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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 '10
 AARON
 Economics, Utility, @, @v, free disposal, Two 75 Minutes

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