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Problem Set 6
Economics 201B 2nd Half  Spring 2006
Due Thursday, 4 May in Lecture
1. Let
A
R
L
be an nonempty open set. Show that
A
does not have Lebesgue measure
zero.
2. Consider the equilibrium correspondence
E
:
R
LI
+
!
2
R
L
1
++
E
(
!
) =
f
^
p
2
R
L
1
++
:
z
(^
p; !
) = 0
g
, and complete the exercise on the second to last page of Lecture
Notes #11. That is, taking it as given that
E
has a closed graph:
(a) show that
E
is upper hemicontinuous.
Hints: You solved a similar problem in
we can±t have prices on the boundary, so showing that E is uhc is more di¢ cult.
(b) having established the upper hemicontinuity of
E
, show that the set of endow
ments that generate critical economies (i.e. the set
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 Spring '06
 ANDERSON
 Economics

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