Short answers. Where appropriate, be sure to justify your responses along with showing the appropriate formulae.

- Consider the following "portfolio choice" problem. The investor has initial wealth w and utility u (x) = ln (x). There is a safe asset (such as a Canadian government treasury bills) 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 q and r0 with probability 1 - q. Let x be the amount invested in the risky asset, so that w - x is invested in the safe asset. Will the investor put more or less investment into the risky asset as their wealth grows?

- In the general equilibrium model, prove that aggregate excess demand necessarily will be zero using Walras Law. In general, what is the implication of the result?

- The implications of the first and second welfare theorems imply that any allocation subsequent to the initial endowment (within the Edgeworth box say) is possible as a Walrasian equilibrium. Is the preceding statement true or false? Explain.