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6.1: Consumption Choices

  • Page ID
    4079
  • 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.

    Table \(\PageIndex{1}\): U.S. Consumption Choices in 2015(Source: http://www.bls.gov/cex/csxann13.pdf)

    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

    fig 6.1.1.png

    Figure \(\PageIndex{1}\): José has income of $56. Movies cost $7 and T-shirts cost $14. The points on the budget constraint line show the combinations of movies and T-shirts that are affordable.

    José wishes to choose the combination that will provide him with the greatest utility, which is the term economists use to describe a person’s level of satisfaction or happiness with his or her choices.

    Let’s begin with an assumption, which will be discussed in more detail later, that José can measure his own utility with something called utils. (It is important to note that you cannot make comparisons between the utils of individuals; if one person gets \(20\) utils from a cup of coffee and another gets \(10\) utils, this does not mean than the first person gets more enjoyment from the coffee than the other or that they enjoy the coffee twice as much.) Table \(\PageIndex{2}\) shows how José’s utility is connected with his consumption of T-shirts or movies. The first column of the table shows the quantity of T-shirts consumed. The second column shows the total utility, or total amount of satisfaction, that José receives from consuming that number of T-shirts. The most common pattern of total utility, as shown here, is that consuming additional goods leads to greater total utility, but at a decreasing rate. The third column shows marginal utility, which is the additional utility provided by one additional unit of consumption. This equation for marginal utility is:

    \[MU = \frac{\text{change in total utility}}{\text{change in quantity}}\]

    Notice that marginal utility diminishes as additional units are consumed, which means that each subsequent unit of a good consumed provides less additional utility. For example, the first T-shirt José picks is his favorite and it gives him an addition of \(22\) utils. The fourth T-shirt is just to something to wear when all his other clothes are in the wash and yields only \(18\) additional utils. This is an example of the law of diminishing marginal utility, which holds that the additional utility decreases with each unit added.

    The rest of Table \(\PageIndex{2}\) shows the quantity of movies that José attends, and his total and marginal utility from seeing each movie. Total utility follows the expected pattern: it increases as the number of movies seen rises. Marginal utility also follows the expected pattern: each additional movie brings a smaller gain in utility than the previous one. The first movie José attends is the one he wanted to see the most, and thus provides him with the highest level of utility or satisfaction. The fifth movie he attends is just to kill time. Notice that total utility is also the sum of the marginal utilities. Read the next Work It Out feature for instructions on how to calculate total utility.

    Table \(\PageIndex{2}\): Total and Marginal Utility

    T-Shirts (Quantity) Total Utility Marginal Utility Movies (Quantity) Total Utility Marginal Utility
    1 22 22 1 16 16
    2 43 21 2 31 15
    3 63 20 3 45 14
    4 81 18 4 58 13
    5 97 16 5 70 12
    6 111 14 6 81 11
    7 123 12 7 91 10
    8 133 10 8 100 9

    Table \(\PageIndex{3}\) looks at each point on the budget constraint in Figure \(\PageIndex{1}\), and adds up José’s total utility for five possible combinations of T-shirts and movies.

    Table \(\PageIndex{3}\): Finding the Choice with the Highest Utility

    Point T-Shirts Movies Total Utility
    P 4 0 81 + 0 = 81
    Q 3 2 63 + 31 = 94
    R 2 4 43 + 58 = 101
    S 1 6 22 + 81 = 103
    T 0 8 0 + 100 = 100

     

    Example \(\PageIndex{1}\): Calculating Total Utility

    Let’s look at how José makes his decision in more detail.

    Step 1: Observe that, at point \(Q\) (for example), José consumes three T-shirts and two movies.

    Step 2: Look at Table \(\PageIndex{2}\). You can see from the fourth row/second column that three T-shirts are worth \(63\) utils. Similarly, the second row/fifth column shows that two movies are worth \(31\) utils.

    Step 3: From this information, you can calculate that point \(Q\) has a total utility of \(94 (63 + 31)\).

    Step 4: You can repeat the same calculations for each point on Table \(\PageIndex{3}\), in which the total utility numbers are shown in the last column.

    For José, the highest total utility for all possible combinations of goods occurs at point \(S\), with a total utility of \(103\) from consuming one T-shirt and six movies.

    Choosing with Marginal Utility

    Most people approach their utility-maximizing combination of choices in a step-by-step way. This step-by-step approach is based on looking at the tradeoffs, measured in terms of marginal utility, of consuming less of one good and more of another.

    For example, say that José starts off thinking about spending all his money on T-shirts and choosing point \(P\), which corresponds to four T-shirts and no movies, as illustrated in Figure \(\PageIndex{1}\). José chooses this starting point randomly; he has to start somewhere. Then he considers giving up the last T-shirt, the one that provides him the least marginal utility, and using the money he saves to buy two movies instead. Table \(\PageIndex{4}\) tracks the step-by-step series of decisions José needs to make (Key: T-shirts are \(\$14\), movies are \(\$7\), and income is \(\$56\)). The following Work It Out feature explains how marginal utility can effect decision making.

    Table \(\PageIndex{4}\): A Step-by-Step Approach to Maximizing Utility

    Try Which Has Total Utility Marginal Gain and Loss of Utility, Compared with Previous Choice Conclusion
    Choice 1: P 4 T-shirts and 0 movies 81 from 4 T-shirts + 0 from 0 movies = 81      –      –
    Choice 2: Q 3 T-shirts and 2 movies 63 from 3 T-shirts + 31 from 0 movies = 94 Loss of 18 from 1 less T-shirt, but gain of 31 from 2 more movies, for a net utility gain of 13 Q is preferred over P
    Choice 3: R 2 T-shirts and 4 movies 43 from 2 T-shirts + 58 from 4 movies = 101 Loss of 20 from 1 less T-shirt, but gain of 27 from two more movies for a net utility gain of 7 R is preferred over Q
    Choice 4: S 1 T-shirt and 6 movies 22 from 1 T-shirt + 81 from 6 movies = 103 Loss of 21 from 1 less T-shirt, but gain of 23 from two more movies, for a net utility gain of 2 S is preferred over R
    Choice 5: T 0 T-shirts and 8 movies 0 from 0 T-shirts + 100 from 8 movies = 100 Loss of 22 from 1 less T-shirt, but gain of 19 from two more movies, for a net utility loss of 3 S is preferred over T

    Example \(\PageIndex{1}\): Decision Making by Comparing Marginal Utility

    José could use the following thought process (if he thought in utils) to make his decision regarding how many T-shirts and movies to purchase:

    Step 1: From Table \(\PageIndex{2}\), José can see that the marginal utility of the fourth T-shirt is \(18\). If José gives up the fourth T-shirt, then he loses \(18\) utils.

    Step 2: Giving up the fourth T-shirt, however, frees up \(\$14\) (the price of a T-shirt), allowing José to buy the first two movies (at \(\$7\) each).

    Step 3: José knows that the marginal utility of the first movie is \(16\) and the marginal utility of the second movie is \(15\). Thus, if José moves from point \(P\) to point \(Q\), he gives up \(18\) utils (from the T-shirt), but gains \(31\) utils (from the movies).

    Step 4: Gaining \(31\) utils and losing \(18\) utils is a net gain of \(13\). This is just another way of saying that the total utility at \(Q\) (\(94\) according to the last column in Table \(\PageIndex{3}\)) is \(13\) more than the total utility at \(P\) (\(81\)).

    Step 5: So, for José, it makes sense to give up the fourth T-shirt in order to buy two movies.

    José clearly prefers point \(Q\) to point \(P\). Now repeat this step-by-step process of decision making with marginal utilities. José thinks about giving up the third T-shirt and surrendering a marginal utility of \(20\), in exchange for purchasing two more movies that promise a combined marginal utility of \(27\). José prefers point \(R\) to point \(Q\). What if José thinks about going beyond \(R\) to point \(S\)? Giving up the second T-shirt means a marginal utility loss of \(21\), and the marginal utility gain from the fifth and sixth movies would combine to make a marginal utility gain of \(23\), so José prefers point \(S\) to \(R\).

    However, if José seeks to go beyond point \(S\) to point \(T\), he finds that the loss of marginal utility from giving up the first T-shirt is \(22\), while the marginal utility gain from the last two movies is only a total of \(19\). If José were to choose point T, his utility would fall to \(100\). Through these stages of thinking about marginal tradeoffs, José again concludes that \(S\), with one T-shirt and six movies, is the choice that will provide him with the highest level of total utility. This step-by-step approach will reach the same conclusion regardless of José’s starting point.

    Another way to look at this is by focusing on satisfaction per dollar. Marginal utility per dollar is the amount of additional utility José receives given the price of the product. For José’s T-shirts and movies, the marginal utility per dollar is shown in Table \(\PageIndex{5}\).

    \[\text{marginal utility per dollar} = \frac{\text{marginal utility}}{\text{price}}\]

    José’s first purchase will be a movie. Why? Because it gives him the highest marginal utility per dollar and it is affordable. José will continue to purchase the good which gives him the highest marginal utility per dollar until he exhausts the budget. José will keep purchasing movies because they give him a greater “bang or the buck” until the sixth movie is equivalent to a T-shirt purchase. José can afford to purchase that T-shirt. So José will choose to purchase six movies and one T-shirt.

    Table \(\PageIndex{5}\): 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

    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
    the additional utility provided by one additional unit of consumption
    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

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