To Buy or Not To Buy
5. Marginal utility & the law of diminishing marginal utility

With the water-diamond paradox on the run, we can delve into the demand side of market life. Why does the demand curve slope downwards? Why do people buy what they buy? Why does Maria buy three gallons of gas, why does Bayla buy a box of chocolates as a gift for her mother, Rodney a diamond for his ear, Paul a ton of soybeans for his firm? And, come to think of it, why are they not buying more---or less?

You can answer such "why" questions in various ways, all of them acceptable for what they want to accomplish. A psychologist might focus on Maria's psyche to figure out why she is not filling up her whole tank with gasoline, or why she refuses to pedal her bicycle to Pilsen instead of driving. A sociologist might speak of the status value of driving a car versus riding a bike.

Without denying that many questions are best answered in other ways, an economist takes a more "behavioral" and price-oriented approach. An economist talks in fact as though she were looking simply at the behavior of the demanders from the outside, with no knowledge of what's going on inside their minds. That's why it's called "behavioral," in honor of a once-popular psychological theory called "behaviorism." Behaviorism said that psychologists should look only at how peoples and rats actually behave, not inquire into their mental states. The economist following behaviorism simply asks how the demanders respond to the stimulus of market prices, as though the demanders were analogous to mice in a soda-drinking experiment. In other words, the economist uses an experimental metaphor to talk about the quantity demanded: "What would happen if Maria were faced with a price of as much as $15 for a gallon of gasoline. $3.05? What if only 50 cents?"

Understand, economists won't necessarily do the literal experiment before they talk about demand curves; often they rely on "thought experiments."

Bayla: But are thought experiments scientific? They sound pretty subjective to me.

McCloskey: Yes, they most certainly are scientific. Every science, from physics to history, uses them. They are not a perfect substitute for empirical research, but they can help to solve certain kinds of empirical problems. The most famous examples are Einstein's various theories. Einstein was not an experimenter. But he was a thought-experimenter. By thinking through, say, what would theoretically happen to light as it passed by our Sun on the way to our eyes he completely changed physics.

The thought experiment about Maria and her gasoline clearly has two sides, her subjective feelings about the gasoline (and its use value for her driving to Pilsen) on the one hand and her objective constraints on the other. Remember the discussion in Chapter 2 of choice and constraints. Maria would like to buy gasoline, but also two other things: dinner and a get-well card for Alan. Those are her feelings - the subjective side of her choice. But she is constrained by her budget and the costs of the things she wants, as we said in Chapter 2.

Why does Maria want to buy X-number of gallons of gasoline, while Alan would prefer to use the money to buy part of a concert ticket? Why did you want a course in economics above a course in physics or dance? Maria demonstrates by her choices what things give her satisfaction, or happiness, or, in Jevons's terminology, "utility." By buying gasoline Maria adds to her total utility. The neoclassical theory of demand supposes that people buy gasoline, or any other commodity, because they add to their total utility.

Utility is the pleasure or satisfaction that consuming or doing something provides.

That seems obvious. What's the big deal?

The big deal comes with the notion of marginal utility where marginal here does not mean "minor" or "beside the point," but its literal Latin meaning of "additional" or "extra."

Marginal utility is the last unit of total utility received, the extra utility from an extra unit of the product.

The notion is simple. Consider the situation of Maria at the gasoline station buying three gallons of gasoline. Buying the first gallon adds a lot to her total utility. It gets her to Midway Airport tonight for work on time. If she didn't buy even this one gallon she'd be out of gasoline in a couple of miles, and therefore out of a job. True, she'll want to buy another, second gallon tomorrow if she only buys one now. But the one gallon is obviously an improvement over an empty tank. The second gallon is a convenience, worth less in utility than the first gallon, but still worth a lot. It means she won't have to worry about gasoline for a couple of days. The third gallon makes her still less worried about accidentally running out - a convenience, but not as much of a convenience as the second gallon.

And so on. Each additional gallon up to the capacity of the tank is an additional convenience, but it is very reasonable to suppose, as economists do, that the marginal (that is, extra) convenience gets lower and lower. This insight has proven to be a critical ingredient in the neoclassical theory of demand. It's named the Law of Diminishing Marginal Utility.

The Law of Diminishing Marginal Utility: As a consumer buys additional units of some good the marginal utility of the last unit will eventually go down.

Concept Check 2: The classic examples of marginal utility getting lower and lower are foods. Argue the case for eating successive numbers of donuts, one at a time. Take the argument to extremes. (Check answer at the end of the chapter).

A wild and crazy example of the Law of Diminishing Marginal Utility is given in The Guinness Book of World Records. Tom Nall once held the world record in tortilla-eating - 74 tortillas at a sitting in Marciano's Mexican Restaurant in Dallas on October 16, 1973. As he ate the 74th tortilla Tom probably said to himself "Man, this doesn't taste anywhere near as good as the first." Even the champion devourer of tortillas feels diminishing marginal utility for tortillas. So does everyone, for nearly everything.

The Law applies to most things: gasoline, cokes, tortillas, shelter (the 21st room in the Hollywood mansion is not as valuable as the earlier ones), clothing (the 3000th pair of shoes does not give Sarah Jessica Parker as much pleasure as her first, or even her 50th), and so forth. And yes, the Law of Diminishing Marginal Utility even applies to Homer J. Simpson and his tasty donuts. "Mmmm. . . enough donuts."

The next step in the argument takes us from Maria's marginal utility to the price she would want to pay for any amount of gasoline. Think of the price as an opportunity cost - the utility of the other goods Maria could have bought with the cash she spent. Suppose Maria pays $4.00 for the four gallons of gasoline (for sake of easy arithmetical computation, we're going to assume from now on the bargain basement price of gasoline to be $1.00 a gallon!). She forsakes the utility of $4.00 worth of ice cream, compact disks, or whatever other desirable things she would have bought buy for the money has she not spent it on gasoline.

When Maria has no gasoline at all she values the first gallon at quite a lot, say **CHECK WITH LATER DIAGRAM $10.00. We're talking now about value in use. That is, if she could only buy one gallon, and there was only one place to buy it, and the one place charged $10.00, she would be just willing to enter the deal. A cent more and she rides her bike or takes the subway. She would be willing if she had to forsake the utility of other things worth $10 in total for that first gallon. Now of course she doesn't have to pay $10, her value in use. She only has to pay $1.00, the value in exchange - that is, the going price at the pump. Take it now, in your mind's gasoline tank, to the extreme. If she had 100 gallons of gasoline (don't ask how she would store it), another gallon would have a very, very low marginal utility to her.

The money-valued satisfaction, the value in use, that an extra gallon of gasoline provides is called "the marginal utility in dollars" of the gasoline. To repeat: it is the dollar value of an extra gallon of gasoline to Maria. It is subjective, internal to Maria's head. Calling it "Maria's" is not merely a cutesy label. It really is not the same for Maria as it is for, say, her friend Alan. It is personal and in the short run it is stable, what each person values the gasoline at. In a phrase, it is the marginal value in use.

Notice that marginal utility is not an unchanging amount. This is crucial to grasp. Marginal utility is not a constant number, like 3.14159 or $3.00. It is a "schedule" of numbers, as economists sometimes put, or as mathematicians out it a "function" of the amount of gasoline Maria in fact buys. Marginal utility goes down as the consumer acquires more and more of the good in question. In other words, the amount of marginal utility of gasoline depends on how many gallons of gasoline Maria already has. It falls with more gallons. As Maria gets more gasoline, the extra utility she gains out of another gallon of it goes down. So she is less and less willing to forsake other goods. As Maria gets more gasoline her willingness to pay for an additional (or "marginal") gallon gets lower. It's shown in Table 5.1.

Table 5.1 Diminishing marginal utility and willingness to pay

When Maria has already purchased this many gallons of gasoline She'll be willing to pay this much for one more gallon
0 $10.00 for the first gallon
1 $5.00 for the second gallon
2 $1.00 for the third gallon
3 $0.90 for the fourth gallon
4 $0.80 for the fifth gallon
5 $0.60 for the sixth gallon
6 $0.5 for the seventh gallon
... 10,000 $0.0001 for the 10,001st gallon
Figure 5.3 Maria's diminishing marginal utility of gasoline

The graph translates Table 5.1 into numbers. The vertical axis indicates how many dollars Maria is willing to give up to acquire each extra gallon of gasoline. The curve tells you that she is willing to give up $5.00 (the number on the vertical axis) to acquire an additional gallon when she already has one gallon (the number on the horizontal axis).

The Table exhibits the Law of Diminishing Marginal Utility. For each additional gallon Maria is willing to sacrifice less money, indicating that in each step the marginal utility goes down. You can see this trend even better when you plot the numbers from the table in a graph. Figure 5.3 shows this result.

Exceptions to the Law of Diminishing Marginal utility are few. Crack, the cheap derivative of cocaine, is one example. Having never smoked crack, you are, like the authors, likely to put a zero or even negative value on "a little bit more." But once someone starts using the stuff, he or she, if addicted, would be willing to steal to get the money to get a little more. (If you find yourself dreaming about it, we recommend you watch a film called "MacArthur Park," starring Thomas Jefferson Byrd. It will kill your fantasy---and save you.) The problem with addictive drugs is that marginal utility rises instead of falling with more use. So you can't get enough. (Contrast the tortilla-eating contest: it's difficult to imagine anyone so addicted to tortillas that the seventy-sixth one at a sitting would be tastier than the first.)

Cigarettes, also addictive, are a more common example of an exception to the law of diminishing marginal utility. Controlled experiments show that the amount of nicotine that cigarette smokers need per day varies from person to person---marginal utility is the same amount for everyone. But the fact of the addiction does not vary. Smokers in laboratory experiments tied up to an intravenous drip will stop smoking as soon as they have been given without their knowing it their daily fix of nicotine. The addiction means that until you reach your daily nicotine fix the marginal utility of another smoke is higher for each additional cigarette. After the daily fix the marginal utility drops to zero. Sets and collections are another minor exception. If I have an almost complete set of baseball cards of the 1952 Dodgers, for example, I am willing to pay a lot of money to complete it. The last card is worth more to me than the first one I bought. But even the exceptions do not violate the Law of Diminishing Marginal Utility entirely. The Law would still hold for additional sets of the 1952 Dodgers. If I had two sets the second one would be less valuable to me than the first.

These examples make the earlier point sharply: "Utility" in modern economics is not a matter of ethical good. It is merely a matter of wanting. The Law of Diminishing Marginal Utility is that the wanting rarely goes up as you get more. Come to think of it, even a crack addict can use only so much of the stuff before they pass out or die. The Law holds, with minor amendments, essentially everywhere.

The Law sounds deeply psychological, and in a way it is. It fits how we feel about most things. That's what the thought experiment is about. But you can believe it for external reasons, too. For one thing, it works in actual experiments with people and with rats.

For another---and this is an economic argument, not a psychological one---it follows logically from the very idea of thoughtful choice. The first thing chosen will of course be the most valuable. If the person choosing is being thoughtful she will choose the most valuable first, of course. It would be silly to choose the least desirable first. The next thing chosen will be less valuable. The last will be least valuable. And that's the Law of Diminishing Marginal Utility.

Ranked projects lead to diminishing marginal utility
Think of all the investment projects available to a society - opening a bagel store, say, or replacing the giant Ferris Wheel near Piccadilly Circus or building a swimming pool for the idle rich or repairing the Picasso sculpture at Daley Plaza. Each project has a net profit attached to it, which can be expressed as the return per dollar of investment. What would a well functioning society do if there were very few resources for investment? Obviously, it would do only the most valuable projects, that is, the ones with the highest return per dollar of investment. As the amount of resources for investment increased it would undertake more projects, going further down what amounts to the curve of the "social marginal utility of projects." The society has a marginal utility curve for projects, like Maria's marginal utility curve for gasoline.

Your mother gives you money "for a mini-refrigerator." She does not want you to use it to buy CDs. Can she stop you from using the money for CDs? Not really, even if she checks your apartment for a refrigerator. She ranks the desires as "refrigerator then CDs." You rank them the other way around. You buy the refrigerator, sure, but since you now have more money in total her gift actually makes it possible to buy more CDs - if you were going to buy some sort of refrigerator anyway. The point is that the gift of money loosens your budget constraint. You then decide how far down the list of desires-CDs, refrigerator, hanging plants, etc.-you want to go. Mom doesn't.

Speaking economics: "Utilitarianism"
The word utility means "usefulness." To economists, revealingly, it has come to mean all of happiness. It entered the conversation of economics a little before the time of Adam Smith's discussion of markets. Smith good friend David Hume used it, for example. "Utility" became especially prominent in the writings of an English philosopher named Jeremy Bentham (1748-1832). Bentham was an astonishing man. By age five he read Latin and French, played the violin, and read lengthy books on history. He went to college when he was 13, graduating at 15. He invented the design of modern prisons, with their central lookout towers. He proposed the Suez and Panama canals decades before the projects were taken seriously. And he specified in his will that his body be dissected in the presence of his friends and his skeleton be kept in a box in University College, London. To this day the skeleton, fully dressed, is displayed in a glass case in the administration building of the College. They put a wax head on his body.

Trained as a lawyer, Bentham came to detest the usual law of England, built up over centuries case by case. He wanted to replace it with a "rational" system, designed anew, which at age 41 he presented to the world in his Principles of Morals and Legislation (1789). The word "utility" in his thinking meant the utility of all members of the whole society taken together: "An action may be said to [conform] to the principle of utility . . . when the tendency it has to augment the happiness of the community is greater than any it has to diminish it" (Vol. 1, p. iii). On this he erected what he himself called "a new religion" - utilitarianism - which dominated social thinking in Europe for a century and more. Utilitarian philosophers such as Bentham did a lot for the expansion of liberty and justice. For example, the University College-London, which Bentham helped found, was the first university in England to admit students regardless of creed, race, gender, or nationality.

The main dogma of utilitarianism is simple. Maria gets a certain amount of happiness from buying three gallons of gasoline, her total value in use from the purchases. If the buying does not diminish someone else's happiness more than hers is increased, then allowing her to buy the two gallons is a good idea for society. In such a way the society will achieve "the greatest happiness of the greatest number."

For society as a whole, however, utilitarianism has serious, even fatal, logical difficulties. The difficulty is to know how to weigh Maria's utility together with Paul's. In dollars it looks easy. But Maria might value the dollars more than does Paul - she might for instance get more joy from living than he does; or she might be poorer, and therefore value each dollar more. So adding up my utility and thine doesn't make a lot of sense.

Yet willingness to pay is still used by economists to decide social issues by "cost-benefit analysis." A road generating $5,000,000 of value in use should not be built if its opportunity cost is $6,000,000. Though the technique produces useful numbers, it is deeply controversial if used as the only guide. As the conservative economist Henry Simon said in 1938, the utility of two different people added together is "something which no one has ever known, or will ever know, anything about."

Concept Check 3: The World Bank in Washington makes loans to poor countries. But naturally it doesn't want the countries to use the money "for" useless, low marginal-utility projects. So it has a rule saying that the loan can be used only for high marginal-utility projects. Question: Do you imagine the rule works? That is, does it prevent countries from engaging in low value projects? (Compare the case to your mother and the money "for" a refrigerator.)