Sunday  July 14, 2024
 AmosWEB means Economics with a Touch of Whimsy!
 HOMOGENEOUS OF DEGREE N: A property of an equation the exists if independent variables are increased by a constant value, then the dependent variable is increased by the value raised to the power of n. The value of n can be greater than, less than, or equal to one. This property often surfaces in the analysis of production functions. If n = 1, then a doubling independent variables results in a doubling of the dependent variable and the production function has constant returns to scale. If n > 1, then a doubling independent variables results in more than a doubling of the dependent variable and the production function has increasing returns to scale. If n < 1, then a doubling independent variables results in less than a doubling of the dependent variable and the production function has decreasing returns to scale.

MARGINAL UTILITY OF INCOME:

The change in utility resulting from a given change in income. This is a specialized case of the general notion of marginal utility, which is simply the change in utility resulting from a given change in the consumption of a good. Marginal utility of income is key to identifying alternative risk preferences, including risk aversion, risk neutrality, and risk loving. These three risk preferences are indicated by three marginal utility of income possibilities, decreasing (risk aversion), increasing (risk loving), and constant (risk neutrality).
The marginal utility of income is defined as the incremental change in utility (or satisfaction) that is due to a unit change in income. The broader concept of marginal utility is the change in utility resulting from a given change in the consumption of a good. The assumption of decreasing marginal utility is important to understanding the negative slope of the market demand curve.

As a general rule the marginal utility of income also declines with an increase in income. However, it can also increase or remain constant. Decreasing marginal utility of income gives rise to risk aversion. Increasing marginal utility of income leads to risk loving. And constant marginal utility of income is the source of risk neutrality.

Differences in the marginal utility of income indicate the relative value a person places on risky income. If a person stands a risky chance of winning or losing income, the marginal utility of income determines how much the person values the income lost versus the income gained.

Risk Preferences

Some people enjoy a risky situation and others do not. This gives rise to three alternative risk preferences -- risk aversion, risk neutrality, and risk loving. These three alternatives are more precisely defined based on the marginal utility of income. As a general rule the marginal utility of income 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.

The three risk preferences are risk aversion, risk neutrality, and risk loving.

• Risk Aversion: This exists when a person has decreasing marginal utility of income. A risk averse person prefers certain income to risky income. With decreasing marginal utility of income the utility obtained from the income won is less than from 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. A risk averse person is better off not wagering.

• Risk Neutrality: This exists when a person has constant marginal utility of income. A risk neutral person prefers certain income equally to risky income. With constant marginal utility of income the utility obtained from the income won is the same as from the income lost. 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 neutral person is indifferent about wagering.

• Risk Loving: This exists when a person has increasing marginal utility of income. A risk loving person prefers risky income to certain income. With increasing marginal utility of income the utility obtained from the income won is greater than from the income lost. Even though the expected income is equal to the certain income, the utility obtained from the risky income exceeds the utility obtained from the certain income. A risk loving person is better off wagering.

Three Curves

Marginal Utility of Income

The three risk preferences are graphically illustrated using marginal utility of income curves. The exhibit to the right does the deed. The horizontal axis measures income and the vertical axis measures utility.

The three alternatives for the marginal utility of income are:

• Decreasing -- Aversion: In this case the marginal utility of income decreases with an increase in income. Click the [Decreasing] button to show the corresponding curve. Note that the curve is relatively steep at low levels of income, then flattens as income increases. A decreasing marginal utility of income gives rise to risk aversion, in which a person prefers certain income over an equal amount of risky income. This occurs because a risk averse person places a greater value on a decrease in income than on an increase in income.

• Constant -- Neutrality: A second alternative exists in which the marginal utility of income is constant. Click the [Constant] button to show the this curve. Note that the curve is a straight line and has a constant slope at all levels of income. A constant marginal utility of income gives rise to risk neutrality, in which a person prefers certain income equally to risky income. This occurs because a risk neutral person places the same value on a decrease in income as on an increase in income.

• Increasing -- Loving: The third alternative is that the marginal utility of income increases with an increase in income. Click the [Increasing] button to show this third curve. Note that the curve is relatively flat at low levels of income, then steepens as income increases. An increasing marginal utility of income gives rise to risk loving, in which a person prefers risky income over an equal amount of certain income. This occurs because a risk loving person places a greater value on an increase in income than on a decrease in income.
The marginal utility of income and corresponding risk preference is not necessarily an intrinsic, unchanging characteristic of a person (like eye color or DNA), but is likely to change as a person's individual circumstances change. That is, a person might have decreasing marginal utility of income over some ranges of income, then increasing marginal utility of income over other ranges, with constant marginal utility of income arising during the transition from one to the other.

 <= MARGINAL UTILITY CURVE MARGINAL UTILITY-PRICE RATIO =>

Recommended Citation:

MARGINAL UTILITY OF INCOME, AmosWEB Encyclonomic WEB*pedia, http://www.AmosWEB.com, AmosWEB LLC, 2000-2024. [Accessed: July 14, 2024].

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