Suppose a person's preferences over lotteries satisfy expected utility, with a utility index u(x) =ln(x). Their initial wealth is $10,000. They are a bad driver, so they have a 50% chance of crashing. Without insurance, a crash costs them $1,000. If they don't crash they keep all $10,000.

Problem 1.1

What is the maximum premium P this person would pay for an insurance policy that will fully repay their $1,000 loss in the event of a crash? How does that compare to the expected value of the cost of a crash?

Problem 1.2

What is the maximum premium P this person would pay for insurance that will pay only $500 in the event of a crash? (Remember, ln(x) + ln(y) = ln(xy).)

Problem 1.3

Does this person prefer the $1,000 insurance at the maximum premium P, the $500 insurance at the maximum premium P, or are they indifferent between the two policies?