Question:

Question 2: An Endowment Economy with Heterogeneous Agents Suppose that there are two agents in an economy: Finn and Rey. There are two goods. Both Finn and Rey are endowed with 61 units of the good 1, and 62 units of good 2. Let :51 be the good 1 and let mg the good 2. Finn and Rey have different preferences: UFf\"\"(931,m2) = ln(931) + 0.7n(a:2) URey(w1,m2) = ln(w1) + 0.9n(a:2) Rey values good 2 more than Finn does. 1. Dene the competitive equilibrium of this economy. 2. Calculate the prices and allocation of the competitive equilibrium. 3. Please draw the Edgeworth box for this economy. Be sure to include the endowment point, the equilibrium allocation, the budget constraint, indifference curves, and a sketch of the contract curve. 4. Dene the problem of a social planner that has weights Am\" and ARey on each of the agents. 5. Assume for this question that Finn has endowments 85'5\"" and 8573\"\" of goods 1 and 2, respectively, and that Rey has endowments eiky and 3391'. Moreover, assume that a?\" + enRey = 2en,Vn. What should be the endowments such that the social planner allocation coincides with the general equilibrium? How this relates to the second welfare theorem? 6. Suppose that there is a government in this economy. The government imposes lump-sum tax Tan and T339 on Finn and Rey, respectively. Define the competitive equilibrium with a government. What should be Tan\" and TBS\" if the government wants to implement the social planner allocation