E
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401
1
Test 1
Thursday 27th January 2011
Answer all questions. Each is worth 10 marks.
1. What are the two main approaches to consumer behaviour in economics? What
elements do they have in common, and how do they di
f
er? What restrictions do they
place on a twogood system of ordinary demand equations?
x
1
(
p
1
,p
2
,w
)
x
2
(
p
1
2
)
ANSWER
The two approaches are the choicebased approach and the preferencebased ap
proach. The
f
rst is founded on the weak axiom of revealed preference; the second on
preference relations. Both approaches assume standard budget constraints in
R
n
+
and
therefore are consistent with the implications of imposing such budget constraints.
The CB approach assumes the consumer’s choices are consistent with the weak ax
iom. The PB approach assumes the consumer’s choices obey the many assumptions
imposed on preference relations (re
F
exivity, completeness, transitivity, continuity,
monotonicity or local nonsatiation, convexity, etc.).
The restrictions on the demand system include the following.
Walras’s Law
p
1
x
1
(
p
1
2
)+
p
2
x
2
(
p
1
2
)=
w
Homogeneity
for all
α
>
0
,x
j
(
α
p
1
,
α
p
2
,
α
w
x
j
(
p
1
2
)
,j
=1
,
2
Denoting the Slutsky substitution matrix by
S
, these identities imply
±
p
1
p
2
²
³
S
11
S
12
S
21
S
22
´
=
±
00
²
and
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2
±
S
11
S
12
S
21
S
22
²±
p
1
p
2
²
=
±
0
0
²
2. Let
X
be a choice set and
(
B
,C
(
·
))
be a choice structure on
X
.
(a) Using mathematics, de
f
ne the weak axiom of revealed preference (WARP).
(b) Do each of the following satisfy WARP? Justify each answer.
(i)
X
=
{
a,b, c
}
,
B
=
{
B
1
,B
2
3
}
1
=
{
a, b
}
2
=
{
b, c
}
3
=
{
c, a
}
(
B
1
)=
{
a
}
(
B
2
{
b
}
(
B
3
{
c
}
;
(ii)
X
=
{
a, b, c
}
,
B
=
{
B
1
2
}
1
=
{
a,b
}
2
=
{
a, b, c
}
(
B
1
{
a
}
(
B
2
{
a, b
}
;
(iii)
X
=
{
a, b, c, d
}
,
B
=
{
B
1
2
}
1
=
{
}
2
=
{
a, b, d
}
(
B
1
{
a, c
}
(
B
2
{
a, d
}
;
ANSWER
(a) WARP can be de
f
ned as:
(*) Assume
B
1
∈
B
2
∈
B
,
{
a, b
}
⊂
B
1
,
{
a, b
}
⊂
B
2
then
a
∈
C
(
B
1
)
and
b
∈
C
(
B
2
)
⇒
a
∈
C
(
B
2
)
.
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 Fall '08
 Burbidge,John
 Economics, Transitivity, p1, p2 x2, x1 > x2, x2 > x1

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