Your current disposable income is $10,000. There is a 10% chance you will get in a serious car accident, incurring damage of $1,900. (There is a 90% chance that nothing will happen.)Your utility function is $U = \sqrt { I }$ ,where I is income. What is the most you would be willing to pay for this policy (rather than no insurance)?
A)$100
B)$190
C)$199
D)$270

Question

Quizplus · Accepted Answer

The most one would be willing to pay for insurance is the difference between the expected utility without insurance and the utility of the expected income with insurance. Without insurance, the expected utility is $0.1 \times \sqrt{8100} + 0.9 \times \sqrt{10000}$. With insurance, if you pay a premium $P$, your income will be $10000 - P$ with certainty, so your utility will be $\sqrt{10000 - P}$. Setting these equal and solving for $P$ gives the maximum premium you would be willing to pay. Calculating directly might be complex without the exact math, but the principle is to find $P$ that equates the expected utility without insurance to the utility with insurance. Given the options, $C$ $199 is the closest to representing the maximum amount one would rationally pay for insurance to match the expected utility without insurance.

Your Current Disposable Income Is $10,000 U=IU = \sqrt { I }U=I​

Your Current Disposable Income Is $10,000 $U = \sqrt { I }$