# Utility

### What Is Utility?

The concept of utility is a quantitative measure of happiness or satisfaction commonly used in economic analysis.

Consumers make a variety of choices based on their abilities and needs. Economists seek ways to judge consumers' experiences to predict their behaviors. One method attempts to gauge customers' emotions and how they influence consumer behavior. Sometimes people purchase things based purely on necessity; other times people's purchasing decisions are based more on desire and feelings about the product.

Simply put, utility (U) is a quantitative measure of happiness or satisfaction used in economic analysis (quantitative means an analysis based on numbers of something and not an individual item). While it is not something consumers consciously measure, it is a useful tool for economists to use to measure consumer behavior. Utility is a number (in units of utility, or utils) that indicates how happy a consumer becomes by consuming a good or group of goods. For a given good, utility (U) is a function of the quantity (Q) consumed of the good (i.e., $\text{Utility}=\text{U(Q)}$), and utility can be represented graphically. Calculating utility is helpful for businesses for many reasons, but it is mostly important for pricing a product appropriately. For instance, if a sock company has plain white socks and polka dot socks, it would be helpful to know that polka dot socks have a higher util (6 compared to 4) and thus could be priced higher than plain white socks. But the utility of the polka dot socks goes down 1 util for each additional pair an individual buys. When a consumer already owns polka dot socks, he or she is not willing to pay as much to buy an additional pair.
In the curve, U represents utility, so U1 is the utility experienced by consuming quantity Q1, and U2 is the utility experienced by consuming quantity Q2. Although this is not technically necessary, utility functions generally start at 0 because consuming no units confers no happiness. In addition, utility curves generally slope upward, which implies higher quantities of consumption confer greater levels of utility; the more units purchased, the higher the consumer's overall happiness. Remember that utility is the happiness from consuming all units and is not a per-unit measure. For instance, an individual is happy after eating one cookie, but after eating 30 cookies, their level of happiness changes.

So far, the assumption is that consumption of a good confers positive utility—it makes the consumer happier. This is why economists refer to "goods." There are also items in the world that make the consumer feel worse and promote negative reactions. Economists refer to these sorts of items as "bads." Examples of "bads" are a television set that arrives broken and cigarettes (over time). It is often the case that positive utility numbers are used for "goods" and negative utility numbers are used for "bads." Disutility is the sadness or lack of satisfaction a consumer gets from consuming an item. Something can also be both a "bad" and a "good" for different consumers. For instance, one person may love sourdough bread but another may be allergic to it. For the person with the allergy, the bread is a "bad," but for the person who loves it, the bread is a "good."

### Cardinal versus Ordinal Properties of Utility

Utility has ordinal but not cardinal properties, meaning utility numbers can be compared but not combined.

One key feature of the concept of utility is that, mathematically speaking, utility has ordinal (theory claiming that it is only necessary to know which option is better, it doesn't matter by how much it is better) but not cardinal (knowing by what degree an option is preferred) properties. The first part of this statement means that utilities can be compared in a "bigger is better" fashion; for example, a utility of 5 is better than a utility of 3 (since $5 \gt 3$) and a utility of 4 is not as good as a utility of 8 (since $4 \lt 8$). Having ordinal properties roughly corresponds to being able to use the greater than, less than, and equals operators. Ordinal determines which opportunity is better, less than, or equal. It is not necessary to determine an exact numerical degree of difference in order to be able to determine these relationships. Ordinal utility is only interested in determining which options are better, worse, or equal. For instance, someone may prefer donuts to bagels, thus the ordinal utility would for donuts would be greater than that of a bagel.

In contrast, the second part of the statement, that utility does not have cardinal properties, means utilities cannot be added or subtracted. In other words, a utility of 5 and a utility of 3 do not combine to give a utility of 8 (or anything else, for that matter). A related property is that a utility of 8 is twice as good as a utility of 4, and so on. In order to determine cardinal properties it is necessary to be able to use arithmetic, there needs to be numerical value given to the utility of options that are being compared.

Utility numbers are only considered in a sense of being bigger than or smaller than another utility number, and additional math is not done with them. Adding 5 to all of the utility numbers, multiplying them all by 3, and so on would not change what they represented in terms of preferences. If someone buying a houseplant rates a fern as a utility of 9 and a cactus with a utility of 4, adding these numbers together will not impact the fact that the fern has a higher utility and is thus preferred.