Question

Problem 2. Al Starr is a talented football player who is beginning his senior year. If he is not seriously injured, he will receive a $1 million contract for playing in the NFL. If an injury ends his football career, he will receive a $25,000 contract as a sports analyst. There is a 10% chance that Al will be injured badly enough to end his career. Al has expected utility preferences with utility function given by ?(?) = √?.

a) What is Al’s expected utility from playing football this year?

b) If Al pays $? for an insurance policy that would give him $1 million if he suffered a careerending injury, then he would be sure to have an income of ($? ??????? − $?) no matter what happened to him. Write an equation that can be solved to find the largest price that Al would be willing to pay for such an insurance policy.

c) Solve the equation in part b) for $?.

Answer 1

a) Expected earning = 0.9*1,000,000 + 0.1*25,000 = $902500

Expected utility = (Expected Earning)^0.5 = 950

b) Since Al will earn 1 million - x no matter what happens, he will try to earn at least as much as he would have expected to earn without the insurance i.e. $902500. Hence the required equation is:

1,000,000 - x = 902,500

c) Hence the maximum amount he would be would be willing to pay = $97,500

(Question is not clear whether the analyst job is still offered or not. If it is, then the equation would be: 1,002,500 - x = 902,500. In this case, answer to part c would be $100,000)