2. Consider an economy with two states: state 1 and state 2. State 1 occurs with probability, 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(12w), when state 1 occurs; when state 2 occurs. She faces an investment environment consisting of a riskless asset (with return ri), 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 - 2, where wo is her initial wealth.) (b) How does your answer in (a) change if 7 = 12? (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, 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(12w), when state 1 occurs; when state 2 occurs. She faces an investment environment consisting of a riskless asset (with return ri), 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 - 2, where wo is her initial wealth.) (b) How does your answer in (a) change if 7 = 12? (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