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14.04
Midterm
Exam
2
Prof.
Sergei
Izmalkov
Wed,
Nov
5
√
1.
Consumer
1
has
expenditure
function
e
1
(
p
1
,p
2
,u
1
)=
u
1
p
1
p
2
and
consumer
2
has
utility
function
u
2
(
x
1
,x
2
)=
2003
x
3
1
x
a
2
.
(a)
What
are
Marshallian
(market)
demand
functions
for
each
of
the
goods
by
each
of
the
consumers?
Denote
theincomeo
fconsumer
1
by
m
1
and
the
income
of
consumer
2
by
m
2
.
(b)
For
what
value(s)
of
the
parameter
a
will
there
exists
an
aggregate
demand
functions
that
is
independent
of
the
distribution
of
income?
2.
Suppose
that
utility
maximization
problems
and
expenditure
minimization
problems
are
well
de
ﬁ
ned
and
utility
and
expenditure
functions
satisfy
all
necessary
“nice”
properties.
(a)
Show
(prove)
that
utility
maximization
implies
expenditure
minimization
and
vice
versa.
(b)
List
all
relevant
identities
that
are
result
of
a.
(c)
Derive
Roy’s
identity.
(d)
Derive
Slutsky
equation.
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This homework help was uploaded on 02/01/2008 for the course ECON 14.04 taught by Professor Izmalkov during the Fall '06 term at MIT.
 Fall '06
 Izmalkov
 Utility

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