Matt's Utility Function If Matt's current wealth is $51,000, then
A) his gain in utility from gaining $1,000 is greater than his loss in utility from losing $1,000. Matt is risk averse.
B) his gain in utility from gaining $1,000 is greater than his loss in utility from losing $1,000. Matt is not risk averse.
C) his gain in utility from gaining $1,000 is less than his loss in utility from losing $1,000. Matt is risk averse.
D) his gain in utility from gaining $1,000 is less than his loss in utility from losing $1,000. Matt is not risk averse.

Question

Matt's Utility Function  If Matt's current wealth is $51,000, then
A) his gain in utility from gaining $1,000 is greater than his loss in utility from losing $1,000. Matt is risk averse. 
B) his gain in utility from gaining $1,000 is greater than his loss in utility from losing $1,000. Matt is not risk averse. 
C) his gain in utility from gaining $1,000 is less than his loss in utility from losing $1,000. Matt is risk averse. 
D) his gain in utility from gaining $1,000 is less than his loss in utility from losing $1,000. Matt is not risk averse.

Quizplus · Accepted Answer

We can determine whether Matt is risk averse by looking at the curvature of his utility function. This utility function is concave, which means that the more money Matt has, the less additional utility he gets from each additional dollar. This is typical of risk aversion.

If Matt's current wealth is $51,000, we can ask whether gaining or losing $1,000 will have a greater impact on his utility. According to the law of diminishing marginal utility, the first $1,000 he gains will have a larger impact on his utility than the second $1,000, and so on. Therefore, the gain in utility from gaining $1,000 will be less than the loss in utility from losing $1,000. This is consistent with risk aversion, and the answer is therefore C.

Matt's Utility Function If Matt's Current Wealth Is $51,000