Q. Dan is a risk adverse individual who maximizes expected value of c1/2, where c is his wealth. Dan he has just bought his 18 year old son a car worth $15,000. After car purchase he has $100,000 in safe assets. Dan's son has a 20% chance of having an accident. If his son has an accident he will cause $5000 damage to car and $10,000 damage to others' property that Dan is responsible for.
a) What is his expected utility if he can't buy auto insurance?
b) Suppose he is offered fair insurance with a $3000 deductible. What premium will he pay and what will be his expected utility with insurance?
c) How much would he be willing to pay in additional premiums to eliminate deductible?
(Note that with this extra payment his insurance will not be fair.)