Question 5. (25 points) Consider a risky prospect in which you may get $40,000 with probability 1/3 and $16,000 with probability 2/3.

Question 5. (25 points) Consider a risky prospect in which you may get $40,000 with probability 1/3 and $16,000 with probability 2/3. Suppose your utility of money is U(money) = money . (a) (5 points) Between a sure income of $23,000 and the risky prospect above, which one would you prefer? Show your work. (b) (5 points) Suppose you have a neighbor who has sure income of $24,000. Your neighbor's utility function is different than yours. His utility function is given by U(money) =money . Consider a scheme in which you will pay the neighbor $m when it's your good luck, and your neighbor will pay you $n when it's your bad luck. What are the conditions that have to be satisfied for you and your neighbor to get into this scheme? YOU: YOUR NEIGHBOR: (c) (10 points) Now, instead of a sure income, suppose the neighbor actually faces the same risky prospect as you, but your luck and the neighbor's luck are always completely opposite: when you get $40,000, your neighbor gets $16,000 and this happens with probability 1/3; when you get $16,000, your neighbor gets $40,000 and this happens with probability 2/3. Your neighbor's utility function is U(money) =money. Consider a risk-sharing scheme in which you and your neighbor share your combined income equally. Is it worthwhile for you and your neighbor to get into this scheme? Show your work.{d} {Sperm} Consider the same situation as in patt {c} above, but instead of sharing equally, suppose your and neighbor's combined income is shamed unequally. What is the minimum your neighbor would accept? If he is given exactly that minimum amount, and you get the rest, then will you accept this scheme