Now consider a different insurance company that does not have the inclination to tailor contracts specifically to individuals. Instead, it will offer a “standard contract” with the premium r =$100 and payout q=$500 to anyone who will purchase it. a. Peter has healthy-state income IH = $500 and sick-state income IS = $0. He has probability of illness p=0.1. Is the standard contract fair and/or full for Peter? If he ends up getting sick, what will his final income be? b. Tim has IH = $500 and IS = $0, but a probability of illness p = 0.2, higher than Peter’s. Is the standard contract fair and/or full for Tim? How does purchasing the standard contract affect Tim’s expected income?c. Jay has IH =$1, 000 and IS =$0, with probability of illness p=0.2. Is the standard contract fair and/or full for Jay?d. Suppose there is a customer named Ronald for whom the standard contract is partial and actuarially unfair in the insurance company’s favor. Give a set of possible values for Ronald’s IH, IS, and p. Recall that we always assume IH >IS. e. Now suppose that we have learned that Ronald’s IS =$200, but we do not know the value of his healthy-state income, or his probability of falling ill. Derive an upper bound for p and a lower bound for IH.f True or false: if we assume all four individuals are risk-averse, then we know that Tim has the most to gain by taking up the contract. Justify your answer.
Now consider a different insurance company that does not have the inclination to tailor contracts specifically to individuals. Instead, it will offer a “standard contract” with the premium r =$100 and payout q=$500 to anyone who will purchase it.
a. Peter has healthy-state income IH = $500 and sick-state income IS = $0. He has probability of illness p=0.1. Is the standard contract fair and/or full for Peter? If he ends up getting sick, what will his final income be?
b. Tim has IH = $500 and IS = $0, but a probability of illness p = 0.2, higher than Peter’s. Is the standard contract fair and/or full for Tim? How does purchasing the standard contract affect Tim’s expected income?
c. Jay has IH =$1, 000 and IS =$0, with probability of illness p=0.2. Is the standard contract fair and/or full for Jay?
d. Suppose there is a customer named Ronald for whom the standard contract is partial and actuarially unfair in the insurance company’s favor. Give a set of possible values for Ronald’s IH, IS, and p. Recall that we always assume IH >IS.
e. Now suppose that we have learned that Ronald’s IS =$200, but we do not know the value of his healthy-state income, or his probability of falling ill. Derive an upper bound for p and a lower bound for IH.
f True or false: if we assume all four individuals are risk-averse, then we know that Tim has the most to gain by taking up the contract. Justify your answer.
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