1. (5 points) Let S = K = 2, q = (2, 1), a = (5, 10), and the payoff matrix is Hi?)- Let p = {g, g} be the probability distribution on the state space. Let the investor's expected utility index be u(:c) = $3. (a) Find the initial wealth of the investor. (b) Check that the assets' returns satisfy the necessary conditions for existence of a solution to the portfolio problem. (c) If the investor buys a portfolio at = (a1, (:3), what her state contingent wealth w = (101,102) will be? (d) Is it possible to nd portfolio shares (an , (12) that replicate any state contingent wealth? Why or why not? (e) Write the investor's problem as a portfolio problem and as a state contingent wealth problem. (f) Solve any one of these problems. If you solve the portfolio problem, calculate which wealth will the investor have in each state when the portfolio is optimal. If you solve the wealth problem, calculate the portfolio which replicates the optimal state contingent wealth. (g) Will the investor nd it optimal to bear risk, or will she not? Discuss your results