# Equal Marginal Utility per Dollar

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### Maximizing Utility

In some instances, relative satisfactions from goods can be approximated by looking at utility in terms of money. We cannot scientifically ascertain whether one person gains more than someone else from an extra dollar of income or extra syrup on a waffle. We may be fairly sure, however, that the personal marginal utilities of each person from particular goods are roughly proportional to the goods’ prices, because people adjust their spending patterns whenever relative prices and marginal utilities are not in balance.

Suppose that you allocate \$12 from your weekly budget for ice cream, your favorite snack. Table 1 lists your total and marginal utilities from macadamia nut crunch and chocolate ice cream cones. How many of each will you buy at \$1 apiece to maximize your satisfaction? Eating five chocolate and seven crunch cones maximizes your total satisfaction at 46 utils per week. No other \$12 combination yields more utility.

 Total (TU) and Marginal (MU) Utilities for Ice Cream Cones When Price = \$1 per Cone Macadamia Nut Crunch Chocolate Quantity TU MU Quantity TU mu 1 8 8 1 5 5 2 15 7 2 9 4 3 21 6 3 12 3 4 25 4 4 14 2 5 28 3 5 15 1 6 30 2 6 15 0 7 31 1 8 31 0

### Balancing Marginal Utilities

In the example shown, your purchasing pattern suggested that you would look at the next cone, whether chocolate or macadamia nut, and determine which flavor provided you with the largest increase in utility.

The principle of equal marginal utilities per dollar: A consumer maximizes utility when the last dollar spent on any good generates the same satisfaction as the last dollar spent on every other good.

Your purchasing pattern becomes stable only when the last dollar spent on ice cream yields the same satisfaction as the last dollar spent on lemonade, clothes, books, or housing.

Satisfaction from the last spending on a good is calculated by dividing its marginal utility by its price. For example, if the last chocolate cone was \$1 and its marginal utility was 1, then MUch/Pch = 1/1 = 1, and the marginal utility per dollar of the last cone was 1. Individuals are in equilibrium when

where a, b, ..., z are the various goods purchased. In our ice cream cone example, the marginal utilities per dollar equaled one for both macadamia nut crunch and chocolate cones. By equating marginal utilities per dollar, utility is maximized. No other allocation of resources will result in higher satisfaction. A little introspection should confirm that your own spending pattern conforms to this principle of equal marginal utilities per dollar.

A corollary of the principle of equal marginal utilities per dollar is that consumer equilibrium requires marginal benefits from every good to be proportional to their relative market prices. Market prices and the subjective demand prices discussed in Chapter 1 are different ways of viewing opportunity costs. Demand prices can be thought of as the ratios of the marginal utilities of various goods. Only if market prices do not exceed demand prices will you buy. In equilibrium, these subjective price ratios must equal the relative market prices for all the goods you choose to purchase. That is, MUa/MUb = Pa/Pb for any two goods we choose to label a and b, respectively.1 Focus 1 addresses the issue of whether economic assumptions about how people process information are reasonable.

### Price Adjustments and Marginal Utility

To summarize, the higher-priced goods you buy uniformly generate more marginal utility than your lower-priced purchases: the more you pay for a good, the more it is worth to you at the margin. You are in equilibrium when the marginal utilities per dollar are equal for all goods. Ultimately, the last dollar you spend on any good yields the same satisfaction as the last dollar spent on any other good. Finally, if you choose not to spend all of your money, the satisfaction you gain from your saving or holding each dollar must equal the satisfaction you would gain from spending it on some other good.

 Table 2 Total (TU) and Marginal (MU) Utilities for Ice Cream Cones When the Price of Macadamia Nut Crunch Rises to \$2 per Cone Macadamia Nut Crunch Chocolate Quantity TU MU MU/P Quantity TU mu MU/P 1 8 8 4.0 1 5 5 5.0 2 15 7 3.5 2 9 4 4.0 3 21 6 3.0 3 12 3 3.0 4 25 4 2.0 4 14 2 2.0 5 28 3 1.5 5 15 1 1.0 6 30 2 1.0 6 15 0 0 7 31 1 0.5 8 31 0 0

### The Law of Diminishing Marginal Utility

The declining marginal utility from lemonade as you drink more and more during a given time interval occurs with virtually all goods and all people. Observing that similar reactions were common, classical economists generalized this behavior into

The law of diminishing marginal utility: The marginal utility from consuming equal units of a good eventually declines as the amount consumed increases.

The word “eventually” is important. Horror movie fanciers might enjoy their first movie this week immensely and their second film even more. But they almost certainly will not enjoy their sixteenth movie of the week as much as their third. Benjamin Franklin’s observation in Poor Richard’s Almanac, “Fish and visitors stink in three days,” says far more about the diminishing marginal utility of visitors than about the deterioration of fish.

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Author: Ralph Byrns

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