Bill is thinking of investing in a Silicon Valley start-up. His von Neumann-Morgenstern utility-of money function is
U(w) = 9+w-(w^2/100) where w denotes wealth measured in thousands of dollars (thus w = 1 means $1,000). Bill's total wealth is $20,000 and he would have to invest it all. With probability 40% the start-up will be a failure and Bill will lose all his investment; with probability 60% it will succeed and he will get his initial investment back plus a profit of $30,000.
a) Should Bill make the investment?
b) Would a risk-neutral person make the investment?