Identifying probabilities can be either subjective or objective. Subjective probabilities depend on what a person thinks could (or should) happen. You think there is a "good chance," say 10%, that you will win the lottery. Objective probabilities are based on historical data, often adjusted with cause-and-effect links. You have one of the 10,000,000 lottery tickets sold, giving you a 0.00001% of winning.

People have different preferences about risk. Some prefer to avoid risk (risk aversion), others are indifferent (risk neutrality), while others enjoy risk (risk loving). Risk aversion in particular is a driving force behind the provision of insurance. Those who dislike risk are willing to pay to avoid it.

Risk versus Uncertainty

Uncertainty is simply the observation that the future is unknown. You don't know what will happen tomorrow. Any number of events might occur. You could eat a ham and swiss cheese sandwich for lunch. Or a meteor could crash through your ceiling and destroy your computer. Or you could have a pop quiz in your anthropology class. Or you might receive an unsolicited telemarketing phone call for vinyl siding. Or the battery in your car might go dead. A lot could happen. Almost anything is possible. Not knowing what will happen is uncertainty.

Risk, in contrast, is assigning quantitative probabilities to the possibilities. For example, you might have a 50% probability of eating a ham and swiss cheese sandwich for lunch tomorrow. And the probability of a meteor crashing through your ceiling and destroying your computer is only 0.00000000001%. An anthropology pop quiz might have a 10% chance of happening. The chance of a call from a vinyl siding telemarketer might be 20%. And a dead car battery has a 2% probability.

Assigning Risk

• Subjective: A common method, used by most people most of the time, of assigning risk probabilities to an uncertain future is subjectively. With this method the probability that an event will happen is based on a "feeling," "notion," or "gut reaction." This subjective feeling might be based on personal experiences or perceptions. It is seldom based on extensive information. It "seems" as though your anthropology instructor gives pop quizzes every other day, resulting in a subjective probability of 50%.


• Objective: The alternative method, one used by insurance companies, government policy makers, and financial investors, of assigning risk is objectively. With this method the probability is determined based on historical data, often with sophisticated statistical analysis. Based on 10 years of data, your anthropology instructor regularly gives 4 pop quizzes during a semester of 40 class periods, a 10% average. This overall average is qualified by noting that half of the quizzes are on Fridays and all come the week before a holiday. This information can be used to determine different quiz probabilities for any given class period.

Risk Preferences

These three alternatives can be more precisely defined based on the marginal utility of income. Marginal utility is the change in utility resulting from a given change in the consumption of a good. Marginal utility of income is then the change in utility resulting from a given change in income. The standard presumption is that marginal utility declines as more of a good is consumed, that is, decreasing marginal utility. As a general rule the marginal utility of income also declines with an increase in income. However, it can also increase or remain constant.

Suppose, for example, that you have $100 of income and are confronted with a $50 wager on the flip of a coin. If the coin comes up heads, then you win $50 and thus have a total of $150. If the coin comes up tails, then you lose $50 and thus have a total of only $50. Risk preferences determine your willingness to decline the wager and keep the $100 of income that you have (certain income) or agree to the wager not knowing whether you will win or lose (risky income).

It is important to note that the income expected from the wager (so called expected income) is actually equal to certain income ($100). That is, because the coin has an equal chance of coming up heads or tails, if you undertake this wager 100 times, you can expect to win 50 times and lose 50 times. The loses exactly equal the wins and the income you can expect the end up with is $100.

These three alternatives give rise to risk aversion, risk loving, and risk neutrality.

• Risk Aversion: This exists when a person has decreasing marginal utility of income. In this case you prefer the certain income to the risky income. With decreasing marginal utility of income you obtain less utility from the income won than the income lost. Even though the expected income is equal to the certain income, the utility obtained from the certain income exceeds the utility obtained from the expected income. The utility from winning is exceeded by the utility from losing. You are better off not wagering.


• Risk Loving: This exists when a person has increasing marginal utility of income. With increasing marginal utility of income you obtain more utility from the income won than the income lost. Even though the expected income is equal to the certain income, the utility obtained from the expected income exceeds the utility obtained from the certain income. The utility from losing is exceeded by the utility from winning. You are better off wagering.


• Risk Neutrality: This exists when a person has constant marginal utility of income. With constant marginal utility of income you obtain the same utility from the income won as the income lost. Not only is the expected income is equal to the certain income, the utility obtained from the expected income is equal to the utility obtained from the certain income. The utility from losing is matches by the utility from winning. You are equally well off wagering or not wagering.