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MIT
14
.
04
Intermediate
Microeconomie
Theory
Fall
2005
Exam
#1
Instructions
Answer
each
of
the
four
problems
on
a
seperate
piece
of
paper.
You
will
have
1.5
hours
to
complete
the
exam.
Problem
1
(
30
minutes
)
Consider
a
consumer
with
a
utility
function
u
Ω
x
1
,
x
2
æ
:
e
Ω
x
1
+
ln
Ω
x
2
ææ
1/3
(3
points)
a)
What
properties
about
utility
functions
will
make
this
problem
easier
to
solve?
(3
points)
b)
Which
of
the
non
negativity
input
demand
constraints
will
bind
for
small
m?
(10
points)
c)
Derive
for
the
marshallian
(uncompensated)
demand
functions
and
the
indirect
utility
function.
(3
points)
d)
Derive
the
expenditure
function
in
terms
of
original
utils
u
.
(6
points)
e)
Suppose
that
there
are
5
people
in
the
economy
each
with
endowments
m
i
,
i
:
1,2,3,4,5.
i)
Suppose
that
m
i
;
p
1

i
.
Construct
the
aggregate
demand
function
for
x
1
and
x
2
.
’
What
properties
do
the
individual
demand
functions
have
that
simplifty
this
problem?
ii)
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 Fall '06
 Izmalkov
 Utility

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