2. Consider an economy with two states: state 1 and state 2. State 1 occurs with probability 7, and state two occurs with probability (1 7). Consider an expected utility maximizer with state dependent utility of wealth as follows: u(w) = log(71W), u(w) = log(72w), when state 1 occurs; when state 2 occurs. She faces an investment environment consisting of a riskless asset (with return rf), and a single risky asset. The return of the risky asset is a in state 1, and b in state 2. Suppose the investor has an initial wealth of wo to spend. (a) Find her optimal portfolio, i.e., her optimal amount x invested in the risky asset. (Her optimal investment in the riskless asset will then be wo X, where wo is her initial wealth.) (b) How does your answer in (a) change if y1 = 72? (c) Suppose the investor has a job that pays an additional income of 1 unit of wealth regardless of whether state 1 or 2 is realized. How does your answer in part (a) change? 2. Consider an economy with two states: state 1 and state 2. State 1 occurs with probability 7, and state two occurs with probability (1 7). Consider an expected utility maximizer with state dependent utility of wealth as follows: u(w) = log(71W), u(w) = log(72w), when state 1 occurs; when state 2 occurs. She faces an investment environment consisting of a riskless asset (with return rf), and a single risky asset. The return of the risky asset is a in state 1, and b in state 2. Suppose the investor has an initial wealth of wo to spend. (a) Find her optimal portfolio, i.e., her optimal amount x invested in the risky asset. (Her optimal investment in the riskless asset will then be wo X, where wo is her initial wealth.) (b) How does your answer in (a) change if y1 = 72? (c) Suppose the investor has a job that pays an additional income of 1 unit of wealth regardless of whether state 1 or 2 is realized. How does your answer in part (a) change