Economics 101Mock Midterm 1February 5, 2011George J. MailathThis is an hour exam. There are two questions, each worth 30 points. Answer each questionin a separate blue book. Make sure to PRINT your name and put your recitation numberon each blue book. Give complete answers, and clearly label all diagrams.1.[30 points]Consider the utility functionu(x1,x2) =x1x2+x1,with budget constraintp1x1+p2x2=I.(a) Form the Lagrange function associated with this utility maximization problemand derive the first-order conditions. What are the demand functions for goods1 and 2. (You need not consider second-order conditions, and you may assumethe solution is interior.)[15 points](b) Calculate the indirect utility function. What is the relationship between theindirect utility function and the expenditure function? Use this relationship tosolve for the expenditure function.[10 points](c) Given the expenditure function from part1(b), calculate the compensated de-mands without separately solving the expenditure minimization problem.
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