3. Demand for a risky asset. Assume that there are two assets, a risky asset with a random return of x dollars per dollar invested and a safe asset with a return of 2 dollars per dollar invested. The random return has a distribution function F(x) that satisfies / xdF(x) > 1. Consider an individual with initial wealth w to invest, which can be divided in any way between the two assets. Let p and y denote the amounts of wealth invested in the risky and the safe asset, respectively. (a) Identify the optimal values of p and 4. (Hint: the optimal values depend on F(), w and the Bernoulli utility function u(-).] (b) Assume that the Bernoulli utility function is u(w) = (w + 10)1/2 and that the random return is normally distributed, that is, F(x) = x. Show that demand in the risky asset found in part (a), p*, increases in wealth. 3. Demand for a risky asset. Assume that there are two assets, a risky asset with a random return of x dollars per dollar invested and a safe asset with a return of 2 dollars per dollar invested. The random return has a distribution function F(x) that satisfies / xdF(x) > 1. Consider an individual with initial wealth w to invest, which can be divided in any way between the two assets. Let p and y denote the amounts of wealth invested in the risky and the safe asset, respectively. (a) Identify the optimal values of p and 4. (Hint: the optimal values depend on F(), w and the Bernoulli utility function u(-).] (b) Assume that the Bernoulli utility function is u(w) = (w + 10)1/2 and that the random return is normally distributed, that is, F(x) = x. Show that demand in the risky asset found in part (a), p*, increases in wealth