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 I_H = $500 and sick-state income I_S = $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 I_H= $500, and I_S = $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 I_H = $1,000 and I_S = $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 I_H, IS, and p. Recall that we always assume I_H > I_S.

e. Now suppose that we have learned that Ronald’s I_S = $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 I_H.

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.