(a) A footballers utility function is () = . He earns $100 million a year if he is healthy, there is a 20% probability that he will get injured and earn $0. Calculate the following:

(i) Expected loss of the footballer. (2 marks)

(ii) Without any insurance, calculate the expected utility of the footballer. (3 marks)

(iii) What if the footballer purchases an insurance, calculate the expected utility of the footballer. (4 marks)

(iv) If the insurance premium is currently at $35,000,000, determine whether the footballer will purchase the insurance. (4 marks)

ANSWERS MUST TYPE