Consider an economy with a risk-free asset with return r_f and two risky assets, one with random return r_1 with expected value E(r_1) and standard deviation sigma_1, and second with random return r_2 with expected value E(r_2) and standard deviation sigma_2. Let rho_12 denote the correlation between the two random returns on the two risky assets. Suppose that an investor forms a portfolio of these three assets by allocating the share w_1 of his or her wealth to risky asset 1, and share w_2 to risky asset 2, and the remaining share 1 - w_1 - w_2 to the risk-free asset. (a) Write down a formula for the expected return mu_P on this portfolio. (b) Next, write down a formula for variance sigma^2 _P of the return on the same portfolio. (c) Suppose that the investor has a preferences defined directly over the mean and variance of the return on his or her portfolio, as described by the utility function U(mu_P, sigma_P) = mu_P - (A/2) sigma^2 _P where A is a parameter that measures the investor's degree of risk aversion. Write down the first order conditions for the investor's optimal choices w^* _1 and w^* _2 for the shares allocated to each of the two risky assets