### To Understand Marginal Utility, We First Must Understand Utility:

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

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

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, such as:

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. 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?)

### Calclulating 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.

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.

### Calclulating 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

That is how we calculate marginal utility. If you have any questions, please leave them at this blog entry.

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

That is how we calculate marginal utility. If you have any questions, please leave them at this blog entry.