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# Utility, Subjective

BIBLIOGRAPHY

In economic theory, subjective utility is the satisfaction a consumer perceives to have received from consuming a product. Subjective utility is usually referred to simply as utility. The early economists Jeremy Bentham and John Stuart Mill maintained that the goal of society is to maximize the total utility of its members. In the early twenty-first century economists refer to this as welfare maximization. Utility theory begins with assumptions as to individuals preferences. When a consumer is willing to trade off one product or product attribute for another (for example, less engine power in exchange for improved gas mileage), it is said that the person has compensatory preferences. When a consumer is unwilling to trade off one product or product attribute for another regardless of the quantity of the second product offered (for example, a family of six needs a car with six seats no matter what the other attributes of the car are), it is said that the person has non-compensatory preferences. Economists typically assume compensatory preferences because they are intuitively justifiable, are easier to represent mathematically, and reflect the vast majority of true preferences. Preferences are typically represented by utility functions, which map consumption to utility.

Utility can be regarded as ordinal or cardinal. Cardinal utility is a numeric measure of utility, where units of utility are called utils. Ordinal utility is an ordering of objects according to utility. For example, an ordinal utility function might show a consumer deriving more utility from apples versus oranges, while a cardinal utility function might show a consumer deriving 100 units of utility from apples versus 80 units from oranges. Thus while ordinal utility is more realistic than cardinal utility in that it is difficult to measure utility numerically, cardinal utility can describe differing strengths of preference that ordinal utility cannot. Economists who use cardinal utility to describe consumer preferences note that, while consumers do not actually measure utility numerically, consumers behave (in the aggregate) as if such a measure were possible.

While utility cannot be directly measured, it is possible to obtain indirect measures by determining how much money a person must be given to compensate that person for the loss of a unit of product. For example, in an experiment a subject who has not eaten breakfast and who knows he or she will not eat dinner is given three slices of pizza for lunch. The person is then offered successively greater amounts of money in exchange for giving up one slice of pizza. The minimum amount of money the subject is willing to accept in exchange for the pizza is the dollar equivalent of the utility the subject expects to obtain from the slice of pizza.

Central to consumer theory is the idea of declining marginal utility. Marginal utility is the additional utility a consumer obtains from consuming one more unit of a product. Marginal utility is assumed to decline as more units of a product are consumed. For example, to a hungry person the first slice of pizza eaten yields significant marginal utility. The second slice yields less marginal utility, because the person has already consumed one slice of pizza and so is less hungry than he or she was prior to consuming the first slice. After consuming the second slice of pizza, the persons total utility is the marginal utility he or she received from the first slice plus the marginal utility he or she received from the second slice. The third slice of pizza yields less marginal utility than the second because the person is even less hungry than he or she was prior to the second slice. Eventually the person will have had enough slices of pizza that he or she does not want any more, even if the pizza is free. At this point the persons marginal utility has declined to zero (or may even be negative), consuming an additional slice of pizza will not increase the persons utility.

The phenomenon of declining marginal utility can be said to occur because consumers obtain utility from two sources: the good consumed and the variety the good represents. The level of variety measures how different the good is from other goods the consumer has consumed recently. For example, someone who is eating potato chips may stop eating not because he or she is full but because he or she is tired of potato chips and now seeks something different (like a soft drink). Without having had a drink, as the person eats more and more potato chips, the marginal utility of an additional potato chip falls because an additional potato chip is more and more like what the person has already consumed. Meanwhile the marginal utility of a soft drink rises because an additional soft drink is less and less like what the person has already consumed. Utility from variety explains why consumers tend to like to consume together things that are markedly different: beer and pizza, hot apple pie and cold ice cream, hot peppers in a sweet sauce.

If consumers can consume at no charge, they will seek out the goods that yield the greatest marginal utility. When consumers must pay for what they consume, they seek out the goods that yield the greatest marginal utility per dollar. This is the phenomenon that results in beer drinkers suddenly becoming scotch drinkers when the drinks are on the house. The consumer obtains greater marginal utility from a scotch than from a beer. But the difference in marginal utilities between the two drinks does not compensate for the difference in price between the two drinks. The consumer is said to attain the optimal consumption combination when the marginal utility per dollar for each of the goods the consumer is consuming is the same. For example, suppose a consumer obtains a marginal utility of 10 from 1 more cup of coffee and a marginal utility of 6 from 1 more bagel. If the bagel costs \$2 and the cup of coffee costs \$1, the consumer will purchase the bagel because the marginal utility per dollar for the bagel (6 / 1 = 6) is greater than that for the coffee (10 / 2 = 5). But having consumed the bagel, the consumers marginal utility for another bagel falls to (for example) 4. Now the marginal utility per dollar for the bagel (4 / 1 = 4) is less than that for the coffee (10 / 2 = 5). So the consumer buys a cup of coffee. Whenever the marginal utility per dollar for one good exceeds that of another good, the consumer consumes more of that good. In the extreme the consumer spreads his or her consumption dollars among many goods such that the marginal utility per dollar is the same for all the goods.

In the presence of uncertainty, consumers are said to maximize expected utility. Expected utility is the level of utility the consumer expects to obtain following resolution of the uncertainty. For example, suppose a person is offered a choice between \$50 cash and a lottery ticket that carries a 50 percent chance to win \$100 and a 50 percent chance to win nothing. The expected value of the lottery ticket is \$50 (\$50 = 0.5 × \$100 + 0.5 × \$0). The expected value of the lottery ticket is the same as the value of the cash. However, some consumers will choose the lottery ticket, while others will choose the cash. The consumers who choose the lottery ticket can be said to expect more utility from the lottery ticket than from the \$50 cash. These consumers are called risk preferential or risk lovers because, apart from the utility they would receive from the money, they receive additional utility from the existence of uncertainty. More formally, the utility the risk preferential consumer expects to get from the lottery ticket exceeds the utility the consumer would get from what he or she expects to win. A risk preferential person will tend to seek out risks even when there is a negative expected return associated with the risk. Similarly a risk averse consumer is one who, apart from the utility he or she would receive from the money, receives disutility from the existence of uncertainty. A risk averse person will tend to avoid risks even when there is a positive expected return associated with the risk. A risk neutral consumer is one who receives neither utility nor disutility from risk. A risk neutral person will neither seek out nor avoid risk for its own sake but will consider only the expected return associated with the risk. If the expected return is positive, the risk neutral person will undertake the risk. If the expected return is negative, the risk neutral person will avoid the risk.

Evidence suggests that peoples attitudes toward risk change depending on the size of the uncertainty relative to their wealth and whether the uncertainty involves gains or losses. On average, the less a persons wealth, the more risk preferential the person tends to be. Also people tend to be more risk preferential with respect to potential gains but risk averse with respect to potential losses. Hence, the same person may both play the lottery (an activity that increases risk but involves potential gain) and purchase insurance (an activity that decreases risk but involves a reduction in potential loss).

SEE ALSO Expected Utility Theory; Marginalism; Ordinality; Risk; Risk Neutrality; Risk Takers; Uncertainty; Utility Function; Utility, Objective; Utility, Von Neumann-Morgenstern

## BIBLIOGRAPHY

Samuelson, Paul A. 1938. The Empirical Implications of Utility Analysis. Econometrica 6 (4): 344356.

Varian, Hal R. 1992. Microeconomic Analysis. New York: Norton.

Von Neumann, John, and Oskar Morgenstern. 1944. Theory of Games and Economic Behavior. Princeton, NJ: Princeton University Press.

Walsh, Adrian, and Tony Lynch. 2003. The Development of Price Formation Theory and Subjectivism about Ultimate Values. Journal of Applied Philosophy 20 (3): 263278.

Antony Davies