Billy has a von Neumann-Morgenstern utility function

12.1 In Problem 12.9, Billy has a von Neumann-Morgenstern utility functionU(c) = c1=2. If Billy is not injured this season, he will receive anincome of 25 million dollars. If he is injured, his income will be only$10,000. The probability that he will be injured is .1 and the probabilitythat he will not be injured is .9. His expected utility is(a)4,510.(b)between 24 million and 25 million dollars.(c)100,000.(d)9,020.(e)18,040.Willy’s only source of wealth is his chocolate factory. He has the utility function pc1=2f+ (1 ? p)c1=2nfwhere pis theprobability of a flood and 1?pis the probability of no flood. Let cfand cnfbe his wealth contingent on a flood and on no flood, respectively. Theprobability of a flood is p= 1=15. The value of Willy’s factory is $600,000 if there is no flood and 0 if there is a flood. Willy can buy insurance where if he buys $xworth of insurance, he must pay the insurance company x=17 whether there is a flood or not, but he gets back $xfrom the company if there is a flood. Willy should buy(a)no insurance since the cost per dollar of insurance exceeds the probabilityof a flood.(b)enough insurance so that if there is a flood, after he collects his insurancehis wealth will be 1/9 of what it would be if there is no flood.(c)enough insurance so that if there is a flood, after he collects his insurance,his wealth will be the same whether there is a flood or not.(d)enough insurance so that if there is a flood, after he collects his insurance,his wealth will be 1/4 of what it would be if there is no flood.(e)enough insurance so that if there is a flood, after he collects his insurancehis wealth will be 1/7 of what it would be if there is no flood.(3) Sally Kink is an expected utility maximizer with utility function pu(c1) + (1 ? p)u(c2) where for any x <4;000, u(x) = 2xand where u(x) = 8;000 + xfor xgreater than or equal to 4,000.(a)Sally will be risk averse if her income is less than 4,000 but risk lovingif her income is more than 4,000.(b)Sally will be risk neutral if her income is less than 4,000 and riskaverse if her income is more than 4,000.(c)For bets that involve no chance of her wealth exceeding 4,000, Sallywill take any bet that has a positive expected net payo(d)Sally will never take a bet if there is a chance that it leaves her withwealth less than 8,000.(e)None of the above are true.Martin’s expected utility function is pc1=21 +(1 ? p)c1=22 where pis the probability that he consumes c1 and 1 ? pis the probability that he consumes c2. Wilbur is oered a choice between getting a sure payment of $Zor a lottery in which he receives $2,500 with probability 0.40 and he receives $900 with probability 0.60. Wilbur will choose the sure payment if(a) Z >1;444 and the lottery if Z <1;444.(b) Z >1;972 and the lottery if Z <1;972.(c) Z >900 and the lottery if Z <900.(d) Z >1;172 and the lottery if Z <1;172.(e) Z >1;540 and the lottery if Z <1;540.Clancy has $4,800. He plans to bet on a boxing match between Sullivan and Flanagan. He nds that he can buy coupons for $6 thatwill pay o $10 each if Sullivan wins. He also nds in another store some coupons that will pay o $10 if Flanagan wins. The Flanagan tickets cost$4 each. Clancy believes that the two ghters each have a probability of 1/2 of winning. Clancy is a risk averter who tries to maximize the expected value of the natural log of his wealth. Which of the following strategies would maximize his expected utility?(a)Don’t gamble at all.(b)Buy 400 Sullivan tickets and 600 Flanagan tickets.(c)Buy exactly as many Flanagan tickets as Sullivan tickets.(d)Buy 200 Sullivan tickets and 300 Flanagan tickets.(e)Buy 200 Sullivan tickets and 600 Flanagan tickets.