Utility is a term in economics that is used to quantify ‘goodness’ in a very general way. It’s used in two slightly different ways:
The first case is simpler. For example, suppose you’re running a conservation effort for a forest and you’re trying to save moose and elk from hunting. You decide that moose are a higher priority than elk, so your objective is 2*(number of moose saved) + (number of elk saved). Then you could say that saving one moose provides 2 utility, and saving one elk provides 1 utility.
The rest of this article will focus on the second case.
Suppose that there are two possible outcomes to a situation, call them A and B. Sometimes, it’s not enough to know that someone prefers outcome A to B, we want to know how much they prefer A to B. To do this we have to assign actual numbers to how much this person likes A or B, and we call this their utility for A or B. We denote their utility for A by $u(A)$, and for B by $u(B)$.
For example, suppose outcome A is a person gets given an apple, and outcome B is they get given a banana. You could ask them, would you prefer an apple or banana? If they say apple, then we know
$$ u(A) \geq u(B). $$
That is, their utility for an apple must be at least as large as their utility for a banana, or they would have chosen a banana. But what if you asked them the following question: would you like a 1/2 chance of getting an apple, or definitely get a banana? If they choose the 1/2 chance for an apple, then we know
$$ \frac{1}{2}u(A) \geq u(B). $$
That is, their utility for an apple must be at least twice as large as their utility for a banana. Note that you can’t actually say what the exact utility values are, you can only say what their relative values are. That is, unless the utility for one particular thing is fixed: for example, if you fix their utility for a banana to be equal to one, then you can say their utility for an apple is at least two.
When someone’s preferences are learned through observing their decisions, they are called revealed preferences. They are different than if you just asked someone, ‘What is you utility for apples and bananas?’, because people often don’t understand their ‘real preferences’ (if the revealed preferences are what you consider ‘real’.)
You may have noticed that I have made some assumptions, mainly that people’s decisions are rational enough that utilities can be assigned to their preferences. This is definitely not an innocuous assumption, because people violate it all the time. For example, a cognitive bias called the ‘relative savings effect’ has been observed where people are willing to put more effort to save say, $10 on a cheaper item than they would to save the save amount on a more expensive item. If you try to assign a utility to saving $10, and a utility to the extra effort it takes to save $10 on an item, there’s no way to explain the relative savings effect. People’s preferences are also affect by things like risk aversion. So utility can’t describe every decision people make, but it’s still extremely helpful for visualizing various concepts.
Utility Versus Dollars
Sometimes, the utility someone has for an outcome can just as easily be described by the dollar value they would be willing to pay for it. Using dollars in place of utility can work just fine if all of the participants value dollars at the same amount, but this is not usually the case when people have disparate wealths. This is because someone with more wealth typically does not value each dollar as much as someone with less wealth, which is a result of ‘diminishing returns’ discussed in the next section. If you’re giving away some gifts to people trying to maximize the joy you bring, you don’t want to give them all to the richest person just because they’d be willing to pay the most for them.
Diminishing returns is when each additional item you receive gives you less benefit than the previous one. This is true for most things: if you’re parched on a hot day, you might be willing to pay up to $10 for a cold glass of water, for example. But you probably wouldn’t be willing to pay as much for a second glass, after you’ve had the first. And you probably wouldn’t be willing to pay anything at all by the 10th glass.
Another way to put this, is that you have ‘diminishing marginal utility’ for the item. ‘Marginal’ means the amount per 1 additional items, so this means that the amount of utility you get for one additional it item is decreasing with the number of items you get.