a) If Ronaldo is paid $10,000,000 for the season. What is Ronaldo\'s Expected Ut
ID: 1094655 • Letter: A
Question
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 permium. That is, the cost of the premium for Ronaldo is F.P*(1+0.05). Will Ronaldo purchase the insurance? Explian 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.
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 permium. That is, the cost of the premium for Ronaldo is F.P*(1+0.05). Will Ronaldo purchase the insurance? Explian 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.Explanation / Answer
Ronaldo's utility function is given by 10*(I)1/2. So for an income of $10,000,000, Ronaldo's expected utility will be
10*(10000000)1/2 = 31627.766016 utils
No
He will pay a premium insurance only when the premium that he pays is less than the expected income next year. Other wise there is a high probability that he might pay a lot and not recover it next year.
The insurance company too will use the logic that it will calculate Ronaldo's expected earnings fo the next year and charge the same as the premium. So that the insurance company doesnt suffer any loss.
If he is injured then he lose 10% of his income. Or he loses $1,000,000
So his expected income will be $10,000,000*0.25 + $9,000,000*0.75 = $9,250,000 This is what he is expected to make next year. SO the difference is what will be charged as fair premium.
Or $750,000 * (1.05) =$787,500 is the premium. $9212,500 is what he will make if he pays for the insurance. This is less than his expected income. Now Ronaldo will not pay for this as he is paying an additional premium will lowers his expected income.
No he will still not accept this as it is lower than his original expected income of $9,250,000. But given a choice to choose between insurnace and fixed pay out, he will choose the later.
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