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 fair price of this policy?
A)$100
B)$190
C)$199
D)$270

Question

Quizplus · Accepted Answer

The expected cost of the insurance policy is: (0.1)(1,900) = $190. 
Without insurance, the expected utility of income is: (0.9)(√(10,000)) + (0.1)(√(8,100)) ≈ 94.24.
With insurance, the expected utility of income is: (0.9)(√(8,100)) + (0.1)(√(8,100)) ≈ 89.99.
Therefore, the expected utility of income with insurance is lower than the expected utility of income without insurance. This means that buying the insurance policy is not the best choice.

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

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