Question 1 (50 marks] Consider the following portfolio choice problem. The investor has initial wealth w and utility u(x) = --. 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 1 - 4 and Ro with probability q. We assume R; 0. Let a be the share of wealth w invested in the risky asset, so that 1-a share of wealth is invested in the safe asset. (a) Find a as a function of w. How does a change with wealth? Explain the intuition. [15 marks) (b) Another investor has the utility function u(x) = in(x). How does a change with wealth? Explain the intuition. [15 marks) (c) Calculate relative risk aversion for two investors using the utility functions in (a) and (b). How do they depend on wealth? How does this account for the qualitative difference in the answers you obtain in parts (a) and (b)? [20 marks)