Problem 2. The owner of an automobile is risk-averse and has the following vN-M utility

function, u (w) = w , where W denotes the automobile value that we will assume equal to

62,500. An accident may occur with probability p. If so, the value of the car becomes

10,000. In this market there is an insurance company that is willing to offer full insurance

at price (premium) . That is, if the car owner pays , the owner will obtain full compensation

for the damages in case of accident.

a) Write down the lotteries faced by the consumer. When will the car-owner be

willing to buy the insurance, in general? Try to get an expression.

b) Next we assume a risk-neutral and non-for-profit insurance company? What would be the premium charged by this insurance company (in general)? What will the premium be if the probability of having an accident is p=0.1? Explain your answer.

c) Suppose now that the probability of having an accident is p=0.1, and the individual can buy partial insurance. Partial insurance works as follows: if the individual buys, say, insurance, where is a constant between 0 and 1, he must pay the premium 9,000 up front. With this insurance, in the event of an accident, the individual gets a payout from the company of times his loss, or 52,500. Write down the lottery in general. If =0.9, will the owner buy that insurance?

d) If the individual can insure partially and he could pick the insurance level he purchases, what level of insurance would he select? (State the problem, and try to solve it numerically).