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Ec701FinalExamF04

# Ec701FinalExamF04 - Name[Last[First EC 701 Michael Manove...

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Name: [Last], [First] EC 701 Microeconomics Michael Manove 20 December 2004 Final Examination Instructions: Answer two of the three parts of Problem 1 (but do not answer all three parts). Then answer Problems 2, 3, 4 and 5. Think before you write. Do not spend too much time on any one problem. If you have to leave the room for any reason, please give the instructor your examination on the way out. You will have 180 minutes to complete a 150-minute exam. I suggest that you do not exceed the recommended times for each question until you have answered all questions. Then you can use the extra time to improve your answers. If you fi nish before 11:45 pm, you may leave, but be extremely quiet on the way out and in the hallway! Problem 1. [20 minutes, total] Prove any two of the following three propositions: a) [10 minutes] Proposition (Slutsky equation for Hicksian demand). If U ( x ) is a strictly quasiconcave and well-behaved utility function and V ( p, w ) is the corresponding indirect utility function, then ∂x i ( p, w ) ∂p j = ∂h i ( p, u ) ∂p j ∂x i ( p, w ) ∂w x j ( p, w ) where x i ( p, w ) is ordinary demand and h i ( p, u ) is Hicksian demand and where u = V ( p, w ) . [You are free to cite theorems about the expenditure function e ( p, u ) in your proof.]

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EC 701 Final Exam December 20, 2004 page 2 b) [10 minutes] Proposition (Law of Supply). Suppose y ( · ) is a supply (derived demand) function. Then for any two price vectors p 0 and p À 0 , we have ( p 0 p )( y ( p 0 ) y ( p )) 0 .
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Ec701FinalExamF04 - Name[Last[First EC 701 Michael Manove...

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