ECN 712
Fall 2009
Professor Schlee
Problem Set VII, Due Tuesday, 27 October
1. Let
X
be a ﬁnite set of outcomes,
L
the set of probablity distributions over
X
and
%
a (complete
and transititve) preference relation on
L
. Assume, as we did in the lecture, that no two (sure)
elements of
X
are indiﬀerent. We proved that if
%
is continuous, monotone and satisﬁes the
independence axiom, then there is an expected utility representation of
%
. Now go in the
other direction: Suppose that there is an expected utility representation of the preference
relation
%
; does it follow that
%
is continuous, monotone and satisﬁes independence?
2. Let
X
=
{
x
1
,...,x
n
}
be a set of outcomes (
n
≥
3), with
x
1
the outcome “death.” Deﬁne
%
as
follows: for any
q,p
∈ L
, if
q
1
> p
1
, then
p
±
q
; if
q
1
=
p
1
, then there is a realvalued function
u
on
{
x
2
,...,x
n
}
such that
p
%
q
precisely when
n
X
i
=2
u
(
x
i
)
p
i
≥
n
X
i
=2
u
(
x
i
)
q
i
.
where
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 Spring '10
 schlee
 Microeconomics, Utility, indirect utility function, utility representation

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