Exam Two Solutions

Exam Two Solutions - ECON 6090 Midterm Two 75 Minutes TWO...

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Unformatted text preview: ECON 6090 - Midterm Two 75 Minutes. TWO SIDES TO EXAM SHEET If you believe a question is unclear, please state how you interpret the question and we will take this into account during grading. In proofs, please use formal mathematical language wherever possible. You must show all work for partial credit to be awarded. 1. Let the choice set be X = R 2 + and consider utility function u ( x ) = p x 1 + p x 2 : Suppose the agent has wealth w and faces prices p = ( p 1 ;p 2 ) . Suppose the government has rationed good 1 so no agent can purchase more than & > units of the good ( & is a &xed parameter of the problem). Let v ( p;w;& ) be the consumer¡s indirect utility. (a) (5 points) L = p x 1 + p x 2 + ¡ & [ w ¡ p ¢ x ] + ¢ & [ & ¡ x 1 ] (b) FOC: 1 x 1 = ¡ & p 1 + ¢ 1 x 2 = ¡ & p 2 (c) @v ( p;w;& ) @& = ¢ 2. Throughout we will solve using u ( x ) = £ ln x 1 + ¤ ln x 2 (a) L = ¡ p ¢ x + ¢ [ £ ln x 1 + ¤ ln x 2 ¡ u ] (b) FOC £ x 1 = ¢ & p 1 ¤ x 2 = ¢ & p 2 1 These imply &...
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This note was uploaded on 01/07/2012 for the course ECON 6090 at Cornell.

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Exam Two Solutions - ECON 6090 Midterm Two 75 Minutes TWO...

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