Consider the following portfolio choice problem. The investor has initial wealth w and utilityu(x)=xn/n . 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, R₁ with probability 1 q and R₀ with probability q. We assume R₁ < 0, R₀ > 0. Let A be the amount invested in the risky asset, so that w A is invested in the safe asset.

1. Does the investor put more or less of his portfolio into the risky asset as his wealth increases?

2. Now find the share of wealth, , invested in the risky asset. How does change with wealth?

3. Calculate relative risk aversion for this investor. How does relative risk aversion depend on wealth?