RISK NEUTRALITY: A preference for risk in which a person is indifferent between guaranteed or certain income over risky income. Risk neutrality arises due to constant marginal utility of income. A risk neutral person has no preference for or against risk. This is one of three risk preferences. The other two are risk aversion and risk loving. Risk neutrality is one of three alternative preferences for risk based on the marginal utility of income. A risk neutral person has constant marginal utility of income. With constant marginal utility of income a risk neutral person obtains the same utility from certain income as an equal amount of income involving risk. With risk, the utility from winning is the same as the utility from losing. The expected income is equal to the certain income and the utility obtained from the certain income is the same as the utility obtained from the expected income. A risk averse person has no particular inclination for, or aversion from, risk. Two other risk preferences are risk aversion and risk loving. A risk averse person has decreasing marginal utility of income and prefers certain income to risky income. A risk loving person has increasing marginal utility of income and prefers risky income to certain income. Risk neutrality, as much as anything else, can be thought of as the dividing line between risk aversion and risk loving. Marginal Utility of Income Marginal Utility of Income The best place to begin a study of risk neutrality is the marginal utility of income. As a general concept, marginal utility is the change in utility resulting from a change in the quantity of a specific good consumed. Marginal utility of income is then the change in utility resulting from a change in income. The standard view in consumer demand theory is that the marginal utility of income decreases with an increase in the quantity consumed. This gives justification for the negatively-sloped demand curve. This view also generally applies to the marginal utility of income. An increase in income results in a decrease in marginal utility. Decreasing marginal utility of income results in risk aversion. However, the marginal utility of income can also increase, leading to risk loving. Or the marginal utility of income can remain constant, leading to risk neutrality. The exhibit to the right presents constant marginal utility of income. The slope of the line is the same at all levels of income. Constant marginal utility of income, represented by a straight line, is the key to risk neutrality. Increasing and decreasing marginal utility of income, represented by a convex curve and a concave curve, give rise to risk loving and risk aversion, respectively. Risk or Certainty? Risk neutrality is revealed by preferences for income obtained with certainty and an equal amount of income that involves risk. Consider these two related concepts: Certain Income: This is income obtained with absolutely certainty. There is no risk involved. In this analysis of risk neutrality, certain income can be thought of as the amount of income that a person has without engaging in a risky situation or wager. There is no chance of receiving any more income or any less income. Risky Income: This is income based on the results of a risky situation, such as a wager. The risky situation might result in more income or less income. The amount of risky income is specified as the expected value, a balance between the probability of the lost income and the probability of gained income. Suppose, for example, that a hypothetical person such as Duncan Thurly has $100 of income and is confronted with a $50 wager on the flip of a coin. If the coin comes up heads, then he wins $50 and thus has a total of $150. If the coin comes up tails, then he loses $50 and thus has a total of only $50. The $100 that Duncan has at the start, and would keep if he did not wager, is the certain income. If he wants to keep this $100, then he can walk away from the wager. The risky income is the amount of income that he can expect to have after the wager. It's not $50 or $150, but the average of the two, $100, weighted by the probability of winning or losing. In other words, the expected income of a 50-50 wager is the amount of income he would expect to end up with after undertaking the wager a number of times, say a 100 or more. If he undertakes this wager 100 times, he can expect to win $50 exactly half of the time and lose $50 exactly half of the time. The loses exactly balance the wins and the income he can expect to end up with is $100. This can be summarized with the following equation. Expected Income = [(p) x income with loss] + [(1-p) x income with win] Expected Income = [(0.5) x $50] + [(0.5) x $150] Expected Income = $100 Expected income is the income generated by a loss, weighted by the probability of losing (p), plus the income generated by a win, weighted by the probability of win (1-p). The expression in the first set of brackets is the income from losing [(0.5) x $50]. The expression in the second set of brackets is the income from winning [(0.5) x $150]. The sum of the two expressions is the income expected from the wager, the average income obtained resulting after many wagers. The Utility of Income While income is obviously important, risk neutrality is indicated by the utility generated by the income. This is where constant marginal utility of income plays a key role. Two related utility concepts are worth noting. One is the utility of expected (or certain) income and the other is expected utility. Utility of Expected Income: This is simply the amount of utility generated by income. It is identified by a utility curve such as presented in the above exhibit. It is the utility generated by certain income. Or it is the utility associated with expected income. In the previous coin-flip example facing Duncan Thurly, the utility of certain income is equal to the utility of income expected. Expected Utility: This is the average utility expected from a risky situation. Like expected income, it is the utility obtained with a loss, weighted by the probability of losing, plus the utility obtained with a win, weighted by the probability of win. The utility of expected income is identified by first identifying the value of expected or average income resulting from the wager, then identifying the utility associated with this value. In contrast, expected utility is identified by separately calculating the income from a loss, and the corresponding and the income from a win, then determining the utility from each. These utility values are then averaged, weighted by the probability of a loss and a win. Expected Utility = [(p) x utility from income with loss] + [(1-p) x utility from income with gain] Working Through a Graph Risk Neutrality Risk aversion can be illustrated using a marginal utility of income curve, such as the one presented in the exhibit to the right. Income is measured on the horizontal axis and utility is measured on the vertical axis. The straight line presented reflects constant marginal utility of income. The slope of the curve is constant at all levels of income. Let's re-evaluate the $50 flip-of-a-coin wager facing Duncan Thurly. First: Take note of $100 of certain income that Duncan has before the wager. Click the [Certain Income] button to identify this amount. Also note the amount of utility generated by this $100 of certain income, measured as U(100) on the vertical axis. Second: Now consider the wager, with a 50-50 chance of Duncan winning or losing $50. Click the [Risky Income] button to identify the possible results. If Duncan loses, he ends up with $50. If he wins, he ends up with $150. Also note that the expected income for this wager is $100, which like certain income generates U(100) utility, as well. Third: Next up is calculating expected utility from the wager. This is accomplished by identifying the utility generated by each separate outcome of the wager. Click the [Expected Utility] button for this information. The utility generated by the income resulting from the loss is measured as U(50) and the utility generated by the income resulting from the win is measured as U(150). Expected utility is then the weighted average of these two values, weighted by the probabilities of winning and losing. It is the seen as the utility associated with the intersection of the $100 of income and a straight line connecting the two utility/income wager possibilities and is measured as EU(100). An important implication is that utility generated by the certain income, U(100), is exactly the same as the expected utility of the wager EU(100). This indicates that Duncan is risk neutral. He prefers certain income equally to risky income. Another important implication can also be had, the risk premium. This is the amount that Duncan would be willing to pay to avoid the risk or to engage in risk. There is no risk premium. Unlike a risk averse person or a risk loving person, Duncan is not willing to pay anything extra to avoid risk or to engage in risk. This can be seen by noting the amount of income that would generate the same utility as the expected utility of the wager. A click of the [Risk Premium] button highlights this point. Note that $100 of income generates the same utility, U(100), as the expected utility from the wager EU(100). Other Risk Preferences Risk neutrality is one of three risk preferences. The other two are risk aversion and risk loving. Risk Aversion: Risk aversion occurs when a person prefers certain income over risky income and arises due to decreasing marginal utility of income. A person with decreasing marginal utility of income obtains less utility from the income won than the income lost. The utility from winning is exceeded by the utility from losing. Even though the expected income is equal to the certain income, the utility obtained from the certain income is greater than of the utility obtained from the expected income. A risk aversion person is better off not wagering. Risk Loving: Risk loving occurs when a person prefers risky income over certain income and arises due to increasing marginal utility of income. A person with increasing marginal utility of income obtains more utility from the income won than the income lost. The utility from winning exceeds the utility from losing. Even though the expected income is equal to the certain income, the utility obtained from the certain income falls short of the utility obtained from the expected income. A risk loving person is better off by wagering. Check Out These Related Terms...      | risk preferences | risk aversion | risk loving | marginal utility of income | risk | uncertainty | risk pooling | risk premium | economics of uncertainty | Or For A Little Background...      | economics | microeconomics | market | scarcity | efficiency | sixth rule of ignorance | marginal utility | demand curve | paper economy | consumer demand theory | And For Further Study...      | public choice | economics of information | innovation | good types | market failures | financial markets | institutions | insurance | information | efficient information search | information search | asymmetric information | adverse selection | moral hazard | signalling | screening | rational ignorance | market failures | Recommended Citation:      RISK NEUTRALITY, AmosWEB Encyclonomic WEB*pedia, http://www.AmosWEB.com, AmosWEB LLC, 2000-2024. [Accessed: December 22, 2024].

Copyright ©2000-2024 AmosWEB*LLC