Peter Brown's utility for total wealth x can be represented by the utility function u(x) =ln(x). He currently has $1000 in cash. A business deal of interest to him yields a reward of $100 with probability 0.5 and $0 with probability 0.5.
a) If he owns this business deal in addition to the $1000, what is the smallest amount for which he would sell the deal?
b) Suppose he does not own the deal what is the largest amount he would pay for the deal?