1
10th April 2006
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. 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).
Assume
B
1
∈
B
,
B
2
∈
B
,
{
a, b
}
⊂
B
1
,
{
a, b
}
⊂
B
2
.ThenWARPsay
s
a
∈
C
(
B
1
)
,
b
∈
C
(
B
2
)
⇒
a
∈
C
(
B
2
)
.
(b) Assume a two-good model and a price-taking consumer whose behaviour is
consistent with WARP. Prove that the substitution e
f
ect (Slutsky method) of a
reduc
t
ioninthep
r
iceo
fgood1canno
tleadtoareduc
t
ioninthecon
sump
t
iono
f
good 1.
Diagram from Econ 201. Note: no indi
f
erence curves or other references to the
preference-based approach are permitted here.
2. Consider a price-taking agent who likes consumption
c
and leisure
l
.Anyt
ime
notspentatleisureisspentworkingandthetimeendowmentis
T
. Denotethepriceof
consumption by
p
, the price of leisure by
w
and the value of the person’s endowment
of money by
m
.L
e
t
c
(
p, w, m, T
)
and
l
(
p, w, m, T
)
be Marshallian demands, and
h
c
(
p, w, u, T
)
and
h
l
(
p, w, u, T
)
be Hicksian demands. Fill in the following tables for
u
=
c
+2
l
1
/
2
,
0
≤
l
≤
T.
Thebudgetconstra
intis
pc
+
wl
=
wT
+
m.
c
(
p, w, m, T
)
l
(
p, w, m, T
)
Range
wT
+
m
p
−
p
w
p