Utility and Preferences

Individuals consume goods and services because they derive pleasure or satisfaction from doing so. Economists use the term utility to describe the pleasure or satisfaction that a consumer obtains from his or her consumption of goods and services. Utility is a subjective measure of pleasure or satisfaction that varies from individual to individual according to each individual's preferences. For example, if an individual's choices for a Saturday evening are to watch television, go out to dinner, or go to a movie, then, depending on that individual's preferences, he or she will attribute different levels of utility to each of these three activities. Of course, it is not possible to measure utility, nor is it possible to claim that one individual's utility is higher than another's. Utility is just a unitless measure that economists have found useful in their explanation of consumer choice.

Total and marginal utility. The utility that an individual receives from consuming a certain amount of a particular good or service is referred to as that individual's total utility. The marginal utility of a good or service is the addition to total utility that an individual receives from consuming one more unit of that good or service.

Law of diminishing marginal utility. The law of diminishing marginal utility states that the marginal utility that one receives from consuming successive units of the same good or service will eventually decrease as the number of units consumed increases. As an example of the law of diminishing marginal utility, consider the utility that one obtains from drinking successive glasses of lemonade on a hot day. Suppose the first glass just begins to quench one's thirst. After two glasses, however, the thirst has all but disappeared. A third glass of lemonade might also provide some utility, but not as much as the second glass. A fourth glass cannot be finished. In this example, the marginal utility—the addition to total utility that one obtains from drinking lemonade on a hot day—is increasing for the first two glasses but is decreasing beginning with the third glass and would continue to decrease if one were to consume further glasses.

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Consumer Surplus

The difference between the maximum price that consumers are willing to pay for a good and the market price that they actually pay for a good is referred to as the consumer surplus. The determination of consumer surplus is illustrated in Figure , which depicts the market demand curve for some good.

The market price is $5, and the equilibrium quantity demanded is 5 units of the good. The market demand curve reveals that consumers are willing to pay at least $9 for the first unit of the good, $8 for the second unit, $7 for the third unit, and $6 for the fourth unit.

However, they can purchase 5 units of the good for just $5 per unit. Their surplus from the first unit purchased is therefore $9 ‐ $5 = $4. Similarly, their surpluses from the second, third, and fourth units purchased are $3, $2, and $1, respectively. These surpluses are illustrated by the vertical bars drawn in Figure . The sum total of these surpluses is the consumer surplus: 

The value $10, however, is only a crude approximation of the true consumer surplus in this example. The true consumer surplus is given by the area below the market demand curve and above the market price. This area consists of a triangle with base of length 5 and height of length 5. Applying the rule for the area of a triangle—one half the base multiplied by height—one finds that the value of the consumer surplus in this example is actually 12.5.

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Individual Demand Market Demand

The consumer equilibrium condition determines the quantity of each good the individual consumer will demand. As the example above illustrates, the individual consumer's demand for a particular good—call it good X—will satisfy the law of demand and can therefore be depicted by a downward‐sloping individual demand curve. The individual consumer, however, is only one of many participants in the market for good X. The market demand curve for good X includes the quantities of good X demanded by all participants in the market for good X. The market demand curve is found by taking the horizontal summation of all individual demand curves. For example, suppose that there were just two consumers in the market for good X, Consumer 1 and Consumer 2. These two consumers have different individual demand curves corresponding to their different preferences for good X. The two individual demand curves are depicted in Figure , along with the market demand curve for good X.

The market demand curve for good X is found by summing together the quantities that both consumers demand at each price. For example, at a price of $1, Consumer 1 demands 2 units while Consumer 2 demands 1 unit; so, the market demand is 2 + 1 = 3 units of good X. In more general settings, where there are more than two consumers in the market for some good, the same principle continues to apply; the market demand curve would be the horizontal summation of all the market participants' individual demand curves.

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Consumer Equilibrium Changes in Prices

The consumer's choice of how much to consume of various goods depends on the prices of those goods. If prices change, the consumer's equilibrium choice will also change. To see how, consider again the example considered above where the consumer must decide how much to consume of goods 1 and 2. Suppose that the price of good 1 increases from $2 per unit to $3 per unit, while the price of good 2 remains unchanged at $1 per unit. Everything else remains the same; the consumer's budget is still $5, and the marginal utility that the consumer receives from each additional unit of goods 1 and 2 is unchanged. However, the ratio of the marginal utility of good 1 to the price of good 1 is now changed, due to the increase in the price of good 1. The new situation is reported in Table .

The increase in the price of good 1 to $3 lowers the marginal utility per dollar spent on good 1 relative to the case where the price of good 1 was $2. The new consumer equilibrium is found as before, by comparing the marginal utility per dollar spent on good 1 with the marginal utility per dollar spent on good 2. The consumer's new equilibrium choice is to consume 1 unit of good 1 and 2 units of good 2 because these quantities have the same marginal utility per dollar spent, and the purchase of these quantities completely exhausts the consumer's budget of $5.

The effect of a price change on the consumer's equilibrium choice is often divided into two effects—known at the substitution effect of a price change and the income effect of a price change.

Substitution effect of a price change. When the price of a good changes, the price of that good relative to the price of other goods also changes. Relative price changes cause consumers to substitute from one good to another—this is known as the substitution effect. The substitution effect is illustrated in the example considered above. As the price of good 1 rises from $2 to $3, good 1 becomes more expensive relative to good 2, and good 2 becomes less expensive relative to good 1. The consumer's response to the price increase is to substitute her consumption away from good 1 and toward good 2; she changes her consumption choice from 2 units of good 1 and 1 unit of good 2 to 1 unit of good 1 and 2 units of good 2.

Income effect of a price change. The income effect takes account of how price changes affect consumption choices by changing the real purchasing power or real income of the consumer. In the example above, the increase in the price of good 1 from $2 to $3 reduces the consumer's real purchasing power. Prior to the price change, the consumer was able to purchase 2 units of good 1 and 1 unit of good 2 using her budget of $5. After the price of good 1 rises to $3, the consumer is no longer able to purchase this same bundle of goods because it would cost $7 and she has only $5. Accordingly, she must reduce her expenditures. The portion of her change in the consumption of good 1 that is attributable to the change in her real purchasing power or real income is the income effect of the price change.

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Consumer Equilibrium

When consumers make choices about the quantity of goods and services to consume, it is presumed that their objective is to maximize total utility. In maximizing total utility, the consumer faces a number of constraints, the most important of which are the consumer's income and the prices of the goods and services that the consumer wishes to consume. The consumer's effort to maximize total utility, subject to these constraints, is referred to as the consumer's problem. The solution to the consumer's problem, which entails decisions about how much the consumer will consume of a number of goods and services, is referred to as consumer equilibrium.

Determination of consumer equilibrium. Consider the simple case of a consumer who cares about consuming only two goods: good 1 and good 2. This consumer knows the prices of goods 1 and 2 and has a fixed income or budget that can be used to purchase quantities of goods 1 and 2. The consumer will purchase quantities of goods 1 and 2 so as to completely exhaust the budget for such purchases. The actual quantities purchased of each good are determined by the condition for consumer equilibrium, which is 

This condition states that the marginal utility per dollar spent on good 1 must equal the marginal utility per dollar spent on good 2. If, for example, the marginal utility per dollar spent on good 1 were higher than the marginal utility per dollar spent on good 2, then it would make sense for the consumer to purchase more of good 1 rather than purchasing any more of good 2. After purchasing more and more of good 1, the marginal utility of good 1 will eventually fall due to the law of diminishing marginal utility, so that the marginal utility per dollar spent on good 1 will eventually equal that of good 2. Of course, the amount purchased of goods 1 and 2 cannot be limitless and will depend not only on the marginal utilities per dollar spent, but also on the consumer's budget.

An example. To illustrate how the consumer equilibrium condition determines the quantity of goods 1 and 2 that the consumer demands, suppose that the price of good 1 is $2 per unit and the price of good 2 is $1 per unit. Suppose also that the consumer has a budget of $5. The marginal utility ( MU) that the consumer receives from consuming 1 to 4 units of goods 1 and 2 is reported in Table . Here, marginal utility is measured in fictional units called utils, which serve to quantify the consumer's additional utility or satisfaction from consuming different quantities of goods 1 and 2. The larger the number of utils, the greater is the consumer's marginal utility from consuming that unit of the good. Table also reports the ratio of the consumer's marginal utility to the price of each good. For example, the consumer receives 24 utils from consuming the first unit of good 1, and the price of good 1 is $2. Hence, the ratio of the marginal utility of the first unit of good 1 to the price of good 1 is 12.

The consumer equilibrium is found by comparing the marginal utility per dollar spent (the ratio of the marginal utility to the price of a good) for goods 1 and 2, subject to the constraint that the consumer does not exceed her budget of $5. The marginal utility per dollar spent on the first unit of good 1 is greater than the marginal utility per dollar spent on the first unit of good 2(12 utils > 9 utils). Because the price of good 1 is $2 per unit, the consumer can afford to purchase this first unit of good 1, and so she does. She now has $5 − $2 = $3 remaining in her budget. The consumer's next step is to compare the marginal utility per dollar spent on the second unit of good 1 with marginal utility per dollar spent on the first unit of good 2. Because these ratios are both equal to 9 utils, the consumer is indifferent between purchasing the second unit of good 1 and first unit of good 2, so she purchases both. She can afford to do so because the second unit of good 1 costs $2 and the first unit of good 2 costs $1, for a total of $3. At this point, the consumer has exhausted her budget of $5 and has arrived at the consumer equilibrium, where the marginal utilities per dollar spent are equal. The consumer's equilibrium choice is to purchase 2 units of good 1 and 1 unit of good 2.

The condition for consumer equilibrium can be extended to the more realistic case where the consumer must choose how much to consume of many different goods. When there are N > 2 goods to choose from, the consumer equilibrium condition is to equate all of the marginal utilities per dollar spent, 

subject to the constraint that the consumer's purchases do not exceed her budget.

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