Consumer Surplus and the Demand Curve

The market in used textbooks is a big business in terms of dollars and cents—several billion dollars each year. More importantly for us, it is a convenient starting point for developing the concepts of consumer and producer surplus. We’ll use the concepts of consumer and producer surplus to understand exactly how buyers and sellers benefit from a competitive market and how big those benefits are. In addition, these concepts play important roles in analyzing what happens when competitive markets don’t work well or there is interference in the market.

So let’s begin by looking at the market for used textbooks, starting with the buyers. The key point, as we’ll see in a minute, is that the demand curve is derived from their tastes or preferences—and that those same preferences also determine how much they gain from the opportunity to buy used books.

Willingness to Pay and the Demand Curve

A used book is not as good as a new book—it will be battered and coffee-stained, may include someone else’s highlighting, and may not be completely up to date. How much this bothers you depends on your preferences. Some potential buyers would prefer to buy the used book even if it is only slightly cheaper than a new one; others would buy the used book only if it is considerably cheaper.

A consumer’s willingness to pay for a good is the maximum price at which he or she would buy that good.

Let’s define a potential buyer’s willingness to pay as the maximum price at which he or she would buy a good, in this case a used textbook. An individual won’t buy the good if it costs more than this amount but is eager to do so if it costs less. If the price is just equal to an individual’s willingness to pay, he or she is indifferent between buying and not buying. For the sake of simplicity, we’ll assume that the individual buys the good in this case.

The table in Figure 4-1 shows five potential buyers of a used book that costs $100 new, listed in order of their willingness to pay. At one extreme is Aleisha, who will buy a second-hand book even if the price is as high as $59. Brad is less willing to have a used book and will buy one only if the price is $45 or less. Claudia is willing to pay only $35 and Darren, only $25. And Edwina, who really doesn’t like the idea of a used book, will buy one only if it costs no more than $10.

The Demand Curve for Used Textbooks With only five potential consumers in this market, the demand curve is step-shaped. Each step represents one consumer, and its height indicates that consumer’s willingness to pay—the maximum price at which he or she will buy a used textbook—as indicated in the table. Aleisha has the highest willingness to pay at $59, Brad has the next highest at $45, and so on down to Edwina with the lowest willingness to pay at $10. At a price of $59, the quantity demanded is one (Aleisha); at a price of $45, the quantity demanded is two (Aleisha and Brad); and so on until you reach a price of $10, at which all five students are willing to purchase a used textbook.

How many of these five students will actually buy a used book? It depends on the price. If the price of a used book is $55, only Aleisha buys one; if the price is $40, Aleisha and Brad both buy used books, and so on. So the information in the table can be used to construct the demand schedule for used textbooks.

As we saw in Chapter 3, we can use this demand schedule to derive the market demand curve shown in Figure 4-1. Because we are considering only a small number of consumers, this curve doesn’t look like the smooth demand curves of Chapter 3, where markets contained hundreds or thousands of consumers. Instead, this demand curve is step-shaped, with alternating horizontal and vertical segments. Each horizontal segment—each step—corresponds to one potential buyer’s willingness to pay.

However, we’ll see shortly that for the analysis of consumer surplus it doesn’t matter whether the demand curve is step-shaped, as in this figure, or whether there are many consumers, making the curve smooth.

Willingness to Pay and Consumer Surplus

Suppose that the campus bookstore makes used textbooks available at a price of $30. In that case Aleisha, Brad, and Claudia will buy books. Do they gain from their purchases, and if so, how much?

The answer, shown in Table 4-1, is that each student who purchases a book does achieve a net gain but that the amount of the gain differs among students.

Potential buyer

Willingness to pay

Price paid

Individual consumer surplus = Willingness to pay – Price paid

Aleisha

$59

$30

$29

Brad

  45

  30

  15

Claudia

  35

  30

    5

Darren

 25

   –

   –

Edwina

 10

   –

   –

All buyers

Total consumer surplus = $49

Table : TABLE 4-1 Consumer Surplus If Price of Used Textbook = $30

Aleisha would have been willing to pay $59, so her net gain is $59 − $30 = $29. Brad would have been willing to pay $45, so his net gain is $45 − $30 = $15. Claudia would have been willing to pay $35, so her net gain is $35 − $30 = $5. Darren and Edwina, however, won’t be willing to buy a used book at a price of $30, so they neither gain nor lose.

Individual consumer surplus is the net gain to an individual buyer from the purchase of a good. It is equal to the difference between the buyer’s willingness to pay and the price paid.

The net gain that a buyer achieves from the purchase of a good is called that buyer’s individual consumer surplus. What we learn from this example is that whenever a buyer pays a price less than his or her willingness to pay, the buyer achieves some individual consumer surplus.

Total consumer surplus is the sum of the individual consumer surpluses of all the buyers of a good in a market.

The sum of the individual consumer surpluses achieved by all the buyers of a good is known as the total consumer surplus achieved in the market. In Table 4-1, the total consumer surplus is the sum of the individual consumer surpluses achieved by Aleisha, Brad, and Claudia: $29 + $15 + $5 = $49.

The term consumer surplus is often used to refer both to individual and to total consumer surplus.

Economists often use the term consumer surplus to refer to both individual and total consumer surplus. We will follow this practice; it will always be clear in context whether we are referring to the consumer surplus achieved by an individual or by all buyers.

Total consumer surplus can be represented graphically. Figure 4-2 reproduces the demand curve from Figure 4-1. Each step in that demand curve is one book wide and represents one consumer. For example, the height of Aleisha’s step is $59, her willingness to pay. This step forms the top of a rectangle, with $30—the price she actually pays for a book—forming the bottom. The area of Aleisha’s rectangle, ($59 − $30) × 1 = $29, is her consumer surplus from purchasing one book at $30. So the individual consumer surplus Aleisha gains is the area of the dark blue rectangle shown in Figure 4-2.

Consumer Surplus in the Used-Textbook Market At a price of $30, Aleisha, Brad, and Claudia each buy a book but Darren and Edwina do not. Aleisha, Brad, and Claudia receive individual consumer surpluses equal to the difference between their willingness to pay and the price, illustrated by the areas of the shaded rectangles. Both Darren and Edwina have a willingness to pay less than $30, so they are unwilling to buy a book in this market; they receive zero consumer surplus. The total consumer surplus is given by the entire shaded area—the sum of the individual consumer surpluses of Aleisha, Brad, and Claudia—equal to $29 + $15 + $5 = $49.

In addition to Aleisha, Brad and Claudia will also each buy a book when the price is $30. Like Aleisha, they benefit from their purchases, though not as much, because they each have a lower willingness to pay. Figure 4-2 also shows the consumer surplus gained by Brad and Claudia; again, this can be measured by the areas of the appropriate rectangles. Darren and Edwina, because they do not buy books at a price of $30, receive no consumer surplus.

The total consumer surplus achieved in this market is just the sum of the individual consumer surpluses received by Aleisha, Brad, and Claudia. So total consumer surplus is equal to the combined area of the three rectangles—the entire shaded area in Figure 4-2. Another way to say this is that total consumer surplus is equal to the area below the demand curve but above the price.

Figure 4-2 illustrates the following general principle: The total consumer surplus generated by purchases of a good at a given price is equal to the area below the demand curve but above that price. The same principle applies regardless of the number of consumers.

When we consider large markets, this graphical representation of consumer surplus becomes extremely helpful. Consider, for example, the sales of iPads to millions of potential buyers. Each potential buyer has a maximum price that he or she is willing to pay. With so many potential buyers, the demand curve will be smooth, like the one shown in Figure 4-3.

Consumer Surplus The demand curve for iPads is smooth because there are many potential buyers. At a price of $500, 1 million iPads are demanded. The consumer surplus at this price is equal to the shaded area: the area below the demand curve but above the price. This is the total net gain to consumers generated from buying and consuming iPads when the price is $500.

Suppose that at a price of $500, a total of 1 million iPads are purchased. How much do consumers gain from being able to buy those 1 million iPads? We could answer that question by calculating the individual consumer surplus of each buyer and then adding these numbers up to arrive at a total. But it is much easier just to look at Figure 4-3 and use the fact that total consumer surplus is equal to the shaded area. As in our original example, consumer surplus is equal to the area below the demand curve but above the price. (To refresh your memory on how to calculate the area of a right triangle, see the appendix to Chapter 2.)

How Changing Prices Affect Consumer Surplus

It is often important to know how much consumer surplus changes when the price changes. For example, we may want to know how much consumers are hurt if a flood in cotton-growing areas of Pakistan drives up cotton prices or how much consumers gain if the introduction of fish farming makes salmon steaks less expensive. The same approach we have used to derive consumer surplus can be used to answer questions about how changes in prices affect consumers.

Let’s return to the example of the market for used textbooks. Suppose that the bookstore decided to sell used textbooks for $20 instead of $30. How much would this fall in price increase consumer surplus?

The answer is illustrated in Figure 4-4. As shown in the figure, there are two parts to the increase in consumer surplus. The first part, shaded dark blue, is the gain of those who would have bought books even at the higher price of $30. Each of the students who would have bought books at $30—Aleisha, Brad, and Claudia—now pays $10 less, and therefore each gains $10 in consumer surplus from the fall in price to $20. So the dark blue area represents the $10 × 3 = $30 increase in consumer surplus to those three buyers.

Consumer Surplus and a Fall in the Price of Used Textbooks There are two parts to the increase in consumer surplus generated by a fall in price from $30 to $20. The first is given by the dark blue rectangle: each person who would have bought at the original price of $30—Aleisha, Brad, and Claudia—receives an increase in consumer surplus equal to the total reduction in price, $10. So the area of the dark blue rectangle corresponds to an amount equal to 3 × $10 = $30. The second part is given by the light blue area: the increase in consumer surplus for those who would not have bought at the original price of $30 but who buy at the new price of $20—namely, Darren. Darren’s willingness to pay is $25, so he now receives consumer surplus of $5. The total increase in consumer surplus is (3 × $10) + $5 = $35, represented by the sum of the shaded areas. Likewise, a rise in price from $20 to $30 would decrease consumer surplus by $35, the amount corresponding to the sum of the shaded areas.

The second part, shaded light blue, is the gain to those who would not have bought a book at $30 but are willing to pay more than $20. In this case that gain goes to Darren, who would not have bought a book at $30 but does buy one at $20. He gains $5—the difference between his willingness to pay of $25 and the new price of $20. So the light blue area represents a further $5 gain in consumer surplus.

The total increase in consumer surplus is the sum of the shaded areas, $35. Likewise, a rise in price from $20 to $30 would decrease consumer surplus by an amount equal to the sum of the shaded areas.

Figure 4-4 illustrates that when the price of a good falls, the area under the demand curve but above the price—which we have seen is equal to total consumer surplus—increases. Figure 4-5 shows the same result for the case of a smooth demand curve, the demand for iPads. Here we assume that the price of iPads falls from $2,000 to $500, leading to an increase in the quantity demanded from 200,000 to 1 million units.

As in the used-textbook example, we divide the gain in consumer surplus into two parts. The dark blue rectangle in Figure 4-5 corresponds to the dark blue area in Figure 4-4: it is the gain to the 200,000 people who would have bought iPads even at the higher price of $2,000. As a result of the price reduction, each receives additional surplus of $1,500. The light blue triangle in Figure 4-5 corresponds to the light blue area in Figure 4-4: it is the gain to people who would not have bought the good at the higher price but are willing to do so at a price of $500. For example, the light blue triangle includes the gain to someone who would have been willing to pay $1,000 for an iPad and therefore gains $500 in consumer surplus when it is possible to buy an iPad for only $500.

A Fall in the Price Increases Consumer Surplus A fall in the price of an iPad from $2,000 to $500 leads to an increase in the quantity demanded and an increase in consumer surplus. The change in total consumer surplus is given by the sum of the shaded areas: the total area below the demand curve and between the old and new prices. Here, the dark blue area represents the increase in consumer surplus for the 200,000 consumers who would have bought an iPad at the original price of $2,000; they each receive an increase in consumer surplus of $1,500. The light blue area represents the increase in consumer surplus for those willing to buy at a price equal to or greater than $500 but less than $2,000. Similarly, a rise in the price of an iPad from $500 to $2,000 generates a decrease in consumer surplus equal to the sum of the two shaded areas.

As before, the total gain in consumer surplus is the sum of the shaded areas: the increase in the area under the demand curve but above the price.

What would happen if the price of a good were to rise instead of fall? We would do the same analysis in reverse. Suppose, for example, that for some reason the price of iPads rises from $500 to $2,000. This would lead to a fall in consumer surplus, equal to the sum of the shaded areas in Figure 4-5. This loss consists of two parts. The dark blue rectangle represents the loss to consumers who would still buy an iPad, even at a price of $2,000. The light blue triangle represents the loss to consumers who decide not to buy an iPad at the higher price.

FOR INQUIRING MINDS: A Matter of Life and Death

In 2013, more than 6,500 Americans died because of a shortage of organs for transplant. As of 2014, more than 122,000 were wait-listed. And as you can see from the accompanying figure, the gap between the number of available organs and the number of organs actually donated continues to grow each year. (The difference you see between the number of living donors and the number of actual transplants is accounted for by organs transplanted from deceased patients.)

Since the number of those who need an organ far exceeds availability, what is the best way to allocate the available organs? A market isn’t feasible. And for understandable reasons, the sale of human body parts is illegal in this country. So the task for establishing a protocol for these situations has fallen to the nonprofit group United Network for Organ Sharing (UNOS).

Kidney transplants, the most common type of organ transplant, were the focus of attention when UNOS decided to reformulate its protocol for allocating organs to transplant recipients. Under previous guidelines, a donated kidney would go to the person who had been waiting the longest. According to this system, an available kidney would go to a 75-year-old who has been waiting for 2 years instead of to a 25-year-old who has been waiting for 6 months, even though the 25-year-old is likely to live longer and benefit from the transplanted organ for a longer period of time.

To address this issue, in 2013 UNOS adopted a new set of guidelines based on a concept it calls “net survival benefit.” Kidneys are ranked according to how long they are likely to last; similarly, recipients are ranked according to how long they are likely to live once receiving a transplanted kidney. Then, under the new guidelines, a kidney is matched to the recipient expected to achieve the greatest survival time from that kidney. In other words, a kidney expected to last many decades will be allocated to a relatively younger person, while older recipients will receive kidneys expected to last a fewer number of years.

Organ Donors, Transplants, and Waitlist, 1989-2013
Source: Based on OPTN data as of January 3, 2014.

By matching the expected life span of a kidney to the expected life span of the recipient following the transplant, the new UNOS guideline tries to avert situations in which (1) a recipient outlives the transplanted kidney, requiring yet another transplant and reducing the number of kidneys available to others; or (2) a kidney significantly outlives its recipient, thereby wasting years of kidney function that could have benefited someone else.

So what does all this have to do with consumer surplus? As you may have guessed, the UNOS concept of “net survival benefit” is a lot like individual consumer surplus—the individual consumer surplus generated from getting a new kidney. In essence, UNOS has devised a system that allocates a kidney according to who gets the greatest individual consumer surplus. This way, the UNOS guidelines attempt to maximize the total consumer surplus from the available pool of kidneys. In terms of results, then, the kidney allocation system under the new UNOS guidelines operates a lot like a competitive market.

!worldview! ECONOMICS in Action: When Money Isn’t Enough

When Money Isn’t Enough

The key insight we get from the concept of consumer surplus is that purchases yield a net benefit to the consumer because the consumer typically pays a price less than his or her willingness to pay for the good. Another way to say this is that the right to buy a good at the going price is a valuable thing in itself.

For those who purchased WWII ration coupons illegally, the right to consumer surplus had a steep price.
Ray Moreton/Keystone/Getty Images

Most of the time we don’t think about the value associated with the right to buy a good. In a market economy we take it for granted that we can buy whatever we want, as long as we are willing to pay the market price.

But that hasn’t always been true. For example, during World War II the demands of wartime production created shortages of consumer goods when these goods were sold at prewar prices. Rather than allow prices to rise, government officials in many countries created a system of rationing. To buy sugar, meat, coffee, gasoline, and many other goods, you not only had to pay cash; you also had to present stamps or coupons from books issued to each family by the government. These pieces of paper, which represented the right to buy goods at the government-regulated price, quickly became valuable commodities in themselves.

As a result, illegal markets in meat stamps and gasoline coupons sprang into existence. Moreover, criminals began stealing coupons and even counterfeiting stamps.

The funny thing was that even if you had bought a gasoline coupon on the illegal market, you still had to pay to purchase gasoline. So what you were buying on the illegal market was not the good but the right to buy the good at the government-regulated price. That is, people who bought ration coupons on the illegal market were paying for the right to get some consumer surplus.

Quick Review

  • The demand curve for a good is determined by each potential consumer’s willingness to pay.

  • Individual consumer surplus is the net gain an individual consumer gets from buying a good.

  • The total consumer surplus in a given market is equal to the area below the market demand curve but above the price.

  • A fall in the price of a good increases consumer surplus through two channels: a gain to consumers who would have bought at the original price and a gain to consumers who are persuaded to buy by the lower price. A rise in the price of a good reduces consumer surplus in a similar fashion.

4-1

  1. Question 4.1

    Consider the market for cheese-stuffed jalapeno peppers. There are two consumers, Casey and Josey, and their willingness to pay for each pepper is given in the accompanying table. (Neither is willing to consume more than 4 peppers at any price.) Use the table (i) to construct the demand schedule for peppers for prices of $0.00, $0.10, and so on, up to $0.90, and (ii) to calculate the total consumer surplus when the price of a pepper is $0.40.

    Quantity of peppers

    Casey’s willingness to pay

    Josey’s willingness to pay

    1st pepper

    $0.90

    $0.80

    2nd pepper

      0.70

      0.60

    3rd pepper

      0.50

      0.40

    4th pepper

      0.30

      0.30

Solutions appear at back of book.