John has the following possible losses:

Loss Amount Probability

$0 0.88

$3,500 0.10

$40,000 0.02

John's wealth today is $40,000 and his utility function isu(w) = 100w^0.4.

Part 1:What is John's expected utilitywithoutinsurance?

Part 2:If John can transfer his risk to an insurer for a premium of $800 , what is his expected utility with insurance?

Part 3:Would John purchase the insurance at that premium level? Be sure to support your answer.

Part 4:What is themaximum premiumJohn would pay for insurance?