Question

3 Consider a standard two agent economy with typical convex pref- erences (our usual kind, the indifference curves become gradually flatter). Pick an arbitrary endowment and draw the Edgeworth box of this econom i. Show the relationship between the initial endowment and the competitive equilibrium allocation. ii. State the First Welfare Theorem. Show that the First Welfare Theorem holds. Hint: This requires a brief mathematical argument iii. State the Second Welfare theorem. Defend it graphically. That is show how a policy maker before any markets open can use lump sum taxes to produce an equilibrium outcome con- sistent with the theorem if the desired portion of the Pareto Frontier is not an equilibrium allocation for the initial endow- ment described in the environment. A good answer labels three points in an Edgeworth box that capture goods moving through time and explains what factors move the outcome from the first to the second to the third point. iv. [Hard question] Suppose the policy maker knows Harriet's preferences but not George's and wants to implement an equi- librium allocation that lands Harriet on to a specific indiffer- ence curve after lump sum taxes. Is this generally possible? u are asked to di-