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 firstorder conditions. What are the demand functions for goods
1 and 2. (You need not consider secondorder 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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 Spring '08
 DANNICATAMBAY
 Economics, Microeconomics, Utility, Utility maximization problem, Expenditure minimization problem, L. Sheila

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