Question

Herr Fenderbender considers himself a great driver. He has just received a Mercedes sports car as a gift from his uncle. His car is worth $90 000, but will have a scrap value of $10 000 in the event of a collision, an event that will occur with a probability of 0.4. He is offered the following insurance policy: In the event of a collision the insurance company will pay Herr Fenderbender $80 000. The insurance company is asking a premium of R = $27 500 which Fenderbender has to pay if the policy is accepted, whether or not there is a collision. Herr Fenderbender has a (von-Neumann Morgenstern) utility function of wealth given by : U= W^1/2

A.Should Herr Fenderbender purchase this insurance? Explain carefully.

B.Should the insurance company be offering him this insurance (the insurance company has a lot of customers and hence is risk neutral; i.e. it has utility function

U =x).

C.Repeat A and B for the case where the insurance premium is R = $37 100.

D.Find the range of values of the insurance premium, R, which will be accepted by Fenderbender AND which the insurance company would be willing to offer. E.Suppose now that the insurance company knows that Herr Fenderbender is a good driver but believes that due to the moral hazard problem, after the insurance policy has been purchased the probability that there will be a collision will rise to 0.5. What does the insurance company believe its expected profit from sale of the policy is, and should the insurance company sell Fenderbender that policy? (R = $37 100)

Answer 1

The below answer sheet considering 4 pages. First i have provided all the given values provided in the question, then used the Von Neuman Morgenstern utility functions in order to calculate the expected utility. Higher value of the expected utility willbe accepted.