Econ805finalanspart2.01

Econ805finalanspart2.01 - Department of Economics The Ohio...

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Department of Economics The Ohio State University Final Exam Answers–Part II–Econ 805 Profs. Levin, Morelli, and Peck March 13, 2001 3. (33 points) The following economy has n consumers and k commodities. Each con- sumer’s utility function satis…es strict monotonicity, strict quasi-concavity, and continuity. Suppose that ( p ¤ ;x ¤ ) is a competitive equilibrium, and that x ¤¤ is a feasible allocation that is not Pareto optimal. For each of the following statements, either prove the statement or provide a counterexample. Carefully explain. [You can use the theorems proven in class without proving them here.] (a) For all i, we have u i ( x ¤ i ) ¸ u i ( x ¤¤ i ) : (b) At least one consumer prefers her competitive equilibrium bundle to any other consumer’s bundle. That is, for some i, we have u i ( x ¤ i ) ¸ u i ( x ¤ h ) for all h. (c) p ¤ ¢ n X i =1 x ¤ i ¸ p ¤ ¢ n X i =1 x ¤¤ i : ANSWER: (a) This statement is false. There must be some allocation that Pareto dominates x ¤¤ , but it does not have to be x ¤ . For example, in the following diagram, x ¤ is the allocation determined by the point (.5, .5), and
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Econ805finalanspart2.01 - Department of Economics The Ohio...

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