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# (Solved): 1. Consider the same setup as in Exercise 4 of Lecture #06. Suppose that there are two agents A and ...

1. Consider the same setup as in Exercise 4 of Lecture #06. Suppose that there are two agents A and B each holding 6 units of apples and 6 units of oranges as initial endowments. The utility functions of agents A and B are given by uA(xA, yA) = x1/3 A y2/3 A and uB(xB, yB) = x2/3 B y1/3B where xA, yA, xB, yB have the same meaning as in the lecture. Let px be the price of apples and py be the price of oranges. (a) Argue that the allocation described by xA = 12,xB = 12,yA = 0,yB = 0 is Pareto efficient. Note that we cannot use the argument with MRS, as the MRS for agent B is undefined. Use the definition of Pareto efficiency in your argument. (b) The allocation in (a) cannot be part of a competitive equilibrium of this economy. However, the Second Fundamental Welfare Theorem states that the allocation in (a) can be a competitive equilibrium if the initial endowments can be redistributed. How should the initial endowments be redistributed so that the allocation in (a) is a competitive equilibrium? In your answer, be sure to also argue that under this redistribution, the allocation in (a) is an equilibrium allocation by finding a pair of equilibrium prices p* x and p* y.

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