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6) Consider an insurance company that offers a \"standard contract\" with the premium r = $100 and payout q = $500 to anyone who will purchase it. a) Peter has healthy-state income 1H = $500 and sick-state income 15 = $0. He has probability of iness p = 0.1. Is the standard contract fair and/or full for Peter? If he ends up getting sick. what will his nal inoome be? 12:) Tim has In = $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 In = $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 In > 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 baund for In . 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