Suppose an investor's utility is given by U(Er_P, sigma^2_P) = Er_p - A/2 sigma^2_pI where E denotes expectation, r_P the return on a portfolio, A denotes risk aversion, and sigma^2_P the variance of the portfolio return. If the investor invests a share w in the market portfolio and the rest in the risk-free asset, derive an expression for the optimal w and give intuition for your