# What is Billy Johns expected utility?

Billy John Pigskin of Mule Shoe Texas has a von Neumann-Morgenstern utility function of the form . Show more Billy John Pigskin of Mule Shoe Texas has a von Neumann-Morgenstern utility function of the form . 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 \$1000000 contract to play professional football. If an injury ends his football career he will receive a \$10000 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 Johns expected utility? __________ (b) If Billy John pays \$p for an insurance policy that would give him \$1000000 if he suffers a careerending injury in college then he would be sure to have an income of \$1000 000 p no matter what happened to him. Write an equation that can be solved to find the largest price Billy John would be willing to pay for such an insurance policy. __________ (c) Solve this equation for p. __________ Show less

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