# 7.1 Consumption choices  (Page 5/22)

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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.

$\begin{array}{rcl}\frac{{\text{MU}}_{1}}{{\text{P}}_{1}}& =& \frac{{\text{MU}}_{2}}{{\text{P}}_{2}}\end{array}$

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:

$\begin{array}{rcl}\frac{22}{\text{14}}& =& \frac{11}{\text{7}}\\ \text{1.6}& =& \text{1.6}\end{array}$

The following Work It Out feature provides step by step guidance for this concept of utility-maximizing choices.

## Maximizing utility

The general rule, $\begin{array}{rcl}\frac{{\text{MU}}_{1}}{{\text{P}}_{1}}& =& \frac{{\text{MU}}_{2}}{{\text{P}}_{2}}\end{array}$ , 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-shirts would exactly offset the marginal utility lost from fewer movies. In other words, the net gain would be zero.

Step 2. Products, however, usually cost more than a dollar, so we cannot trade a dollar’s worth of movies. The best we can do is trade two movies for another T-shirt, since in this example T-shirts cost twice what a movie does.

Step 3. If we trade two movies for one T-shirt, we would end up at point R (two T-shirts and four movies).

Step 4. Choice 4 in [link] shows that if we move to point S, we would lose 21 utils from one less T-shirt, but gain 23 utils from two more movies, so we would end up with more total utility at point S.

In short, the general rule shows us the utility-maximizing choice.

There is another, equivalent way to think about this. The general rule can also be expressed as the ratio of the prices of the two goods should be equal to the ratio of the marginal utilities. When the price of good 1 is divided by the price of good 2, at the utility-maximizing point this will equal the marginal utility of good 1 divided by the marginal utility of good 2. This rule, known as the consumer equilibrium    , can be written in algebraic form:

$\begin{array}{rcl}\frac{{\text{P}}_{1}}{{\text{P}}_{2}}& =& \frac{{\text{MU}}_{1}}{{\text{MU}}_{2}}\end{array}$

Along the budget constraint, the total price of the two goods remains the same, so the ratio of the prices does not change. However, the marginal utility of the two goods changes with the quantities consumed. At the optimal choice of one T-shirt and six movies, point S, the ratio of marginal utility to price for T-shirts (22:14) matches the ratio of marginal utility to price for movies (of 11:7).

## Measuring utility with numbers

This discussion of utility started off with an assumption that it is possible to place numerical values on utility, an assumption that may seem questionable. You can buy a thermometer for measuring temperature at the hardware store, but what store sells an “utilimometer” for measuring utility? However, while measuring utility with numbers is a convenient assumption to clarify the explanation, the key assumption is not that utility can be measured by an outside party, but only that individuals can decide which of two alternatives they prefer.

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