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 ,where I is income.What is the fair price of this policy?

Question

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  ,where I is income.What is the fair price of this policy?

Quizplus · Accepted Answer

To find the fair price of the policy, we need to calculate the expected utility with and without the policy. 
Without the policy, the expected utility is:
0.9*U($10,000) + 0.1*U($8,100) = 0.9*(11ln(10,000)) + 0.1*(11ln(8,100)) = 9.62

With the policy, the expected utility is:
0.9*U($9,810) + 0.1*U($8,910) = 0.9*(11ln(9,810)) + 0.1*(11ln(8,910)) = 9.61

The difference in expected utility is 0.01. Using the risk premium method, the fair price of the policy is equal to the expected cost of the loss, which is 0.1*$1,900 = $190. Therefore, the best choice is B.

Your Current Disposable Income Is $10,000