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Econ 6202, Fall 2009
Dmitry Shapiro
Problem Set 3
Due Tuesday September 22
1. (JR 2.8) The consumer buys bundle
x
i
at price
p
i
,i
= 0
,
1. Separately for parts (a)
to (d), state whether these indicated choices satisfy WARP:
(a)
p
0
= (1
,
3)
,x
0
= (4
,
2);
p
1
= (3
,
5)
,x
1
= (3
,
1).
(b)
p
0
= (1
,
6)
,x
0
= (10
,
5);
p
1
= (3
,
5)
,x
1
= (8
,
4).
(c)
p
0
= (1
,
2)
,x
0
= (3
,
1);
p
1
= (2
,
2)
,x
1
= (1
,
2).
(d)
p
0
= (2
,
6)
,x
0
= (20
,
10);
p
1
= (3
,
5)
,x
1
= (18
,
4).
2. Consider the set outcome
C
=
{
c
1
,c
2
,c
3
}
, and let
L
denote the set of simple lotteries
over
C
. Suppose that the preference relation
”
over
L
satisﬁes the independence
axiom, and that
c
1
”
c
2
”
c
3
. Show that
c
1
”
L
”
c
3
for every lottery
L
.
3. Suppose that
U
:
L →
R
represents the preference relation
”
. Show that if
U
has
the expected utility form, then
”
satisﬁes the independence axiom.
4. Consider the following lotteries: (
L
1
) $5000 for sure; (
L
2
) a
1
10
chance of $30,000
and a
89
100
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 Fall '09
 SHAPIRO

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