MS2011 - Economics 104B Midterm Exam Spring 2011 1. (5pt)...

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Unformatted text preview: Economics 104B Midterm Exam Spring 2011 1. (5pt) When John has 10 units of good 1 and 5 units of good 2, his MRS of good 1 for good 2 is 4 (i.e., his MU 1 /MU 2 = 4). When Maria has 5 units of good 1 and 15 units of good 2, her MRS of good 1 for good 2 is 2 (i.e., her MU 1 /MU 2 = 2). If John trades 3 units of good 2 for 1 unit of good 1 with Maria, both their MRS’s of good 1 for 2 after trade become 3. Is the allocation after trade Pareto optimal? Is the allocation a competitive equilibrium equilibrium allocation? Explain your answer. Answer: The allocation after the proposed trade is Pareto optimal because the consumers’ MRSs are identical. Consider prices p * 1 and p * 2 such that p * 1 /p * 2 = 3 and denote by x * = ( x * J ,x * M ) the allocation after trade. Then, x * J = (11 , 2) , x * M = (4 , 18) and p * 1 x * J 1 + p * 2 x * J 2 = 10 p * 1 + 5 p * 2 , p * 1 x * M 1 + p * 2 x * M 2 = 5 p * 1 + 15 p * 2 . This means that the allocation after trade satisfies both consumers’ budget constraints at prices p * 1 and p * 2 . The allocation is a competitive equilibrium allocation if they are also utility-maximizing subject to budget constraints....
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This note was uploaded on 12/26/2011 for the course ECON 104B taught by Professor Qin during the Fall '09 term at UCSB.

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MS2011 - Economics 104B Midterm Exam Spring 2011 1. (5pt)...

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