# 6.1: Consumption Choices

Skills to Develop

• Calculate total utility
• Propose decisions that maximize utility
• Explain marginal utility and the significance of diminishing marginal utility

Information on the consumption choices of Americans is available from the Consumer Expenditure Survey carried out by the U.S. Bureau of Labor Statistics. Table $$\PageIndex{1}$$ shows spending patterns for the average U.S. household. The first row shows income and, after taxes and personal savings are subtracted, it shows that, in 2015, the average U.S. household spent $$\48,109$$ on consumption. The table then breaks down consumption into various categories. The average U.S. household spent roughly one-third of its consumption on shelter and other housing expenses, another one-third on food and vehicle expenses, and the rest on a variety of items, as shown. Of course, these patterns will vary for specific households by differing levels of family income, by geography, and by preferences.

 Average Household Income before Taxes $62,481 Average Annual Expenditures$48.109 Food at home $3,264 Food away from home$2,505 Housing $16,557 Apparel and services$1,700 Transportation $7,677 Healthcare$3,157 Entertainment $2,504 Education$1,074 Personal insurance and pensions $5,357 All else: alcohol, tobacco, reading, personal care, cash contributions, miscellaneous$3,356

## Total Utility and Diminishing Marginal Utility

To understand how a household will make its choices, economists look at what consumers can afford, as shown in a budget constraint line, and the total utility or satisfaction derived from those choices. In a budget constraint line, the quantity of one good is measured on the horizontal axis and the quantity of the other good is measured on the vertical axis. The budget constraint line shows the various combinations of two goods that are affordable given consumer income. Consider the situation of José, shown in Figure $$\PageIndex{1}$$. José likes to collect T-shirts and watch movies.

In Figure $$\PageIndex{1}$$, the quantity of T-shirts is shown on the horizontal axis, while the quantity of movies is shown on the vertical axis. If José had unlimited income or goods were free, then he could consume without limit. But José, like all of us, faces a budget constraint. José has a total of $$\56$$ to spend. The price of T-shirts is $$\14$$ and the price of movies is $$\7$$. Notice that the vertical intercept of the budget constraint line is at eight movies and zero T-shirts ($$\56/\7=8$$). The horizontal intercept of the budget constraint is four, where José spends of all of his money on T-shirts and no movies ($$\56/14=4$$). The slope of the budget constraint line is rise/run or $$-8/4=-2$$. The specific choices along the budget constraint line show the combinations of T-shirts and movies that are affordable.

A Choice between Consumption Goods

## A Rule 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.

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.

$\frac{MU_1}{P_1} = \frac{MU_2}{P_2}$

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:

$\frac{M22}{\14} = \frac{11}{\7}$

$1.6 = 1.6$

The following Example provides step by step guidance for this concept of utility-maximizing choices.

Example $$\PageIndex{1}$$: Maximizing Utility

The general rule, $$\frac{MU_1}{P_1} = \frac{MU_2}{P_2}$$, 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 Table $$\PageIndex{4}$$ 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:

$\frac{P_1}{P_2} = \frac{MU_1}{MU_2}$

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.

To understand this point, think back to the step-by-step process of finding the choice with highest total utility by comparing the marginal utility that is gained and lost from different choices along the budget constraint. As José compares each choice along his budget constraint to the previous choice, what matters is not the specific numbers that he places on his utility—or whether he uses any numbers at all—but only that he personally can identify which choices he prefers.

In this way, the step-by-step process of choosing the highest level of utility resembles rather closely how many people make consumption decisions. We think about what will make us the happiest; we think about what things cost; we think about buying a little more of one item and giving up a little of something else; we choose what provides us with the greatest level of satisfaction. The vocabulary of comparing the points along a budget constraint and total and marginal utility is just a set of tools for discussing this everyday process in a clear and specific manner. It is welcome news that specific utility numbers are not central to the argument, since a good utilimometer is hard to find. Do not worry—while we cannot measure utils, by the end of the next module, we will have transformed our analysis into something we can measure—demand.

## Key Concepts and Summary

Economic analysis of household behavior is based on the assumption that people seek the highest level of utility or satisfaction. Individuals are the only judge of their own utility. In general, greater consumption of a good brings higher total utility. However, the additional utility received from each unit of greater consumption tends to decline in a pattern of diminishing marginal utility.

The utility-maximizing choice on a consumption budget constraint can be found in several ways. You can add up total utility of each choice on the budget line and choose the highest total. You can choose a starting point at random and compare the marginal utility gains and losses of moving to neighboring points—and thus eventually seek out the preferred choice. Alternatively, you can compare the ratio of the marginal utility to price of good 1 with the marginal utility to price of good 2 and apply the rule that at the optimal choice, the two ratios should be equal:

$\frac{MU_1}{P_1} = \frac{MU_2}{P_2}$

## References

U.S. Bureau of Labor Statistics. 2015. “Consumer Expenditures in 2013.” Accessed March 11, 2015. http://www.bls.gov/cex/csxann13.pdf.

U.S. Bureau of Labor Statistics. 2015. “Employer Costs for Employee Compensation—December 2014.” Accessed March 11, 2015. http://www.bls.gov/news.release/pdf/ecec.pdf.

U.S. Bureau of Labor Statistics. 2015. “Labor Force Statistics from the Current Population Survey.” Accessed March 11, 2015. http://www.bls.gov/cps/cpsaat22.htm.

## Glossary

budget constraint line
shows the possible combinations of two goods that are affordable given a consumer’s limited income
consumer equilibrium
when the ratio of the prices of goods is equal to the ratio of the marginal utilities (point at which the consumer can get the most satisfaction)
diminishing marginal utility
the common pattern that each marginal unit of a good consumed provides less of an addition to utility than the previous unit
marginal utility
marginal utility per dollar
the additional satisfaction gained from purchasing a good given the price of the product; MU/Price
total utility
satisfaction derived from consumer choices