Billy John Pigskin of Mule Shoe, Texas, has a von Neumann- Morgenstern utility function of the form u(c) = √ c. Billy John also weighs about 300 pounds and can outrun jackrabbits and pizza delivery trucks. Billy John is beginning his senior year of college football. If he is not seriously injured, he will receive a $1,000,000 contract for playing professional football. If an injury ends his football career, he will receive a $10,000 contract as a refuse removal facilitator in his home town. There is a 10% chance that Billy John will be injured badly enough to end his career.
(a) What is Billy John’s expected utility?
(b) If Billy John pays $p for an insurance policy that would give him $1,000,000 if he suffered a career-ending injury while in college, then he would be sure to have an income of $1, 000, 000 − p no matter what happened to him. Write an equation that can be solved to find the largest price that Billy John would be willing to pay for such an insurance policy.
(c) Solve this equation for p.