# Principles of Economics/Utility

## Definition of Utility

In ordinary uses, the term utility denotes the usefulness of a good or service; however, in economics, the term utility is the ability to gain or not to gain from a decision based on individual preferences. Utility is the want-satisfying "power" of any commodity or the capacity of a commodity to give satisfaction. Utility may measure how much one enjoys a movie, or the sense of security one gets from buying a deadbolt.

No matter the object, a person can measure the utility of the object. Some examples include the utility from eating an apple, from living in a certain house, and from voting for a specific candidate, from having a given wireless phone plan. In fact, every decision that an individual makes in their daily life can be viewed as a comparison between the utility gained from pursuing one option or another.

Example: Sally wakes up in the morning, and her mother offers her the choice of a grapefruit or cereal. Sally, in an instant, compares the utility she would derive from both choices and selects the cereal. Sally's mother then needs to take Sally to school. She can either walk or drive. Sally's mother considers the benefits of exercise and fresh air, which compose the utility she would derive from walking, and also considers the time savings and comfort of driving. Sally's mother decides to drive.

In this example, it can be seen that utility is measured in numbers that are purely cardinal, rather than ordinal. The numbers used to measure utility (often in a unit called the "util") is useful only for comparison. If the utility given by one thing is ${\displaystyle 100{\text{ utils}}}$  and the utility given by another is ${\displaystyle 12,000{\text{ utils}}}$ , we can only say that the utility of the latter is greater. We could not say that the individual gets "${\displaystyle 120}$  times more utility" from this option, because utility is not a quantity. Furthermore, the sign of utility may be positive or negative with no effect on its interpretation. If one option gives ${\displaystyle -15{\text{ utils}}}$  and another gives ${\displaystyle -12{\text{ utils}}}$ , selecting the second is not, as it might seem, the "lesser of two evils", but can only be interpreted as the better option.

Also illustrated in the example above is that what may seem "better" in terms of "usefulness" for a person is not reflected in their utility. For example, Sally gains more utils from eating the cereal, but maybe the cereal is very unhealthy compared to the grapefruit. This consideration will be accounted for in Sally's utility according to how much she cares about it. If Sally does care about the nutritional value of her food, this would mean that the grapefruit would provide a greater utility than if she does not care about nutrition at all. The same is true for her mother's decision about driving to school. If she is environmentally conscious, driving would have given less utility than if she is not. These factors may, though not necessarily, affect the outcome of the decision. This point leads to the statement that, when measuring utility, we assume that all things have been taken into account. The amount of utility that Sally gets from her cereal takes into account all factors relevant to that decision.

In conclusion, utility is the measure of how much an individual values a particular good in a particular situation, which depends entirely on the preferences of that individual, rather than some external or universal measure. While an apple and an orange may give utility values of ${\displaystyle 5{\text{ utils}}}$  and ${\displaystyle 10{\text{ utils}}}$ , respectively, to one individual, they may give ${\displaystyle 1,250{\text{ utils}}}$  and ${\displaystyle -180{\text{ utils}}}$  to another. These values depend only on how an individual values each object.

## Rationality and Utility

We usually say that an individual is "rational" if that individual maximizes utility in their decisions to care about life and money. That is, whenever an individual is to choose between a group of options, they are rational if they choose the option that, all else equal, gives the greatest success (to them). Recalling that utility includes every element of a decision, this assumption is not particularly difficult to accept. If, when everything is taken into account, one decision provides the greatest utility, then, ideally, the individual would choose the most preferable option.

This should not necessarily be taken to mean that individuals who fail to quantify and measure every decision act irrationally. Rather, a rational individual is one who always selects an option that they prefer the most.

The rationality assumption may seem trivial, but it is basic to the study of economics. This assumption gives a basis for modeling human behavior and decision making. If we could not assume rationality, it would be impossible to say, when presented with a set of choices, what an individual would select. The notion of rationality is therefore central to any understanding of microeconomics.

## Measurement

There are no real methods of measuring utility outside of a purely theoretical framework. An option giving ${\displaystyle 100{\text{ utils}}}$  has no real interpretation, except that it is preferred to an option giving ${\displaystyle 50{\text{ utils}}}$ , but it is less preferred than an option giving ${\displaystyle 101{\text{ utils}}}$ . The numbers used to model utility are only determined in the functional form of the model from which they result. It is meaningless, for example, to ask "how many utils does this apple give you?" It could only be meaningful to ask, "Would you prefer an apple or an orange?" in any non-theoretical framework.

Therefore, the purpose of using the units "util" is to relatively measure the enjoyment of the individual. If you are in pain and have to go to the hospital or clinic, receptionists, doctors, and nurses ask you to rate your pain from one to ten. "Rating pain" is not useful for measuring any quantifiable data. Rather, the individual gives a relative value of "their pain." In the context of utils, the hospital example would go like this:

Doctor: "On a scale of ${\displaystyle -1{\text{ utils}}}$  to ${\displaystyle -10{\text{ utils}}}$ , what is your utility of pain compared to another you had in the past?"
Patient: "${\displaystyle -5{\text{ utils}}}$  compared to ${\displaystyle -3{\text{ utils}}}$ ."

## Being "better off"

In microeconomic theory, we often say that an individual is made "better off" if one circumstance is preferred to another (that is, gives greater utility), and that individual is put into it. A simple example would be giving a child a cookie. Assuming the child enjoys cookies, the child is "better off" with the cookie than without it. Again, in this example we say he is "better off" only in terms of his preferences, rather than in terms of his health, etc.