Mia Dribble has a utility function u=W 2/3 . Mia is a basketball star starting her senior year. If she makes it through her senior year without a serious injury, she will receive a $8,000,000 contract for playing in the new professional women's basketball league (the $8,000,000 includes endorsements). If she injures herself, she will receive a $64,000 contract for selling concessions at the basketball arena. There is a 20 percent chance that Mia will injure herself badly enough to end her career.
(i) What is Mia's expected utility? What is the expected value and the variance of her income?
(ii) What is Mia's risk premium?
(iii) Suppose that Mia; is offered an insurance policy at the rate p=0.25 How much of insurance would Mia buy?