David's Utility Function If David's current wealth is $61,000, then
A) his gain in utility from gaining $1,000 is less than his loss in utility from losing $1,000. David is risk averse.
B) his gain in utility from gaining $1,000 is less than his loss in utility from losing $1,000. David is not risk averse.
C) his gain in utility from gaining $1,000 is greater than his loss in utility from losing $1,000. David is risk averse.
D) his gain in utility from gaining $1,000 is greater than his loss in utility from losing $1,000. David is not risk averse.

Question

David's Utility Function  If David's current wealth is $61,000, then
A) his gain in utility from gaining $1,000 is less than his loss in utility from losing $1,000. David is risk averse. 
B) his gain in utility from gaining $1,000 is less than his loss in utility from losing $1,000. David is not risk averse. 
C) his gain in utility from gaining $1,000 is greater than his loss in utility from losing $1,000. David is risk averse. 
D) his gain in utility from gaining $1,000 is greater than his loss in utility from losing $1,000. David is not risk averse.

Quizplus · Accepted Answer

The answer can be found by examining David's utility function. If the utility function is concave (i.e. exhibits diminishing marginal utility), David is risk averse. If the utility function is linear, David is risk-neutral. If the utility function is convex (i.e. exhibits increasing marginal utility), David is risk-loving.

From the provided utility function, we can see that it is concave (i.e. diminishing marginal utility of wealth), since the second derivative is negative. Therefore, David is risk averse.

Since David is risk averse, he values losses more than gains. This means that the loss in utility from losing $1,000 is greater than the gain in utility from gaining $1,000, given his current wealth of $61,000. Therefore, choice A is the correct answer.

David's Utility Function If David's Current Wealth Is $61,000