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. If this policy is priced at $40, what is the change in your expected utility if you purchase the policy rather than no insurance?
A)1
B)0.8
C)0.2
D)0

Question

Quizplus · Accepted Answer

Without insurance:
- Expected utility: √10000 = 100
- Expected utility in case of accident: √8100 = 90

With insurance:
- Expected utility: √9960 = 99.799
- Expected utility in case of accident: √8100 = 90

Therefore, the change in expected utility is:

ΔU = EU with insurance - EU without insurance
ΔU = 99.799 - 100
ΔU = -0.201

So, the change in expected utility is negative, which means that purchasing the insurance decreases your expected utility. Therefore, the best choice is not to purchase the insurance.

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

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