Question

2.Clarence Bunsen is an expected utility maximizer. His preferences among contingent commodity bundles are represented by the expected utility function:?(?1,?2,?1,?2)=?1√?1+?2√?2.Clarence’s friend, Hjalmer Ingqvist, has offered to bet him $1,000 on the outcome of the toss of a coin. That is, if the coin comes up heads, Clarence must pay Hjalmer $1,000 and if the coin comes up tails, Hjalmer must pay Clarence $1,000. The coin is a fair coin, so that the probability of heads and the probability of tails are both 1/2. If he doesn’t accept the bet, Clarence will have $10,000 with certainty. In the privacy of his car dealership office over at Bunsen Motors, Clarence is making his decision.Let Event 1 be “coin comes up heads” and let Event 2 be “coin comes up tails.”

a)If Clarence accepts the bet, then in Event 1, he will have ____ dollars and in Event 2, he will have ___dollars.

b)Since the probability of each event is 1/2, Clarence’s expected utilityfor a gamble in which he gets c1 in Event 1 and c2 in Event 2 can bedescribed by the formula ___. Therefore Clarence’sexpected utility if he accepts the bet with Hjalmer will be ___.

c)If Clarence decides not to bet, then in Event 1, he will have___dollars and in Event 2, he will have ___dollars.

d)Therefore if he doesn’t bet, his expected utility will be ___.

e)Having calculated his expected utility if he bets and if he does not bet,Clarence determines which is higher and makes his decision accordingly.Does Clarence take the bet?

Answer 1