Suppose you have $10 to invest. You can invest your money in either a risky stock or a safe bond (those are your only two options; all of your money must be in these two assets and ONLY these two assets). The bond is riskless, and offers a guaranteed 2% return. The stock is risky, and can either go up or down. If the stock goes up, it will go up by 5%, if it goes down, it will go down by 2%. How much money, x, should you invest in the stock if your utility function is u(W ) = ln(W ), and the probability the stock will go up is 58% and the probability the stock will go down is 42%?

Hint: Maximize expected utility - and be sure to write things down carefully!