Short Answers - True/False

Where appropriate, be sure to justify your responses along with showing the appropriate formulae, as no marks will be rewarded without justification.

5. In an exchange economy, there are two people, A and B, and two goods, x and y. The utility functions of A and B are given by ui=xiyi for i=A, B. Person A starts with 72.000 units of x and zero units of y. Person B starts with zero units of x and 8.000 units of y. If the price of good y is 1, what is the competitive equilibrium of good x?

6. 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?

7. 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?