This preview shows page 1. Sign up to
14.04
Midterm
Exam
1
Prof.
Sergei
Izmalkov
Wed,
Oct
1
,
y
t
)
for
t
= 1
, . . . , N
be
a
set
of
observed
choices
that
satisfy
WAPM,
let
Y I
and
Y O
be
the
inner
and
outer
bounds
to
the
true
production
set
Y
. Let
π
+
(
p
)
,
π
(
p
)
, and
π
−
(
p
)
be
pro
fi
t
functions
associated
with
Y O
,
Y
, and
Y I
correspondingly.
(a)
Show
that
for
all
p
,
π
+
(
p
)
≥
π
(
p
)
≥
π
−
(
p
)
.
(b)
If
for
all
p
,
π
+
(
p
) =
π
(
p
) =
π
−
(
p
)
,
what
you
can
say
about
Y O
,
Y
, and
Y I
?
Provide
formal
arguments.
(c)
For
(
p
1
,
y
1
) = ([1
,
1]
,
[
−
3
,
4])
, and
(
p
2
,
y
2
) = ([2
,
1]
,
[
−
1
,
2])
construct
Y I
and
Y O
(graphically).
What
can
you
say
about
returns
to
scale
in
the
technology
these
observations
are
coming
from?
Hint:
think
y
= (
−
x, y
)
.
t
1. Let
(
p
2.
Given
the
production
function
f
(
x
1
, x
2
, x
3
) =
x
1
min
{
x
2
, x
3
}
a
striction
you
have
to
impose
on
a
?
a
(a) Calculate pro
fi
t maximizing supply and demand functions, and the pro
fi
t function. What re-
(b) Fix
Calculate conditional demands and the cost function
(
)
y
c w , w , y
.
.
1
2
,
y
(c)
Solve
the
problem
py
−
c
(
w
1
, w
2
, y
)
→
max
,
do
you
obtain
the
same
solution
as
in
2
a
?
Explain
This is the end of the preview.
Sign up
to access the rest of the document.
- Fall '06
- Izmalkov
