Ronaldo plays soccer for a living in a famous European club (A.C. Milan). Although he enjoys playing soccer he does it for the money, and derives utility from his yearly income playing soccer. Assume Ronaldo faces a utility function of the form U= 10\sqrt{I} , where log is the logarithm base 10, and I is Ronaldo's income. Assume also that Ronaldo is considering whether to play next season given that there is a 75% chance of injury, and therefore a loss in his yearly income of 10% for missed games and medical expenses.
a) If Ronaldo is paid $10,000,000 for the season. What is Ronaldo's Expected Utility if he decides to play the season? Use 6 decimal points when calculating U.
b) Assume that there is only one company that will insure Ronaldo. The insurance company offers to insure him for the fair premium plus an additional 5% of the fair premium. That is, the cost of the premium for Ronaldo is F.P*(1+0.05). Will Ronaldo purchase the insurance? Explain why or why not.
c) Finally, assume that Manchester United offers Ronaldo $9,245,000 regardless of wheter he has an injury or not in the upcoming season. Will Ronaldo accept this offer? Explain why or why not.
Please answer these questions in details.