Utility is a way of measuring how much satisfaction or happiness a consumer gets from consuming goods or services. Think of it as a score on a happiness meter. The higher the score, the more you enjoy that item.
In economics we write it as a function: \$U(x1, x2, \dots)\$, where each \$x_i\$ is the quantity of a good.
Marginal Utility is the extra satisfaction you get from consuming one more unit of a good.
Mathematically: \$MUi = \frac{\partial U}{\partial xi}\$
Example: If you eat a slice of pizza, the first slice might give you a lot of joy (\$MU\$ high). The second slice might still be good but not as exciting, so its \$MU\$ is lower.
When you have a fixed amount of money, the EMP tells you how to spend it so that your total utility is maximised.
It says: Spend your money until the last dollar spent on each good gives the same extra utility.
In formula form: \$\frac{MU1}{P1} = \frac{MU2}{P2} = \dots\$
Where \$P_i\$ is the price of good \$i\$.
Imagine you have £10 to spend on two items:
Suppose the marginal utilities are:
| Good | MU | MU ÷ Price |
|---|---|---|
| Chocolate | 8 | 4 |
| Apple | 5 | 5 |
Since \$MU{Apple}/P{Apple} > MU{Chocolate}/P{Chocolate}\$, you should buy more apples until the ratios equalise. This maximises your total happiness.