Exercise 4

Exercise 4. (35 points) Consider a pureexchange economy with two goods {1, 2} and two consumers {24, B}. A and B wish to trade with one another to maximize their individual utilities. Suppose A is endowed with 1 unit of good 1 and half a unit of good 2, i.e., MA = (1, ). B is endowed with 1 unit of good 1 and 1.5 units of good 2, i.e., tag 2 (1, g). In addition, suppose their utility functions are given by uA($A) = (film?) (Jeff/46623)\" 23 DU 8 U5 U H (1) Draw an Edgeworth box indicating the endowment and preferences for this problem. (2) Find the set of Pareto optimal allocations of this economy. (3) Find the equilibrium consumptions of A and B and determine the equilibrium price ratio that supports them. (4) Is the equilibrium allocation in (3) Pareto optimal? (5) Show that there are gains from trade in this situation (compared to the endowment point). From what endowment point leading to the same equilibrium allocation would there be no gains from trade? (6) Suppose that instead of the above utility function, uB(xB) = ($)3/8(m23)1/3. How does this change the equilibrium consumption you found in part (3)? What is the intuition for this? (7) Go back to the original problem. Suppose the government decides that the competitive equilibrium is not a good allocation and they would prefer for A and B to consume respectively (2, g) and g, 2). Is this a competitive equilibrium for some endowments? Why or why not? Is it attainable from the initial endowments? (8) Suppose that the government can announce that 101 2 p2 = 1. Would this achieve the government's desired allocations? (9) Could the government achieve its objective through lump sum redistribution (i.e., a change of the initial endowments such that there are still 2 units of each good in this economy)? If so, how could it redistribute to achieve its desired allocation