Exam Two - ECON 6090 Midterm Two 75 Minutes THREE PAGES TO...

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75 Minutes. THREE PAGES TO EXAM Comments before you start: If you believe a question is unclear, please state how you inter- pret the question. In proofs use formal mathematical language. You must show all work for partial credit to be awarded. You do not need to simplify solutions (ex: You may leave a term like 8 0 : 3 ± p 4) : You do need to solve integrals where required. 1. Let the choice set be X = R 2 + and consider utility function u ( x ) = ln [ x 1 ² 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 & > 0 units of the good ( is an exogenous parameter). Let v ( ) be the (a) (3 points) Write down the Lagrangian, L , for the Util- ity Maximization Problem incorporating the wealth and rationing constraints : (b) (2 points) Write down ( do not solve! ) the ±rst order conditions of the problem ( rL = 0) (c) (3 points) Use the
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Exam Two - ECON 6090 Midterm Two 75 Minutes THREE PAGES TO...

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