127 Reading: A Tool for Maximizing Utility
A Tool for Maximizing Utility
This process of decision making suggests a rule to follow when maximizing utility. Since the price of T-shirts is twice as high as the price of movies, to maximize utility the last T-shirt chosen needs to provide exactly twice the marginal utility (MU) of the last movie. If the last T-shirt provides less than twice the marginal utility of the last movie, then the T-shirt is providing less “bang for the buck” (i.e., marginal utility per dollar spent) than if the same money were spent on movies. If this is so, José should trade the T-shirt for more movies to increase his total utility. Marginal utility per dollar measures the additional utility that José will enjoy given what he has to pay for the good.
Review José’s T-shirts and movies marginal utility per dollar Table again.
| Table 6.3. 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 |
If the last T-shirt provides more than twice the marginal utility of the last movie, then the T-shirt is providing more “bang for the buck” or marginal utility per dollar, than if the money were spent on movies. As a result, José should buy more T-shirts. Notice that at José’s optimal choice of point S, the marginal utility from the first T-shirt, of 22 is exactly twice the marginal utility of the sixth movie, which is 11. At this choice, the marginal utility per dollar is the same for both goods. This is a tell-tale signal that José has found the point with highest total utility.
This argument can be written as a general rule: the utility-maximizing choice between consumption goods occurs where the marginal utility per dollar is the same for both goods.
[latex]\displaystyle\frac{MU_1}{P_1}=\frac{MU_2}{P_2}[/latex]
A sensible economizer will pay twice as much for something only if, in the marginal comparison, the item confers twice as much utility. Notice that the formula for the table above is
[latex]\displaystyle\frac{22}{14}=\frac{11}{7}[/latex]
[latex]1.6=1.6[/latex]
The following feature provides step-by-step guidance for this concept of utility-maximizing choices.
Maximizing Utility
The general rule, [latex]\displaystyle\frac{MU_1}{P_1}=\frac{MU_2}{P_2}[/latex], means that the last dollar spent on each good provides exactly the same marginal utility. So:
Step 1. If we traded a dollar more of movies for a dollar more of T-shirts, the marginal utility gained from T-sh