Anyone in this position may not be attending class or reading the text book. If you are taking a class and paying ANY attention AT ALL you simply MUST have SOME clue. If you REALLY have no clue after reading your text and attending class, perhaps you are in the wrong class? Perhaps you need to go have a maningful chat with yout academic advisor.I am very confused by this question and I don't even know where to begin.
Having said that:
His expected utility, without insurance is simply: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).
First, we would have to define what "fully" means. Does it mean $25 MM? Does it mean the Expected Utility from above? Perhaps it means to pay $20 MM if he is injured?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?
In the last case, he is out $2,000 right from the start. What say you? What, exactly, does "fully" mean?