Expected utility & Insurance (for risk adverse individuals)?
John is a professional football player and next year will be able to sign a $25 million contract if he does not get injured this year. If he gets injured this year, his value will be significantly reduced and he will only be able to sign a contract for $5 million. Suppose that the probability he gets injured is 5%. His utility function is of the form U = W^(1/2), where W is his wealth. (therefore he is risk adverse).
Suppose that an insurace company offers to insure him at a premium of $0.10 per $1 of coverage. Would John choose to FULLY insurance himself? (hint: think of the idea of actuarilly fair/unfair game) Explain, and show graphically.
I am very confused by this question and I don't even know where to begin. Can someone kindly explain the answer to this question. If at all possible, please explain how the graph would look like as well.
Your help is very much appreciated!:)
[note: this question is posted eariler in other forum, yet nobody has answered it so far]