1. PROBLEM Consider the following "portfolio choice" problem. The investor has initial wealth w and utility u(x) = -2-2. There is a safe asset (such as a US government bond) that has net real return of zero. There is also a risky asset with a random net return that has only two possible returns, R > 0 with probability q and Ro 0, so the risky asset pays more than the safe asset in expectation. Let A be the amount invested in the risky asset, so that w-A is invested in the safe asset. (i) Find the value of A that maximizes the agent's payoff (note that A depends on w, R, and R). Does the investor put more or less of his portfolio into the risky asset as his wealth increases? (ii) Find the agent's coefficient of absolute risk aversion A(z) = 2. How does it depend on wealth? How does this account for the the answer you obtained in part (i)