3. (5 p.) Donna has the wealth of 90, but if she becomes ill, she will have to pay medical bills, reducing her wealth to 45. The probability that Donna will fall ill is 1/3. Donna's utility function is given by u(w)= -120/w where w denotes wealth. Donna has the option of buying insurance coverage for illness from an insurance company. Suppose Donna can buy X units of cover by paying a premium of X3 (i.e. the insurance company pays X to Donna if she falls ill, and Donna pays the insurance company X3 whether she is ill or not ill). (a) What is the optimal choice of X by Donna? Justify your answer and explain the result. (b) Suppose insurance company proceeds from linear pricing policy to a two-part tariff. According to the new policy Donna should pay fixed fee F irrespective of the amount of insurance purchased and in addition she pays X/3 for X units of cover, where the level of cover (X) is chosen by Donna. Find the maximum fixed fee that Donna is willing to pay for this insurance. Explain your derivation carefully. (e) Provide graphical solution for part (b) using wealth-utility graph. (d) Consider two other agents, Bill and Ann, that have the same initial endowment as Donna and the same probability to fall ill. Assume that Bill is risk-neutral while Ann is risk averse. Denote by T and T the maximum fixed fee that Bill and Ann are willing to pay for the right to purchase X units of insurance cover by paying a premium of X/3, assuming that each individual can choose the optimal amount of insurance according to his/her preferences. Is it true that T"