A risk-averse consumer has a utility function log(W), where W_> is his wealth. He has an investment opportunity which multiplies his wealth by a factor of 1 + r, where r =0.5, -0.5 with probabilities (0.5,0.5) respectively.

part a) Suppose that W=1. Would he accept/not accept the investment?

part b) Suppose that W is unknown. Find the levels of (if any) such that he would be indifferent between accepting and not accepting the investment