Arya is a soccer player. If she is healthy she makes 1000000 a year. She may...

Arya is a soccer player. If she is healthy she makes 1000000 a year. She may get injured. If she gets injured and cannot play she will only get 160000 instead. The probability of her getting injured is 25%. She has the following utility function for consumption

U(c)=sqrt(c)

(a) What is her expected consumption from playing soccer?

(b) What is her expected utility from playing soccer?

(c) Prove that she is risk-averse.

(d) Someone offers her a job as a host for a TV show that pays $700000 a year. Will she accept it? Why/ Why not? Show me your work.

(e) What is the lowest paying job she will accept to quit her soccer career and not have any income uncertainty?

(f) She is thinking about buying insurance against injury. Draw her budget constraint with insurance coverage. Label it well.

(g) What is the fair price for her? How much insurance will she buy if this insurance price is available? Show your work

Arya 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 Arya, 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 Arya 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.

Expert Solution

Rahul Sunny answered 2 years ago

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