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1
6th December 2008
Instructions
: Answer 7 of the following 9 questions. All questions are of equal
weight. Indicate clearly on the
f
rst page which questions you want marked.
1. Assume some consumer chooses bundle
x
j
at prices
p
j
,
j
=1
,
2
,
3
,
where
p
1
=(
1
,
1
,
2)
;
x
1
=(5
,
19
,
9)
p
2
=(
1
,
1
,
1)
;
x
2
=(12
,
12
,
12)
p
3
=(
1
,
2
,
1)
;
x
3
=(27
,
11
,
1)
.
Show these data satisfy WARP. Is there an intransitivity in the revealed prefer
ences? Justify your answer.
ANSWER
Cost of these bundles
at these
prices
1
2
3
Deductions
1
42
48
40
Bundle 1 is revealed preferred to 3
2
33
36
39
Bundle 2 is revealed preferred to 1
3
52
48
50
Bundle 3 is revealed preferred to 2
These preferences are consistent with WARP but clearly they violate transitivity.
2. Consider the twostate world of Andy and Brian. In the good state each has
awea
ltho
f
80
;inthebadstateeachhasawea
ltho
f
40
, assuming they do not trade
with each other. Let the probability of the good state be
3
/
4
.
The only way in which
they di
f
er is Andy is risk averse and Brian is risk neutral. Describe as precisely as
you can the Pareto e
ﬃ
cient allocations for these two people. Now suppose there are
many Andys and an equal number of Brians. Describe as precisely as you can the
competitive equilibrium of this economy.
ANSWER
Draw an Edgeworth rectangle with wealth in the good state along the horizontal
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risk averse so his indi
f
erence curves are convex to his origin. Brian is risk neutral
so his indi
f
erence curves are straight lines; in fact, they have a numerical slope
equal to the probability of the good state over the probability of the bad state,
which is
3
/
4
over
1
/
4
or
3
. The tangencies trapped between the Andy and Brian
indi
f
erence curves through their endowment points form the core – that is, the
Pareto e
ﬃ
cient allocations where neither person is worse o
f
. As in earlier general
equilibrium examples in class the o
f
er curves will intersect on Brian’s indi
f
erence
curve through his endowment point. In the competitive equilibrium each Brian will
completely insure each Andy. The equation for a line with a slope of
−
3
, passing
through
(80
,
40)
is
w
A
b
=280
−
3
w
A
g
.
We know that when the Andys are o
f
ered fair insurance they will choose to insure
completely
±
w
A
b
=
w
A
g
²
so solving these two equations in the competitive equilibrium
w
A
b
=
w
A
g
=
280
4
=70
w
B
g
=1
6
0
−
70 = 90
w
B
b
=8
0
−
70 = 10
P
w
g
P
w
b
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 Fall '08
 Burbidge,John

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