Only 2) and 3)

Consider the following "portfolio choice" problem. The investor has initial wealth w and utility u (x) = In (a). 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, with probability q and Ro with probability 1 4. Let A be the amount invested in the risky asset, so that w - A is invested in the safe asset. 1. Find A as a function of w. Does the investor put more or less of his portfolio into the risky asset as his wealth increases? 2. Another investor has the utility function u (x) = -2-1 How does her investment in the risky asset change with wealth? 3. Find the coefficients of absolute risk aversion r(x) = for the two investors. How do they depend on wealth? How does this account for the qualitative difference in the answers you obtain in parts (1) and (2)