Consider a two-person (A and B), two-commodity (1 and 2) pure exchange economy. Suppose that individual A's preferences can be represented by the utility function UA (q1A ,q2A) = (q1A) to the power of 1/3 and q2A to the power of (2/3) , where qA 1 is individual A's consumption of commodity one and qA 2 is individual A's consumption of commodity two. Similarly, suppose that individual B's preferences can be represented by the utility function UB (q1B ,q2B) = (q1B) to thew power of (1/3) and (q2B) to the power of (2/3) , where qB 1 is individual B's consumption of commodity one and qB 2 is individual B's consumption of commodity two. Individual A is endowed with one unit of commodity one and two units of commodity two, while individual B is endowed with two units of commodity one and one unit of commodity two.

1. Find the set of Pareto ecient allocations for this economy. (5 marks.)

2. Find the set of individually rational allocations for this economy. (5 marks.)

3. Find the contract curve for this economy. (You should use the denition of the contract curve that was specied in class rather than the one that is used in the textbook for this course.) (5 marks.)

4. Assuming that both consumers are price takers, nd the competitive equilibrium for this economy. Be sure to specify the equilibrium consumption of each commodity by each player and the equilibrium price ratio (p = p1 p2). (5 marks.) 5. Illustrate this economy and your answers to the earlier parts of this question using an Edgeworth-Bowley box diagram. (5 marks.)