701_prelim_2011_fall 2011-08-05 final version-1_701-1_0

701_prelim_2011_fall 2011-08-05 final version-1_701-1_0 -...

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Microeconomic Theory I Preliminary Examination University of Pennsylvania August 15, 2011 Instructions This exam has 5 questions and a total of 100 points. You have two hours to complete it. Answer each question in a SEPARATE exam book. If you need to make additional assumptions, state them clearly. Be concise. Write clearly so that you might get partial credit. Good luck!
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1. (20 pts) Suppose u is a continuous utility function representing a continuous and locally non-satiated preference relation on R n + . Let p R n ++ be a price vector. Let e ( p , u ) and h ( p , u ) be the expenditure function and the Hicksian demand correspondence, respectively. Prove the following properties: (a) (5 pts) Show that e ( p , u ) is homogenous of degree one in p :forany p , u , and a scalar λ R ++ , e p , u ) = λ e ( p , u ) . (b) (5 pts) Show that e ( p , u ) is nondecreasing in p and strictly increasing in u . (c) (5 pts) Show that e ( p , u ) is concave in p . (d) (5 pts) Suppose p , p ) R n ++ and let x h ( p , u ) and x ) h b p ) , u c . Then b p ) p c · b x ) x c 0 . 2. (25 pts) There are two commodities, leisure and consumption. Three workers wish to insure them-
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This note was uploaded on 10/23/2011 for the course ECON 501 taught by Professor Zobuz during the Spring '11 term at Istanbul Technical University.

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701_prelim_2011_fall 2011-08-05 final version-1_701-1_0 -...

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