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.If this policy is priced at $40,what is the change in your expected utility if you purchase the policy rather than no insurance?

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.If this policy is priced at $40,what is the change in your expected utility if you purchase the policy rather than no insurance?

Quizplus · Accepted Answer

The expected utility of having no insurance is (0.9)*(1+$10000) + (0.1)*(1+$8100) = $9910.
The expected utility of purchasing the policy is (0.9)*(1+($10000-$40-$40)) + (0.1)*(1+($8100-$40-$1900)) = (0.9)*(1+$9920) + (0.1)*(1+$8020) = $9919.2.
The change in expected utility is $9919.2 - $9910 = $9.2 in favor of purchasing the insurance which is equivalent to an increase of (9.2/$9910) = 0.00093 or 0.093% in expected utility. Therefore, the best choice is to purchase the insurance. 
Option B is the closest answer (0.8) to the calculated change in expected utility (0.093), so it is the most appropriate choice.

Your Current Disposable Income Is $10,000