## Rules for Maximizing Utility

### 3. A Rule for Maximizing Utility

This process of decision making described previously suggests a rule to follow when maximizing utility. Since the price of T-shirts is not the same as the price of movies, it's not enough to just compare the marginal utility of T-shirts with the marginal utility of movies. Instead, we need to control for the prices of each product. We can do this by computing and comparing marginal utility per dollar of expenditure for each product. Marginal utility per dollar is the amount of additional utility José receives given the price of the product.

$\begin{array}{rcl}\text{marginal utility per dollar}& =& \dfrac{\text{marginal utility}}{\text{price}}\end{array}$

For José's T-shirts and movies, the marginal utility per dollar is shown in Table 2.

Table 2. Marginal Utility per Dollar
Quantity of T-Shirts Total Utility Marginal Utility Marginal Utility per Dollar Quantity of Movies Total Utility Marginal Utility Marginal Utility per Dollar
1 22 22 22/$14=1.6 1 16 16 16/$7=2.3
2 43 21 21/$14=1.5 2 31 15 15/$7=2.14
3 63 20 20/$14=1.4 3 45 14 14/$7=2
4 81 18 18/$14=1.3 4 58 13 13/$7=1.9
5 97 16 16/$14=1.1 5 70 12 12/$7=1.7
6 111 14 14/$14=1 6 81 11 11/$7=1.6
7 123 12 12/$14=1.2 7 91 10 10/$7=1.4

#### A RULE FOR MAXIMIZING UTILITY

If a consumer wants to maximize total utility, for every dollar that they spend, they should spend it on the item which yields the greatest marginal utility per dollar of expenditure.