Ann is an expected utility maximizer and her utility function is given by u(x) = x0.5. Ann’s friend, Bob has offered to bet with her $10,000 on the outcome of the toss of a coin. That is, if the coin comes up heads, Ann must pay Bob $10,000 and if the coin comes up tail, Bob must pay Ann $10,000. The coin is a fair coin, so that the probability of heads and the probability of tails are both 1/2. Ann has $100,000 and is trying to figure out whether she should take the bet. Note that if Ann accepts the bet and heads comes up, she will have 100,000-10,000 = 90,000.
(a) If Ann accepts the bet, then if tails comes up, she will have how much money?
(b) What is Ann’s expected utility if she accepts the bet?
(c) What is Ann’s expected utility if she does not accept the bet?
(d) Does Ann take the bet? Explain why or why not Ann takes the bet.
(e) Ann later asks herself, If I make a bet where I lose all my money, that is all my $100,000 if the coin comes up heads, what is the smallest amount that I would have to win in the event of tails in order to make the bet a good one for me to take? Find the answer to Ann’s question.