Before we can delve into marginal utility, we first need to understand the basics of utility. *The Glossary of Economics Terms* defines utility as follows:

Utility is the economist's way of measuring pleasure or happiness and how it relates to the decisions that people make. Utility measures the benefits (or drawbacks) from consuming a good or service or from working. Although utility is not directly measurable, it can be inferred from the decisions that people make.

Utility in economics is typically described by a utility function- for example:

- U(x) = 2x + 7, where U is utility and X is wealth

### Marginal Analysis in Economics

The article Marginal Analysis describes the use of marginal analysis in economics:

From an economist's perspective, making choices involves making decisions 'at the margin' - that is, making decisions based on small changes in resources:

- How should I spend the next hour?
- How should I spend the next dollar?

### Marginal Utility

Marginal utility, then, asks how much a one-unit change in a variable will impact our utility (that is, our level of happiness. In other words, marginal utility measures incremental utility received from one additional unit of consumption. Marginal utility analysis answers questions such as:

- How much happier, in terms of 'utils', will an additional dollar make me (that is, what is the marginal utility of money?)
- How much less happy, in terms of 'utils', will working an additional hour make me (that is, what is the marginal disutility of labor?)

Now we know what marginal utility is, we can calculate it. There are two different ways to do so.

### Calculating Marginal Utility Without Calculus

Suppose you have the following utility function: U(b, h) = 3b * 7h

Where:

- b = number of baseball cards
- h = number of hockey cards

And you're asked "Suppose you have 3 baseball cards and 2 hockey cards.

What is the marginal utility of adding a 3rd hockey card?"

First step is to calculate the marginal utility of each scenario:

- U(b, h) = 3b * 7h
- U(3, 2) = 3*3 * 7*2 = 126
- U(3, 3) = 3*3 * 7*3 = 189

The marginal utility is simply the difference between the two: U(3,3) - U(3, 2) = 189 - 126 = 63.

### Calculating Marginal Utility With Calculus

Using calculus is the fastest and easiest way to calculate marginal utility. Suppose you have the following utility function: U(d, h) = 3d / h where:

- d = dollars paid
- h = hours worked

Suppose you have 100 dollars and you worked 5 hours; what is the marginal utility of dollars? To find the answer, take the first (partial) derivative of the utility function with respect to the variable in question (dollars paid):

- dU/dd = 3 / h
- Substitute in d = 100, h = 5.
- MU(d) = dU/dd = 3 / h = 3 /5 = 0.6

Note, however, that using calculus to calculate marginal utility will generally result in slightly different answers than calculating marginal utility using discrete units.