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Problem Set 4
Economics 201B 2nd Half  Spring 2006
Due Thursday, 20 April in Lecture
1. In this problem, you are asked to prove in detail some of the steps from the Second
Welfare Theorem in a production economy. Let
(
x
; y
)
be a P.O. allocation, let pref
set
Y
j
to produce goods in such a way that strictly positive total consumption is possible.
That is,
9
y
j
2
Y
j
such that
!
+
P
j
y
j
>>
0
if
0
2
Y
j
8
j
and
! >>
0
).
A
i
=
f
x
0
i
:
x
0
i
i
x
i
g
A
=
P
i
A
i
. Show that
A
is
convex.
(b) In the proof, we show that
9
p
6
= 0
s.t.
sup
p
±
(
Y
+
f
!
g
)
²
inf
p
±
A
. Show that
inf
p
±
A
=
P
i
inf
p
±
A
i
.
(c) Later in the proof, we establish that
p
³
0
, and that (
p
; x
; y
; T
) is a Walrasian
quasiequilibrium with transfers. That is,
x
i
is in the quasidemand set for each
agent and
y
j
Show that (
p
; x
; y
; T
) is a
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 Spring '06
 ANDERSON
 Economics

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