Nineteenth-century economists were fascinated by utilitarianism, a school of thought founded by Jeremy Bentham, an eccentric English philosopher.

Utilitarianism is the idea that the pleasure or pain from any activity respectively adds or detracts from a person’s utility, or satisfaction.

Utilitarians proposed numerous social reforms in hopes of achieving their central goal, the greatest happiness for the greatest number. Utilitarians assumed that individual pleasure can be measured and then summed, each person being weighted equally, to calculate aggregate social welfare.

 

Imagine that people were born with forehead gauges that recorded satisfaction in utils, an imaginary measurement, much as your electric meter measures kilowatts. Over lunch your gauge registers the following: 1 burger = 73 utils; 17 french fries = 31 utils; a small cola = 24 utils; and a net gain = 128 utils. Measuring the subjective value of national income would be a snap: simply sum everyone’s gains in total utility. A utilitarian goal would boil economic policy down to doing whatever was necessary to maximize the utility score.

 

The appealing goal of achieving the greatest happiness for the greatest number remains a basis for policies advocated by many politicians, but it raises some acute normative issues. The Russian author Fyodor Dostoyevski criticised utilitarians with his anguished question, “What if eternal happiness for the rest of humanity could be bought with the death by torture of an innocent babe?” Policies that unambiguously maximize social utility in an ethical manner could not be devised even if utilometers existed.

 

Utility analysis offers rich insights into human behavior. Although subjective gains from a dollar’s worth of goods may vary considerably among individuals, the following section shows how we can approximate the relative satisfactions from various goods to a given individual by looking at utility in monetary terms.

 

Modern economics rejects direct utility measures because (a) most of us cannot specify our preferences more precisely than by a rank order (first, second, and so on) of possible bundles of goods, and (b) satisfaction is not scientifically comparable between individuals. There is no way to ascertain exactly how much anyone likes candy (or anything else) relative to someone else’s enjoyment of candy. This led economists to develop indifference analysis, a more scientific technique explored at the end of the chapter.

Total and Marginal Utility

Suppose you enjoy quenching your thirst on hot days with fresh lemonade. If we measure utility in dollar terms, then the marginal utility of lemonade, MUL, is roughly the amount you would willingly pay for an extra lemonade. For example, after three sets of tennis on a 90° afternoon, suppose you stroll into your town’s only air-conditioned lemonade stand, where the server, an old friend, informs you that icy, fresh lemonade is now $1 per glass. Your throat parched, you decide that one glass is barely worth $1. As you finish it and rise to leave, the ade-tender offers you a break: a second lemonade for only $0.85. “All right,” you say, “just one more.” After gulping it down, you are already off your stool when the ade-tender asks, “How about another for $0.60?” Sitting back down, you put money on the counter. After your third lemonade, she asks, “How about a fourth at the old price of $0.50?” Somewhat befuddled, you nod your head. The four lemonades have cost you $2.95 ($1.00 + $0.85 + $0.60 + $0.50), and your total utility is shown in Panel A of Figure 1. Notice that total utility is rising as you drink these additional lemonades.

 

After the fourth glass, you are ready to face the heat, but the ade-tender offers you still another glass, this one for only $0.25. You cannot pass up the bargain. Then she invites you to have a sixth lemonade on the house. It is 90° in the shade, so you assent. Feeling a bit waterlogged, you turn down the offer of a seventh, even though it is free. “Tell you what,” she says, “will you drink it if I pay you $0.50?” Being an impoverished student, you agree. You also drink an eighth, for which you are paid $1. Ultimately, however, you approach your capacity. You agree to drink the ninth for the $3 she offers, but only if you can wait a half-hour. Since it’s now or never, you decide to pass. (You would drink the ninth for $25, but she will not offer that much.)

 

Marginal utilities from different goods reflect our subjective preferences.

Marginal utility (MU) is the gain in satisfaction derived through the consumption of one additional unit of a good.

Panel B of Figure 1 shows how the marginal utilities in dollars are related to your total satisfaction from lemonade (Panel A). The points on both curves are connected as if the server had offered these deals by sips rather than glassfuls. Study the relationship between total utility and marginal utility. The accumulated area under the marginal utility curve (note the expanded vertical axis) equals the height of the total utility curve. That is, total utility is the sum of the marginal utilities for each lemonade you drank.

The Law of Diminishing Marginal Utility

The declining marginal utility from lemonade as you drink more and more during a given time interval occurs with virtually all goods and all people. Observing that similar reactions were common, classical economists generalized this behavior into

The law of diminishing marginal utility: The marginal utility from consuming equal units of a good eventually declines as the amount consumed increases.

The word “eventually” is important. Horror movie fanciers might enjoy their first movie this week immensely and their second film even more. But they almost certainly will not enjoy their sixteenth movie of the week as much as their third. Benjamin Franklin’s observation in Poor Richard’s Almanac, “Fish and visitors stink in three days,” says far more about the diminishing marginal utility of visitors than about the deterioration of fish.

 

Maximizing Utility

We see that relative satisfactions from goods can be approximated by looking at utility in terms of money. We cannot scientifically ascertain whether one person gains more than someone else from an extra dollar of income or extra syrup on a waffle. We may be fairly sure, however, that the personal marginal utilities of each person from particular goods are roughly proportional to the goods’ prices, because people adjust their spending patterns whenever relative prices and marginal utilities are not in balance.

 

Suppose that you allocate $12 from your weekly budget for your favorite treat, ice cream. Table 1 lists your total and marginal utilities from macadamia nut crunch and chocolate ice cream cones. How many of each will you buy at $1 apiece to maximize your satisfaction? Eating five chocolate and seven crunch cones maximizes your total satisfaction at 46 utils per week. No other $12 combination yields more utility.

 

Let’s see how this purchasing pattern develops. Table 1 shows that your first macadamia nut cone generates 8 utils while your first chocolate cone yields only 5 utils. Thus, your first purchase will be a macadamia nut cone. What flavor would you buy second? Each cone is $1, and a second macadamia nut yields extra satisfaction of 7 utils. Your third choice will also be macadamia nut, which increases your satisfaction by 6 utils. Now, your fourth macadamia nut cone only yields 4 utils compared to 5 utils for your first chocolate cone. Thus, your fourth cone will be chocolate. You will ultimately spend the $12 on seven macadamia nut and five chocolate cones per week. Notice that the decision for each purchase hinges on the flavor with the greatest marginal utility per dollar spent.

Balancing Marginal Utilities

In the example shown in Table 1, your purchasing pattern suggested that you would look at the next cone, whether chocolate or macadamia nut, and determine which flavor provided you with the largest increase in utility.

The principle of equal marginal utilities per dollar: A consumer maximizes utility when the last dollar spent on any good generates the same satisfaction as the last dollar spent on every other good.

Your purchasing pattern becomes stable only when the last dollar spent on ice cream yields the same satisfaction as the last dollar spent on lemonade, clothes, books, or housing.

 

Satisfaction from the last spending on a good is calculated by dividing its marginal utility by its price. For example, if the last chocolate cone was $1 and its marginal utility was 1, then MUch/Pch = 1/1 = 1, and the marginal utility per dollar of the last cone was 1. Individuals are in equilibrium when

where a, b, ..., z are the various goods purchased. In our ice cream cone example, the marginal utilities per dollar equaled one for both macadamia nut crunch and chocolate cones. By equating marginal utilities per dollar, utility is maximized. No other allocation of resources will result in higher satisfaction. A little introspection should confirm that your own spending pattern conforms to this principle of equal marginal utilities per dollar.

 

A corollary of the principle of equal marginal utilities per dollar is that consumer equilibrium requires marginal benefits from every good to be proportional to their relative market prices. Market prices and the subjective demand prices discussed in Chapter 1 are different ways of viewing opportunity costs. Demand prices can be thought of as the ratios of the marginal utilities of various goods. Only if market prices do not exceed demand prices will you buy. In equilibrium, these subjective price ratios must equal the relative market prices for all the goods you choose to purchase. That is, MUa/MUb = Pa/Pb for any two goods we choose to label a and b, respectively.1 Focus 1 addresses the issue of whether economic assumptions about how people process information are reasonable.

Price Adjustments and Marginal Utility

Let’s use this format to describe how quantities demanded adjust as relative prices change. First, consider what would happen to your equilibrium purchases of ice cream cones (from Table 1) if a worldwide macadamia nut crop failure boosted the price of macadamia nut crunch to $2 per cone. Your utility schedules along with the new prices are shown in Table 2. You now buy only four macadamia nut crunch cones, and your consumption of chocolate cones drops to four per week. Marginal utilities per dollar now equal 2. Adjusting your spending pattern to various possible prices for macadamia nut ice cream traces out the demand curve shown in Figure 2.

 

To summarize, the higher-priced goods you buy uniformly generate more marginal utility than your lower-priced purchases: the more you pay for a good, the more it is worth to you at the margin. You are in equilibrium when the marginal utilities per dollar are equal for all goods. Ultimately, the last dollar you spend on any good yields the same satisfaction as the last dollar spent on any other good. Finally, if you choose not to spend all of your money, the satisfaction you gain from your saving or holding each dollar must equal the satisfaction you would gain from spending it on some other good.

Effects of Price Changes

You will buy less of any good that rises in price, substituting for it goods that decline in relative price. Another effect when the price of a good rises is that the purchasing power of your income shrinks. This drop in purchasing power reduces your total ability to buy consumer goods and services. How purchasing patterns respond when the prices of goods change can be decomposed into substitution effects and income effects.

• Substitution Effects  Substitution is the primary cause of negative slopes along demand curves.

The substitution effect is that portion of the change in quantity demanded due solely to a change in relative prices.2

Most goods have numerous possible uses. When the price of a good is reduced, it will be advantageous to devote the good to more of these uses.

 

For example, buses now provide low-priced transportation for many of us. Rides would be economical for far more people if fares were $0, and the homeless might sleep on warm buses instead of in cold alleys or under bridges. A $15 bus fare would induce most of us to walk, drive cars, or hire taxis. When ballpoint pens were introduced in the 1940s, they were refillable, cost about $25 each, and were a status symbol for busy executives. They now cost about a quarter, are used by almost everyone, and are discarded when the ink runs dry. Expensive ink pens are rare, and pencils are less commonly used than they would be if ballpoints still cost $25.

These examples suggest that we substitute some uses of some goods for similar uses of related goods as relative prices change. The critical point is that it is always advantageous to substitute away from goods that become relatively more costly and to expand uses for goods that become cheaper. Substitution effects are always negative and underpin the law of demand: quantity demanded falls as price increases, and vice versa.

 

The substitution effect is the change in purchasing patterns caused by changes in relative prices alone, artificially assuming constancy in total purchasing power. But rising prices, for example, will reduce the purchasing power of your income. We need to deal separately with how such changes in real income alter purchasing patterns.

• Income Effects  The purchasing power of your dollars falls if prices rise, but a dollar buys more consumer goods if prices fall.

Income effects are adjustments people make because the purchasing power of a given income is altered when prices change.

Suppose that a $400 tuition per semester hour absorbs so much of your budget that you initially take classes only part-time. If stellar performance elicited a 90% scholarship, you could afford everything you bought previously and might simply pocket the $360 per semester hour your scholarship now covers. Instead, you would probably enroll in more courses, in part because of substitution in response to this drop in the relative cost of tuition, but also because of the now greater purchasing power of your income. This income effect would allow enrollment in even more courses, or you might buy more books, a better calculator, nicer clothes, tastier food, or more frequent concert tickets.

 

The income effect may be negative, positive, or zero. All else being equal, when the price of a good rises, your purchasing power falls. For normal goods, the income effect is positive. For example, a decrease in the price of gasoline increases the purchasing power of your income. This alone results in higher levels of gas purchases. However, the income effect is negative for inferior goods such as lard, potatoes, lye soap, or black-eyed peas. For example, if your diet largely consists of potatoes because you are poor and they are cheap, your purchasing power increases if the price of potatoes falls and you can afford to buy tastier foods to secure your caloric needs. Even though you may buy more potatoes because of the substitution effect, the independent effect of your higher real income is to reduce potato consumption.

 

In summary, when prices fall, consumers substitute towards lower-priced goods and are able to buy more of all goods as their overall purchasing power grows. Falling prices generate these two benefits for consumers, but as we see next, market-set prices generate an additional benefit known as consumer surplus.