Consumers and Utility

One task for decentralized markets is to enable consumers to choose the goods and services that will give them the most satisfaction. Instead of "satisfaction" or "pleasure," we use the term utility. We say that consumers try to maximize utility.

When you go into an ice cream shop, what are you likely to order? One scoop of chocolate in a sugar cone? Two scoops of pistachio? Frozen yogurt in a cup? A large sundae?

As an economist, I cannot predict which choice you will make. But I'll bet you never walk up to the counter and say, "Give me ten gallons of every flavor you've got in the freezer." Why not?

You might say that you do not order all of that ice cream because you could not afford it. That may be true, and that is a reasonable answer. However, you might have enough money or credit to pay for gallons of ice cream. Even so, you would not buy that much. Eating ice cream obeys the law of diminishing returns. You do not spend more than a few dollars at a time on ice cream, because the additional ice cream is not worth as much to you as the first scoop or two.

Here is a numerical example that we can use to drive home this point, which is really nothing but common sense. Suppose that each scoop of ice cream costs one dollar, and that the total utility you get from the ice cream you consume at a single sitting obeys this pattern:

Number of ScoopsTotal Utility
(satisfaction, measured in \$)
Total Cost
1\$4.00\$1.00
2\$5.70\$2.00
3\$7.10\$3.00
4\$7.80\$4.00
5\$6.90\$5.00

Given these figures for satisfaction and cost, what is the optimal number of scoops of ice cream for you to order?

If you look at the table and say that the optimal number of scoops of ice cream is 4, then you've got the wrong answer. It is a reasonable mistake, but it is important to understand why it is wrong.

It is true that \$7.80 is the most satisfaction that you can get from ice cream, because after that you become satiated and your satisfaction goes down after eating more ice cream. But optimization means comparing benefits and costs, and when you take cost into account, 4 scoops of ice cream is too many.

What a consumer tries to do is maximize consumer's surplus, which is the difference between benefits and costs. With 4 scoops of ice cream, the consumer's surplus is \$7.80 - \$4.00, or \$3.80. With 3 scoops of ice cream, the consumer's surplus is \$7.10 - \$3.00, or \$4.10. With 2 scoops of ice cream, the consumer's surplus is \$5.70 - \$2.00, or \$3.70.

The consumer should order 3 scoops of ice cream, because that is what maximizes consumer's surplus. Another way to see this is to compare marginal benefits with marginal costs. Marginal means "the next unit's." To maximize consumer's surplus, we keep consuming more units as long as the marginal benefit exceeds the marginal cost. Starting with no scoops of ice cream, the first scoop brings \$4 of marginal benefits at \$1 of marginal cost. The second scoop brings \$1.70 of marginal benefit (the difference between \$5.70 for two scoops and \$4.00 for one scoop) at \$1 of marginal cost. The third scoop brings \$1.40 of marginal benefit at \$1 of marginal cost. The fourth scoop brings only \$0.70 of marginal benefit at \$1.00 of marginal cost. The marginal cost of the fourth scoop exceeds the marginal benefit, which is why the consumer should stop with 3 scoops.

(If the jargon of calculus appeals to you, then think of marginal as the first derivative of a function. By the same token, the law of diminishing returns is a statement about the second derivative, namely that it is negative.)

Who in the world thinks this way about ordering ice cream? Does anybody assign a dollar value to the satisfaction they get from each scoop of ice cream, and then pick the number of scoops to order based on such a valuation schedule? Of course not.

Economists believe that consumers make these sorts of decisions instinctively. In fact, consumers probably solve their optimization problems better intuitively than they could by trying to use explicit numerical modeling. Milton Friedman, a Nobel Prize winner and outstanding economics teacher, uses the metaphor of a billiard player. A great billiard player does not line up her shots by doing calculations based on the laws of physics. However, to a scientist observing her behavior, it will appear that she is acting as if she were making such calculations. To economists, consumers are like expert billiard players, successfully solving complex problems using experience and instinct.

We say that consumers get the most possible utility out of what their endowment allows them to consume. You might say that you enjoy listening to music. An economist would say that you get utility out of listening to music. It sounds as though "utility" is just jargon, and in a way, that is all it is. However, having an unusual expression allows us to articulate its properties without having to deal with the baggage of what people mean by terms like "enjoyment" or"pleasure" or "satisfaction."

Economists like to use the term utility function. Using this concept, we might say that my utility is a function of the amount of cookies that I eat, the amount of hours each week I spend folk dancing, the reliability of my car, the comfort of my clothes, the quality of the work of my tax accountant, and on and on. Every good or service that I buy goes into my utility function. In addition, the sheer amount of leisure time that I have goes into my utility function.

Some characteristics of utility functions

We assume that my utility depends on the goods and services that I consume, not on the goods and services that you consume. In reality, people like to see their friends get stuff, and they may even like to see their enemies lose stuff. However, it is easiest to work with a utility function that depends only on what I consume, not on what other people consume. We say that we assume that utility is not interdependent between consumers.

We assume that more of something is always better than less. I always would like more comfortable clothes, a more reliable car, and so on. If something is a "bad," like smelly garbage or getting mugged, then what goes in my utility function is something like "avoiding smelly garbage" or "security from mugging." That is, we take the opposite of a bad and use that as the element in the utility function.

Although more is always better than less, we invoke the principle of diminishing marginal returns. We say that with every good or service, the consumer reaches a point of diminishing marginal utility, meaning that the next unit of consumption brings less utility than the last unit of consumption. For example, when I have had nothing to eat in the morning, the first bowl of cereal gives me a lot of utility. The second bowl of cereal still gives me some utility. By the time we get to the fifth bowl, the utility is still positive, but it is small. In other words, I get diminishing marginal utility from eating cereal in the morning.

Think of some goods and services that you like to consume. Describe how the principle of diminishing marginal utility applies.

"If the principle of diminishing marginal utility did not apply, then once you consume one of something you would consume as much as you possibly could." Comment.

For each good or service in the economy, every consumer will act as if he increased his purchase of the good or service until the dollar value of the utility from the next unit no longer exceeds the price. We say that the consumer equates marginal utility to price.