ONLY D,E,F

(a)Premium (r) = $100 Payout (q)= $500 Healthy state Income I_h = $500 Sick state Income I_s = $0 Probability of Illness = 0.10

Fair contract = Premium (r) = prob.(p) x payout (q) Unfair contact = Premium (r) > prob.(p) x payout (q) Unfair contract = $100 > .10 x $500 Unfair contact = $100 > $50 Expected profit = healthy income (I_h) - premium(r) Expected profit= $500 -$100 = $400 Expected profit = Sick income (IS) - premium(r) + payout(q) Expected profit = $0 - $100 + $500 Sick state income = $400 Its an unfair contract. Profit = $400

(b)Premium (r) = $100 Payout (q)= $500 Healthy state Income I_h = $500 Sick state Income I_S = $0 Probability of Illness = 0.20

Fair contract = Premium (r) = prob.(p) x payout (q) Unfair contact = Premium (r) > prob.(p) x payout (q) fair contract = $100 = 0.20 x $500 fair contact = $100 = $100 Expected profit = premium(r) - prob.(p) x payout(q) Expected profit= $100 - 0.20 x $500 Expected profit = $0 Its a fair contract. Profit = $0

(c)Premium (r) = $100 Payout (q)= $500 Healthy state Income I_h = $1000 Sick state Income I_S = $0 Probability of Illness = 0.20

Fair contract = Premium (r) = prob.(p) x payout (q) Unfair contact = Premium (r) > prob.(p) x payout (q) fair contract = $100 = .20 x $500 fair contact = $100= $100

6) Consider an insurance company that offers a "standard contract" with the premium r $10o and payout q $50o to anyone who will purchase it. a) Peter has healthy-state income IH $50o and sick-state income Is $o. He has probability of illness pJo.1. Is the standard contract fair and/or full for Peter? If heends up getting sick, what will his final income be? b) Tim has IH $50o and Is $o, but a probability of illness p o.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, ooo and Is $o, with probability of illness p o.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 $20o, 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 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