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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 consumers 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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