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Mock_1_Midterm_101_2011 - Economics 101 Mock Midterm 1...

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Economics 101 Mock Midterm 1 February 5, 2011 George J. Mailath This is an hour exam. There are two questions, each worth 30 points. Answer each question in a separate blue book. Make sure to PRINT your name and put your recitation number on each blue book. Give complete answers, and clearly label all diagrams. 1. [30 points] Consider the utility function u ( x 1 ,x 2 ) = x 1 x 2 + x 1 , with budget constraint p 1 x 1 + p 2 x 2 = I . (a) Form the Lagrange function associated with this utility maximization problem and derive the first-order conditions. What are the demand functions for goods 1 and 2. (You need not consider second-order conditions, and you may assume the solution is interior.) [15 points] (b) Calculate the indirect utility function. What is the relationship between the indirect utility function and the expenditure function? Use this relationship to solve for the expenditure function. [10 points] (c) Given the expenditure function from part 1(b) , calculate the compensated de- mands without separately solving the expenditure minimization problem.
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