Assume that Mr A and Mr B have the same utility function for

Assume that Mr. A and Mr. B have the same utility function for a change, x, in their fortune, given by U ( x ) = x 1/3 . Suppose now that one of the two men receives, as a gift, a lottery ticket which yields either a reward of r dollars (r > 0) or a reward of 0 dollars, wi th probability ½ each. Show that there exists a number b > 0 having the following property: Regardless of which man receives the lottery ticket, he can sell it to the other man for b dollars and the sale will be advantageous to both men.

Solution

there are a value that is

1/2 + 1/3 = 5/6