Question:

Jacob plays in the NFL (National Football League) and next year will be able to sign a $25 million contract if he does not get injured this year. If he gets injured this year, his value will be significantly reduced and he will only be able to sign a contract for $5 million. Suppose that the probability he gets injured is 5%. His utility function is of the form U = √W, where W is his wealth.

1.What is Jacob’s expected utility?

2.What is the certainty equivalent of the risky prospect he faces?

3.What is his reservation price for an insurance policy that offers him full coverage in the event of loss?

4.Suppose that an insurance company offers to insure him at a premium of $0.10 per $1 of coverage. Would Jacob fully insurance himself? If not, how much will he insurance?

Thanks in advance.