tastes—such as the taste for water on a hot day or for a comfortable place to sleep at night—are largely biological in origin. But many others are heavily shaped by culture, and even basic cravings may be socially molded. For example, people raised in southern India develop a taste for hot curry dishes, while those raised in France generally prefer milder foods. Tastes for some items may remain stable for many years, but tastes for others may be highly volatile. Although books about the Titanic disaster have been continuously available since the vessel sank in spring 1912, not until the appearance of James Cameron's blockbuster film did these books begin to sell in large quantities. In spring 1998, five of the 15 books on The New York Times paperback bestseller list were about the Titanic itself or one of the actors Page 115in the film. Yet none of these books, or any other book about the Titanic, made the bestseller list in the years since then. Still, echoes of the film continued to reverberate in the marketplace. In the years since its release, for example, demand for ocean cruises has grown sharply, and several television networks have introduced shows set on cruise ships. Peer influence provides another example of how social forces often influence demand. Indeed, it is often the most important single determinant of demand. For instance, if our goal is to predict whether a young man will purchase an illegal recreational drug, knowing how much income he has is not very helpful. Knowing the prices of whiskey and other legal substitutes for illicit drugs also tells us little. Although these factors do influence purchase decisions, by themselves they are weak predictors. But if we know that most of the young man's best friends are heavy drug users, there's a reasonably good chance that he'll use drugs as well. Another important way in which social forces shape demand is in the relatively common desire to consume goods and services that are recognized as the best of their kind. For instance, many people want to hear Placido Domingo sing not just because of the quality of his voice, but because he is widely regarded as the world's best—or at least the world's best known—living tenor. Consider, too, the decision of how much to spend on an interview suit. Employment counselors never tire of reminding us that making a good first impression is extremely important when you go for a job interview. At the very least, that means showing up in a suit that looks good. But looking good is a relative concept. If everyone else shows up in a $200 suit, you'll look good if you show up in a $300 suit. But you won't look as good in that same $300 suit if everyone else shows up in suits costing $1,000. The amount you'll choose to spend on an interview suit, then, clearly depends on how much others in your circle are spending.

INCOME AND SUBSTITUTION EFFECTS REVISITED

In Chapter 3, Supply and Demand, we saw that the quantity of a good that consumers wish to purchase depends on its own price, on the prices of substitutes and complements, and on consumer incomes. We also saw that when the price of a good changes, the quantity of it demanded changes for two reasons: the substitution effect and the income effect. The substitution effect refers to the fact that when the price of a good goes up, substitutes for that good become relatively more attractive, causing some consumers to abandon the good for its substitutes. The income effect refers to the fact that a price change makes the consumer either poorer or richer in real terms. Consider, for instance, the effect of a change in the price of one of the ice cream flavors in the preceding examples. At the original prices ($2 per pint for chocolate, $1 per pint for vanilla), Sarah's $400 annual ice cream budget enabled her to buy at most 200 pints per year of chocolate or 400 pints per year of vanilla. If the price of vanilla rose to $2 per pint, that would reduce not only the maximum amount of vanilla she could afford (from 400 to 200 pints per year), but also the maximum amount of chocolate she could afford in combination with any given amount of vanilla. For example, at the original price of $1 per pint for vanilla, Sarah could afford to buy 150 pints of chocolate while buying 100 pints of vanilla, but when the price of vanilla rises Page 124to $2, she can buy only 100 pints of chocolate while buying 100 pints of vanilla. As noted in Chapter 3, Supply and Demand, a reduction in real income shifts the demand curves for normal goods to the left. The rational spending rule helps us see more clearly why a change in the price of one good affects demands for other goods. The rule requires that the ratio of marginal utility to price be the same for all goods. This means that if the price of one good goes up, the ratio of its current marginal utility to its new price will be lower than for other goods. Consumers can then increase their total utility by devoting smaller proportions of their incomes to that good and larger proportions to others.

NEEDS VERSUS WANTS

In everyday language, we distinguish between goods and services people need and those they merely want. For example, we might say that someone wants a ski vacation in Utah, but what he really needs is a few days off from his daily routine; or that someone wants a house with a view, but what she really needs is shelter from the elements. Likewise, because people need protein to survive, we might say that a severely malnourished person needs more protein. But it would strike us as odd to say that anyone—even a malnourished person—needs more prime filet of beef because health can be restored by consuming far less expensive sources of protein. Economists like to emphasize that once we have achieved bare subsistence levels of consumption—the amount of food, shelter, and clothing required to maintain our health—we can abandon all reference to needs and speak only in terms of wants. This linguistic distinction helps us to think more clearly about the true nature of our choices. For instance, someone who says, "Californians don't have nearly as much water as they need" will tend to think differently about water shortages than someone who says, "Californians don't have nearly as much water as they want when the price of water is low." The first person is likely to focus on regulations to prevent people from watering their lawns, or on projects to capture additional runoff from the Sierra Nevada mountains. The second person is more likely to focus on the artificially low price of water in California. Whereas remedies of the first sort are often costly and extremely difficult to implement, raising the price of water is both simple and effective.

CONCEPT CHECK 5A.3 Show the effect on the budget constraint B1 in Figure 5A.3 of a rise in the price of vanilla from $10 per pint to $20 per pint and a rise in the price of chocolate from $5 per pint to $10 per pint. Note from Concept Check 5A.3 that the effect of doubling the prices of both vanilla and chocolate is to shift the budget constraint inward and parallel to the original budget constraint. The important lesson of this exercise is that the slope of the budget constraint tells us only about relative prices, nothing about how high prices are in absolute terms. When the prices of vanilla and chocolate change in the same proportion, the opportunity cost of chocolate in terms of vanilla remains the same as before.

Income Changes The effect of a change in income is much like the effect of an equal proportional change in all prices. Suppose, for example, that our hypothetical consumer's income is cut by half, from $100 per year to $50 per year. The horizontal intercept of her budget constraint will then fall from 20 pints per year to 10 pints per year and the vertical intercept from 10 pints per year to 5 pints per year, as shown in Figure 5A.4. Thus the new budget, B2, is parallel to the old, B1, each with a slope of -1/2. In terms of its effect on what the consumer can buy, cutting income by half is thus no different from doubling each price. Precisely the same budget constraint results from both changes.

TRANSLATING WANTS INTO DEMAND

It's a simple fact of life that although our resources are finite, our appetites for good things are boundless. Even if we had unlimited bank accounts, we'd quickly run out of the time and energy needed to do all the things we wanted to do. Our challenge is to use our limited resources to fulfill our desires to the greatest possible degree. That leaves us with a practical question: How should we allocate our incomes among the various goods and services that are available? To answer this question, it's helpful to begin by recognizing that the goods and services we buy are not ends in themselves, but rather means for satisfying our desires.

THE RATIONAL SPENDING RULE The examples we have worked through illustrate the rational spending rule for solving the problem of how to allocate a fixed budget across different goods. The optimal, or utility-maximizing, combination must satisfy this rule. The Rational Spending Rule: Spending should be allocated across goods so that the marginal utility per dollar is the same for each good. The rational spending rule can be expressed in the form of a simple formula. If we use MUC to denote marginal utility from chocolate ice cream consumption (again measured in utils per pint) and PC to denote the price of chocolate (measured in dollars per pint), then the ratio MUC/PC will represent the marginal utility per dollar spent on chocolate, measured in utils per dollar. Similarly, if we use MUV to denote the marginal utility from vanilla ice cream consumption and PV to denote the price of vanilla, then MUV/PV will represent the marginal utility per dollar spent on vanilla. The marginal utility per dollar will be exactly the same for the two types—and hence total utility will be maximized—when the following simple equation for the rational spending rule for two goods is satisfied:

MUdPc=MUvPv The rational spending rule is easily generalized to apply to spending decisions regarding large numbers of goods. In its most general form, it says that the ratio of marginal utility to price must be the same for each good the consumer buys. If the ratio were higher for one good than for another, the consumer could always increase her total utility by buying more of the first good and less of the second. Strictly speaking, the rational spending rule applies to goods that are perfectly divisible, such as milk or gasoline. Many other goods, such as bus rides and television sets, can be consumed only in whole-number amounts. In such cases, it may not be possible to satisfy the rational spending rule exactly. For example, when you buy one television set, your marginal utility per dollar spent on televisions may be somewhat higher than the corresponding ratio for other goods, yet if you bought a second set, the reverse might well be true. Your best alternative in such cases is to allocate each additional dollar you spend to the good for which your marginal utility per dollar is highest. Cost-Benefit Notice that we have not chosen to classify the rational spending rule as one of the Core Principles of economics. We omit it from this list not because the rule is unimportant, but because it follows directly from the Cost-Benefit Principle. As we noted earlier, there is considerable advantage in keeping the list of Core Principles as small as possible.

John spends all of his income on two goods: food and shelter. The price of food is $5 per pound and the price of shelter is $10 per square yard. At his current consumption levels, his marginal utilities for the two goods are 20 utils per pound and 30 utils per square yard, respectively. Is John maximizing his utility? If not, how should he reallocate his spending? In Chapter 1, Thinking Like an Economist, we saw that people often make bad decisions because they fail to appreciate the distinction between average and marginal costs and benefits. As the following example illustrates, this pitfall also arises when people attempt to apply the economist's model of utility maximization.

Marginal vs. Average Utility Should Eric consume more apples? Eric gets a total of 1,000 utils per week from his consumption of apples and a total of 400 utils per week from his consumption of oranges. The price of apples is $2 each, the price of oranges is $1 each, and he consumes 50 apples and 50 oranges each week. True or false: Eric should consume more apples and fewer oranges. Eric spends $100 per week on apples and $50 on oranges. He thus averages (1,000 utils/week)/($100/week) = 10 utils per dollar from his consumption of apples and (400 utils/week)/($50/week) = 8 utils per dollar from his consumption of oranges. Many might be tempted to respond that because Eric's average utility per dollar for apples is higher than for oranges, he should consume more apples. But knowing only his average utility per dollar for each good doesn't enable us to say whether his current combination is optimal. To make that determination, we need to compare Eric's marginal utility per dollar for each good. The information given simply doesn't permit us to make that comparison.

ALLOCATING A FIXED INCOME BETWEEN TWO GOODS

Most of the time we face considerably more complex purchasing decisions than the one Sarah faced. For one thing, we generally must make decisions about many goods, not just a single one like ice cream. Another complication is that the cost of consuming additional units of each good will rarely be zero. To see how to proceed in more complex cases, let's suppose Sarah must decide how to spend a fixed sum of money on two different goods, each with a positive price. Should she spend all of it on one of the goods or part of it on each? The law of diminishing marginal utility suggests that spending it all on a single good isn't a good strategy. Rather than devote more and more money to the purchase of a good we already consume in large quantities (and whose marginal utility is therefore relatively low), we generally do better to spend that money on other goods we don't have much of, whose marginal utility will likely be higher. The simplest way to illustrate how economists think about the spending decisions of a utility-maximizing consumer is to work through a series of examples, beginning with the following.

Our task in this chapter will be to explore the demand side of the market in greater depth than was possible in Chapter 3, Supply and Demand. There we merely asked you to accept as an intuitively plausible claim that the quantity demanded of a good or service declines as its price rises. This relationship is known as the law of demand, and we'll see how it emerges as a simple consequence of the assumption that people spend their limited incomes in rational ways. In the process, we'll see more clearly the dual roles of income and substitution as factors that account for the law of demand. We'll also see how to generate market demand curves by adding the demand curves for individual buyers horizontally. Finally, we'll see how to use the demand curve to generate a measure of the total benefit that buyers reap from their participation in a market. THE LAW OF DEMAND With our discussion of the free ice cream offer in mind, let us restate the law of demand as follows: Law of Demand

People do less of what they want to do as the cost of doing it rises. Cost-Benefit By stating the law of demand this way, we can see it as a direct consequence of the Cost-Benefit Principle, which says that an activity should be pursued if (and only if) its benefits are at least as great as its costs. Recall that we measure the benefit of an activity by the highest price we'd be willing to pay to pursue it—namely, our reservation price for the activity. When the cost of an activity rises, it's more likely to exceed our reservation price, and we're therefore less likely to pursue that activity. The law of demand applies to BMWs, cheap key rings, and "free" ice cream, not to mention manicures, medical care, and acid-free rain. It stresses that a "cost" is the sum of all the sacrifices—monetary and nonmonetary, implicit and explicit—we must make to engage in an activity.

Why does California experience chronic water shortages?

Some might respond that the state must serve the needs of a large population with a relatively low average annual rainfall. Yet other states, like New Mexico, have even less rainfall per person and do not experience water shortages nearly as often as California. California's problem exists because local governments sell water at extremely low prices, which encourages Californians to use water in ways Page 116that make no sense for a state with low rainfall. For instance, rice, which is well suited for conditions in high-rainfall states like South Carolina, requires extensive irrigation in California. But because California farmers can obtain water so cheaply, they plant and flood hundreds of thousands of acres of rice paddies each spring in the Central Valley. Two thousand tons of water are needed to produce one ton of rice, but many other grains can be produced with only half that amount. If the price of California water were higher, farmers would simply switch to other grains. Likewise, cheap water encourages homeowners in Los Angeles and San Diego to plant water-intensive lawns and shrubs, like the ones common in the East and Midwest. By contrast, residents of cities like Santa Fe, New Mexico, where water prices are high, choose native plantings that require little or no watering. Why do farmers grow water-intensive crops like rice in an arid state like California?

APPLYING THE RATIONAL SPENDING RULE The real payoff from learning the law of demand and the rational spending rule lies in using these abstract concepts to make sense of the world around you. To encourage you in your efforts to become an economic naturalist, we turn now to a sequence of Economic Naturalist examples in this vein.

Substitution at Work In the first of these examples, we focus on the role of substitution. When the price of a good or service goes up, rational consumers generally turn to less expensive substitutes. Can't meet the payments on a new car? Then buy a used one, or rent an apartment on a bus or subway line. French restaurants too pricey? Then go out for Chinese, or eat at home more often. National Football League tickets too high? Watch the game on television, or read a book. Can't afford a book? Check one out of the library, or download some reading matter from the Internet. Once you begin to see substitution at work, you'll be amazed by the number and richness of the examples that confront you every day.

In Figure 5A.13, note that the marginal rate of substitution at F is exactly the same as the absolute value of the slope of the budget constraint. This will always be so when the best affordable bundle occurs at a point of tangency. The condition that must be satisfied in such cases is therefore (5A.3) In the indifference curve framework, Equation 5A.3 is the counterpart to the rational spending rule developed in the main text of Chapter 5, Demand. The right-hand side of Equation 5A.3 represents the opportunity cost of chocolate in terms of vanilla. Thus, with PC = $5 per pint and PV = $10 per pint, the opportunity cost of an additional pint of chocolate is one-half pint of vanilla. The left-hand side of Equation 5A.3 is |ΔV/ΔC|, the absolute value of the slope of the indifference curve at the point of tangency. It is the amount of additional vanilla the consumer must be given in order to compensate her fully for the loss of one pint of chocolate. In the language of cost-benefit analysis discussed in Chapter 1, Thinking Like an Economist, the slope of the budget constraint represents the opportunity cost of chocolate in terms of vanilla, while the slope of the indifference curve represents the benefits of consuming chocolate as compared with consuming vanilla. Since the slope of the budget constraint is -1/2 in this example, the tangency condition tells us that one-half pint of vanilla would be required to compensate for the benefits given up with the loss of one pint of chocolate. If the consumer were at some bundle on the budget line for which the two slopes were not the same, then it would always be possible for her to purchase a better bundle. To see why, suppose she were at a point where the slope of the indifference curve (in absolute value) is less than the slope of the budget constraint, as at point E in Figure 5A.13. Suppose, for instance, that the MRS at E is only 1/4. This tells us that the consumer can be compensated for the loss of one pint of chocolate by being given an additional one-quarter pint of vanilla. But the slope of the budget constraint tells us that by giving up one pint of chocolate, he can purchase an additional one-half pint of vanilla. Since this is one-quarter pint more than he needs to remain equally satisfied, he will clearly be better off if he purchases more vanilla and less chocolate than at point E. The opportunity cost of an additional pint of vanilla is less than the benefit it confers.

Suppose that the marginal rate of substitution at point A in Figure 5A.13 is 1.0. Show that this means that the consumer will be better off if he purchases less vanilla and more chocolate than at A. The single exception to this statement involves the vertical intercept, (0, 10), which lies on both the original and the new budget constraints. 1The actual reduction would be slightly larger than 16 utils because her marginal utility of chocolate rises slightly as she consumes less of it. 2The actual increase will be slightly smaller than 24 utils because her marginal utility of vanilla falls slightly as she buys more of it. *Denotes more difficult problem.

In the main text of Chapter 5, Demand, we showed why the rational spending rule is a simple consequence of diminishing marginal utility. In this appendix, we introduce the concept of indifference curves to develop the same rule in another way. As before, we begin with the assumption that consumers enter the marketplace with well-defined preferences. Taking prices as given, their task is to allocate their incomes to best serve these preferences. There are two steps required to carry out this task. The first is to describe the various combinations of goods the consumer is able to buy. These combinations depend on her income level and on the prices of the goods she faces. The second step is to select from among the feasible combinations the particular one that she prefers to all others. This step will require some means of describing her preferences. We begin with the first step, a description of the set of possibilities.

THE BUDGET CONSTRAINT As before, we keep the discussion simple by focusing on a consumer who spends her entire income on only two goods: chocolate and vanilla ice cream. A bundle of goods is the term used to describe a particular combination of the two types of ice cream, measured in pints per year. Thus, in Figure 5A.1, one bundle (bundle A) might consist of five pints per year of chocolate and seven pints per year of vanilla, while another (bundle B) consists of three pints per year of chocolate and eight pints per year of vanilla. For brevity's sake, we may use the notation (5, 7) to denote bundle A and (3, 8) to denote bundle B. More generally, (C0, V0) will denote the bundle with C0 pints per year of chocolate and V0 pints per year of vanilla. By convention, the first number of the pair in any bundle represents the good measured along the horizontal axis.

(An Indifference Curve. An indifference curve, such as IC1, is a set of bundles that the consumer prefers equally. Any bundle, such as K, that lies above an indifference curve is preferred to any bundle on the indifference curve. Any bundle on the indifference curve, in turn, is preferred to any bundle, such as L, that lies below the indifference curve.) An indifference curve also permits us to compare the satisfaction implicit in bundles that lie along it with those that lie either above or below it. It permits us, for example, to compare bundle C (7, 3) to a bundle like K (12, 2), which has less vanilla and more chocolate than C has. We know that C is equally preferred to N (12, 1) because both bundles lie along the same indifference curve. K, in turn, is preferred to N because it has just as much chocolate as N and one pint per year more vanilla. So if K is preferred to N, and N is just as attractive as C, then K must be preferred to C. By analogous reasoning, we can say that bundle A is preferred to L. A and M are equivalent, and M is preferred to L since M has just as much chocolate as L and two pints per year more of vanilla. In general, bundles that lie above an indifference curve are all preferred to the bundles that lie on it. Similarly, those that lie on an indifference curve are all preferred to those that lie below it. We can represent a useful summary of the consumer's preferences with an indifference map, an example of which is shown in Figure 5A.9. This indifference map shows just four of the infinitely many indifference curves that, taken together, yield a complete description of the consumer's preferences. As we move to the northeast on an indifference map, successive indifference curves represent higher levels of satisfaction. If we want to know how a consumer ranks any given pair of bundles, we simply compare the indifference curves on which they lie. The indifference map shown tells us, for example, that Z is preferred to Y because Z lies on a higher indifference curve (IC3) than Y does (IC2). By the same token, Y is preferred to A, and A is preferred to X. (Part of an Indifference Map. The entire set of a consumer's indifference curves is called the consumer's indifference map. Bundles on any indifference curve are less preferred than bundles on a higher indifference curve and more preferred than bundles on a lower indifference curve. Thus, Z is preferred to Y, which is preferred to A, which is preferred to X.)

TRADE-OFFS BETWEEN GOODS An important property of a consumer's preferences is the rate at which she is willing to exchange, or "trade off," one good for another. This property is represented at any point on an indifference curve by the marginal rate of substitution (MRS), which is defined as the absolute value of the slope of the indifference curve at that point. In the left panel of Figure 5A.10, for example, the marginal rate of substitution at point T is given by the absolute value of the slope of the tangent to the indifference curve at T, which is the ratio ΔVT/ΔCT. (The notation ΔVT means "small change in vanilla from the amount at point T.") If we take ΔCT units of chocolate away from the consumer at point T, we have to give her ΔVT additional units of vanilla to make her just as well off as before. If the marginal rate of substitution at T is 1.5, that means that the consumer must be given 1.5 pints per year of vanilla in order to make up for the loss of 1 pint per year of chocolate. The Marginal Rate of Substitution. MRS at any point along an indifference curve is defined as the absolute value of the slope of the indifference curve at that point. It is the amount of vanilla the consumer is willing to give up to get another pint of chocolate. Whereas the slope of the budget constraint tells us the rate at which we can substitute vanilla for chocolate without changing total expenditure, the MRS tells us the rate at which we can substitute vanilla for chocolate without changing total satisfaction. Put another way, the slope of the budget constraint is the marginal cost of chocolate in terms of vanilla, while the MRS is the marginal benefit of chocolate in terms of vanilla. A common (but not universal) property of indifference curves is that the more a consumer has of one good, the more she must be given of that good before she will be willing to give up a unit of the other good. Stated differently, MRS generally declines as we move downward to the right along an indifference curve. Indifference curves that exhibit diminishing marginal rates of substitution are thus convex—or bowed outward—when viewed from the origin. The indifference curves shown in Figures 5A.8, 5A.9, and 5A.10 all have this property, as does the curve shown in Figure 5A.11. This property is the indifference curve analog of the concept of diminishing marginal utility discussed in the main text of Chapter 5, Demand. (FIGURE 5A.11 Diminishing Marginal Rate of Substitution. The more vanilla the consumer has, the more she is willing to give up to obtain an additional unit of chocolate. The marginal rates of substitution at bundles A, B, and C are 3, 1, and 1/5, respectively.) In Figure 5A.11, note that at bundle A, vanilla is relatively plentiful and the consumer would be willing to sacrifice three pints per year of it in order to obtain an additional pint of chocolate. Her MRS at A is 3. At B, the quantities of vanilla and chocolate are more balanced, and there she would be willing to give up only one pint per year to obtain an additional pint per year of chocolate. Her MRS at B is 1. Finally, note that vanilla is relatively scarce at C, where the consumer would need five additional pints per year of chocolate in return for giving up one pint per year of vanilla. Her MRS at C is 1/5. Intuitively, diminishing MRS means that consumers like variety. We are usually willing to give up goods we already have a lot of in order to obtain more of those goods we now have only little of.

Is Sarah maximizing her utility from consuming chocolate and vanilla ice cream? Sarah's total ice cream budget and the prices of the two flavors are the same as in the previous examples. If her marginal utility from consuming each type varies with the amounts consumed, as shown in Figure 5.5, and if she is currently buying 250 pints of vanilla and 75 pints of chocolate each year, is she maximizing her utility? As you can easily verify, the combination of 250 pints per year of vanilla and 75 pints per year of chocolate again costs a total of $400, exactly the amount of Sarah's ice cream budget. Her marginal utility from chocolate is now 20 utils per pint [Figure 5.5(b)], and since chocolate still costs $2 per pint, her spending on chocolate now yields additional utility at the rate of (20 utils/pint)/($2/pint) = 10 utils per dollar. Sarah's marginal utility for vanilla is now 10 utils per pint [Figure 5.5(a)], and since vanilla still costs $1 per pint, her last dollar spent on vanilla now also yields (10 utils/pint)/($1/pint) = 10 utils per dollar. So at her new rates of consumption of the two flavors, her spending yields precisely the same marginal utility per dollar for each flavor. Thus, if she spent a little less on chocolate and a little more on vanilla (or vice versa), her total utility would not change at all. For example, if she bought two more pints of vanilla (which would increase her utility by 20 utils) and one fewer pint of chocolate (which would reduce her utility by 20 utils), both her total expenditure on ice cream and her total utility would remain the same as before. When her marginal utility per dollar is the same for each flavor, it's impossible for Sarah to rearrange her spending to increase total utility. Therefore, 250 pints of vanilla and 75 pints of chocolate per year form the optimal combination of the two flavors. At her current consumption levels, marginal utility per dollar is exactly the same for each flavor.

TRANSLATING WANTS INTO DEMAND The Scarcity Principle challenges us to allocate our incomes among the various goods that are available so as to fulfill our desires to the greatest possible degree. The optimal combination of goods is the affordable combination that yields the highest total utility. For goods that are perfectly divisible, the rational spending rule tells us that the optimal combination is one for which the marginal utility per dollar is the same for each good. If this condition were not satisfied, the consumer could increase her utility by spending less on goods for which the marginal utility per dollar was lower and more on goods for which her marginal utility was higher.

THE BEST AFFORDABLE BUNDLE We now have all the tools we need to determine how the consumer should allocate her income between two goods. The indifference map tells us how the various bundles are ranked in order of preference. The budget constraint, in turn, tells us which bundles are affordable. The consumer's task is to put the two together and choose the most preferred affordable bundle. (Recall from Chapter 1, Thinking Like an Economist that we need not suppose that consumers think explicitly about budget constraints and indifference maps when deciding what to buy. It is sufficient that people make decisions as if they were thinking in these terms, just as experienced bicyclists ride as if they knew the relevant laws of physics.) For the sake of concreteness, we again consider the choice between vanilla and chocolate ice cream that confronts a consumer with an income of M = $100 per year facing prices of PV = $10 per pint and PC = $5 per pint. Figure 5A.13 shows this consumer's budget constraint and part of her indifference map. Of the five labeled bundles—A, D, E, F, and G—in the diagram, G is the most preferred because it lies on the highest indifference curve. G, however, is not affordable, nor is any other bundle that lies beyond the budget constraint. In general, the best affordable bundle will lie on the budget constraint, not inside it. (Any bundle inside the budget constraint would be less desirable than one just slightly to the northeast, which also would be affordable.)

The Best Affordable Bundle. The best the consumer can do is to choose the bundle on the budget constraint that lies on the highest attainable indifference curve. Here, that is bundle F, which lies at a tangency between the indifference curve and the budget constraint. Where, exactly, is the best affordable bundle located along the budget constraint? We know that it cannot be on an indifference curve that lies partly inside the budget constraint. On the indifference curve IC1, for example, the only points that are even candidates for the best affordable bundle are the two that lie on the budget constraint, namely A and E. But A cannot be the best affordable bundle because it is equally preferred to D, which in turn is less desirable than F. So A also must be less desirable than F. For the same reason, E cannot be the best affordable bundle. Since the best affordable bundle cannot lie on an indifference curve that lies partly inside the budget constraint, and since it must lie on the budget constraint itself, we know it has to lie on an indifference curve that intersects the budget constraint only once. In Figure 5A.13, that indifference curve is the one labeled IC2, and the best affordable bundle is F, which lies at the point of tangency between IC2 and the budget constraint. With an income of $100 per year and facing prices of $5 per pint for chocolate and $10 per pint of vanilla, the best this consumer can do is to buy 4 pints per year of vanilla and 12 pints per year of chocolate. The choice of bundle F makes perfect sense on intuitive grounds. The consumer's goal, after all, is to reach the highest indifference curve she can, given her budget constraint. Her strategy is to keep moving to higher and higher indifference curves until she reaches the highest one that is still affordable. For indifference maps for which a tangency point exists, as in Figure 5A.13, the best bundle will always lie at the point of tangency. (See Problem 6 for an example in which a tangency does not exist.)

Why are automobile engines smaller in England than in the United States? In England, the most popular model of BMW's 5-series car is the 516i, whereas in the United States it is the 530i. The engine in the 516i is almost 50 percent smaller than the engine in the 530i. Why this difference? In both countries, BMWs appeal to professionals with roughly similar incomes, so the difference cannot be explained by differences in purchasing power. Rather, it is the direct result of the heavy tax the British levy on gasoline. With tax, a gallon of gasoline sells for more than two times the price in the United States. This difference encourages the British to choose smaller, more fuel-efficient engines.

The Importance of Income Differences The most obvious difference between the rich and the poor is that the rich have higher incomes. To explain why the wealthy generally buy larger houses than the poor, we need not assume that the wealthy feel more strongly about housing than the poor. A much simpler explanation is that the total utility from housing, as with most other goods, increases with the amount that one consumes. Does the quantity of horsepower demanded depend on gasoline prices? As the next example illustrates, income influences the demand not only for housing and other goods, but also for quality of service

CONSUMER PREFERENCES For simplicity, we again begin by considering a world with only two goods, chocolate and vanilla ice cream, and assume that a particular consumer is able to rank different bundles of goods in terms of their desirability or order of preference. Suppose this consumer currently has bundle A in Figure 5A.6, which has six pints per year of chocolate and four pints per year of vanilla. If we then take one pint per year of chocolate away from her, she is left with bundle D, which has only five pints per year of chocolate and the same four pints per year of vanilla. Let us suppose that this consumer feels worse off than before, as most people would, because although D has just as much vanilla as A, it has less chocolate. We can undo the damage by giving her some additional vanilla. If our goal is to compensate for exactly her loss, how much extra vanilla do we need to give her? (Ranking Bundles. This consumer will prefer A to D because A has more chocolate than D and just as much vanilla. She is assumed to prefer bundle A to bundle E and to prefer bundle F to bundle A. This means there must be a bundle between E and F (shown here as B) that she likes equally well as A. This consumer is said to be indifferent between A and B. If she moves from A to B, her gain of two pints per year of vanilla exactly compensates for her loss of one pint per year of chocolate. She will prefer F to B because F has more vanilla than B and just as much chocolate. For the same reason, she will prefer B to E and E to D.) Suppose we start by giving her an additional half pint per year, which would move her to bundle E in Figure 5A.6. For some consumers, that might be enough to make up for the lost pint of chocolate, even though the total amount of ice cream at E (9.5 pints per year) is smaller than at A (10 pints per year). Indeed, consumers who really like vanilla might actually prefer E to A. But we'll assume that this particular consumer would still prefer A to E. So to compensate fully for her lost pint of chocolate, we would have to give her more than an additional half pint of vanilla. Suppose we gave her a lot more vanilla—say, an additional four pints per year. This would move her to bundle F in Figure 5A.6, and we'll assume that she regards the extra four pints per year of vanilla at F as more than enough to compensate for the lost pint of chocolate.

The fact that this particular consumer prefers F to A but prefers A to E tells us that the amount of extra vanilla needed to exactly compensate for the lost pint of chocolate must be between one-half pint per year (the amount of extra vanilla at E) and four pints per year (the amount of extra vanilla at F). Suppose, for the sake of discussion, that she would feel exactly compensated if we gave her an additional two pints of vanilla. This consumer would then be said to be indifferent between bundles A and B in Figure 5A.6. Alternatively, we could say that she likes the bundles A and B equally well, or that she regards these bundles as equivalent. Now suppose that we again start at bundle A and pose a different question: How many pints of vanilla would this consumer be willing to sacrifice in order to obtain an additional pint of chocolate? This time let's suppose that her answer is exactly one pint. We have thus identified another point—call it C—that is equally preferred to A. In Figure 5A.7, C is shown as the bundle (7, 3). C is also equally preferred to B (since C is equally preferred to A, which is equally preferred to B). (Equally Preferred Bundles. This consumer is assumed to be indifferent between the bundles A and C. In moving from A to C, her gain of one pint per year of chocolate exactly compensates for her loss of one pint per year of vanilla. And since she was indifferent between A and B, she also must be indifferent between B and C.) If we continue to generate additional bundles that the consumer likes equally well as bundle A, the end result is an indifference curve, a set of bundles all of which the consumer views as equivalent to the original bundle A, and hence also equivalent to one another. This set is shown as the curve labeled IC1 in Figure 5A.8. It is called an indifference curve because the consumer is indifferent among all the bundles that lie along it.

A bundle is a specific combination of goods. Bundle A has five units of chocolate and seven units of vanilla. Bundle B has three units of chocolate and eight units of vanilla. Note that the units on both axes are flows, which means physical quantities per unit of time—in this case, pints per year. Consumption is always measured as a flow. It is important to keep track of the time dimension because, without it, there would be no way to evaluate whether a given quantity of consumption was large or small. (Again, suppose all you know is that your consumption of vanilla ice cream is four pints. If that's how much you eat each hour, it's a lot. But if that's all you eat in a decade, it's not very much.) Suppose the consumer's income is M = $100 per year, all of which she spends on some combination of vanilla and chocolate. (Note that income is also a flow.) Suppose further that the prices of chocolate and vanilla are PC = $5 per pint and PV = $10 per pint, respectively. If she spent her entire income on chocolate, she could buy M/PC = ($100/year) ÷ ($5/pint) = 20 pints/year. That is to say, she could buy the bundle consisting of 20 pints per year of chocolate and 0 pints per year of vanilla, denoted (20, 0). Alternatively, suppose she spent her entire income on vanilla. She would then get the bundle consisting of M/PV = ($100/year) ÷ ($10/pint) = 10 pints per year of vanilla and 0 pints per year of chocolate, denoted (0, 10). In Figure 5A.2, these polar cases are labeled K and L, respectively. The consumer is also able to purchase any other bundle that lies along the straight line that joins points K and L. (Verify, for example, that the bundle (12, 4) lies on this same line.) This line is called the budget constraint, and is labeled B in the diagram.

The line B describes the set of all bundles the consumer can purchase for given values of income and prices. Its slope is the negative of the price of chocolate divided by the price of vanilla. In absolute value, this slope is the opportunity cost of an additional unit of chocolate: the number of pints of vanilla that must be sacrificed in order to purchase one additional pint of chocolate at market prices. Note that the slope of the budget constraint is its vertical intercept (the rise) divided by its horizontal intercept (the corresponding run): -(10 pints/year)(20 pints/years)= -1/2 The minus sign signifies that the budget line falls as it moves to the right—that it has a negative slope. More generally, if M denotes income and PC and PV denote the prices of chocolate and vanilla respectively, the horizontal and vertical intercepts will be given by (M/PC) and (M/PV), respectively. Thus, the general formula for the slope of the budget constraint is given by -(M/PV)/(M/PC) = -PC/PV, which is simply the negative of the price ratio of the two goods. Given their respective prices, it is the rate at which vanilla can be exchanged for chocolate. Thus, in Figure 5A.2, one pint of vanilla can be exchanged for two pints of chocolate. In the language of opportunity cost from Chapter 1, Thinking Like an Economist, we would say that the opportunity cost of an additional pint of chocolate is PC/PV = 1/2 pint of vanilla. In addition to being able to buy any of the bundles along her budget constraint, the consumer is also able to purchase any bundle that lies within Page 138the budget triangle bounded by it and the two axes. D is one such bundle in Figure 5A.2. Bundle D costs $65 per year, which is well below the consumer's ice cream budget of $100 per year. Bundles like E that lie outside the budget triangle are unaffordable. At a cost of $140 per year, E is simply beyond the consumer's reach.

Because marginal utility is the change in utility that occurs as we move from one quantity to another, when we graph marginal utility, we normally adopt the convention of plotting each specific marginal utility value halfway between the two quantities to which it corresponds. Thus, in Figure 5.2, we plot the marginal utility value of 40 utils per cone midway between one cone per hour and two cones per hour, and so on. (In this example, the marginal utility graph is a downward-sloping straight line for the region shown, but this need not always be the case.)

The more cones Sarah consumes each hour, the smaller her marginal utility will be. For Sarah, consumption of ice cream cones satisfies the law of diminishing marginal utility. The tendency for marginal utility to decline as consumption increases beyond some point is called the law of diminishing marginal utility. It holds not just for Sarah's consumption of ice cream in this illustration, but also for most other goods for most consumers. If we have one brownie or one Ferrari, we're happier than we are with none; if we have two, we'll be even happier—but not twice as happy—and so on. Though this pattern is called a law, there are exceptions. Indeed, some consumption activities even seem to exhibit increasing marginal utility. For example, an unfamiliar song may seem irritating the first time you hear it, but then gradually become more tolerable the next few times you hear it. Before long, you may discover that you like the song, and you may even find yourself singing it in the shower. Notwithstanding such exceptions, the law of diminishing marginal utility is a plausible characterization of the relationship between utility and consumption for many goods. Unless otherwise stated, we'll assume that it holds for the various goods we discuss.

Cost-Benefit

What will Sarah do when she gets to the front of the line? At that point, the opportunity cost of the time she spent waiting is a sunk cost and is hence irrelevant to her decision about how many cones to order. And since there is no monetary charge for the cones, the cost of ordering an additional one is zero. According to the Cost-Benefit Principle, Sarah should therefore continue to order cones as long as the marginal benefit (here, the marginal utility she gets from an additional cone) is greater than or equal to zero. As we can see from the entries in Table 5.2, marginal utility is positive up to and including the fifth cone but becomes negative after five cones. Thus, as noted earlier, Sarah should order five cones.

Is Sarah maximizing her utility from consuming chocolate and vanilla ice cream? Sarah's total ice cream budget and the prices of the two flavors are the same as in the earlier example. If her marginal utility from consuming each type varies with the amount consumed, as shown in Figure 5.4, and if she's currently buying 300 pints of vanilla and 50 pints of chocolate each year, is she maximizing her utility?

When Sarah increases her consumption of vanilla (a), her marginal utility of vanilla falls. Conversely, when she reduces her consumption of chocolate (b), her marginal utility of chocolate rises. Note first that the direction of Sarah's rearrangement of her spending makes sense in light of the original example, in which we saw that she was spending too much on chocolate and too little on vanilla. Spending $100 less on chocolate ice cream causes her marginal utility from that flavor to rise from 16 to 24 utils per pint [Figure 5.4(b)]. By the same token, spending $100 more on vanilla ice cream causes her marginal utility from that flavor to fall from 12 to 8 utils per pint [Figure 5.4(a)]. Both movements are a simple consequence of the law of diminishing marginal utility. Since chocolate still costs $2 per pint, her spending on chocolate now yields additional utility at the rate of (24 utils/pint)/($2/pint) = 12 utils per dollar. Similarly, since vanilla still costs $1 per pint, her spending on vanilla now yields additional utility at the rate of only (8 utils/pint)/($1/pint) = 8 utils per dollar. So at her new rates of consumption of the two flavors, her spending yields higher marginal utility per dollar for chocolate than for vanilla—precisely the opposite of the ordering we saw in the original example. Sarah has thus made too big an adjustment in her effort to remedy her original consumption imbalance. Starting from the new combination of flavors (300 pints per year of vanilla and 50 pints per year of chocolate), for example, if she then bought two fewer pints of vanilla (which would reduce her utility by about 16 utils) and used the $2 she saved to buy an additional pint of chocolate (which would boost her utility by about 24 utils), she would experience a net gain of about 8 utils. So, again, her current combination of the two flavors fails to maximize her total utility. This time, she is spending too little on chocolate and too much on vanilla. What is Sarah's optimal combination of the two flavors? In other words, among all the combinations of vanilla and chocolate ice cream that Sarah can afford, which one provides the maximum possible total utility? The following example illustrates the condition that this optimal combination must satisfy.

Why are waiting lines longer in poorer neighborhoods? As part of a recent promotional campaign, a Baskin-Robbins retailer offered free ice cream at two of its franchise stores. The first was located in a high-income neighborhood, the second in a low-income neighborhood. Why was the queue for free ice cream longer in the low-income neighborhood? Residents of both neighborhoods must decide whether to stand in line for free ice cream or go to some other store and avoid the line by paying the usual price. If we make the plausible assumption that people with higher incomes are more willing than others to pay to avoid standing in line, we should expect to see shorter lines in the high-income neighborhood.

Why are lines longer in low-income neighborhoods? Similar reasoning helps explain why lines are shorter in grocery stores that cater to high-income consumers. Keeping lines short at any grocery store means hiring more clerks, which means charging higher prices. High-income consumers are more likely than others to be willing to pay for shorter lines. RECAP THE RATIONAL SPENDING RULE Application of the rational spending rule highlights the important roles of income and substitution in explaining differences in consumption patterns—among individuals, among communities, and across time. The rule also highlights the fact that real, as opposed to nominal, prices and income are what matter. The demand for a good falls when the real price of a substitute falls or the real price of a complement rises.