Elizabeth is one of many athletes who are facing risk of injury for which the insurance company provides coverage. There are two groups of athletes. High-risk athletes who get injured 40% of the time and lower risk athletes, like Elizabeth, who get injured only 25% of the time. The insurance company cannot observe how high the risk of injury is for any athlete but they know that half of the athletes are high risk and the other half are low risk.

(h) What is the lowest price the insurance company is willing to offer if they can only offer one price and cannot discriminate? Show your work.

(i) Will Elizabeth get insured at this price? How much insurance will she buy? Why is this coverage amount different than the one above. Show your work.

(j) Discuss a real life example of the insurance problem we have in this question.