School

Witwatersrand **We aren't endorsed by this school

Course

ECON 4036A

Subject

Economics

Date

Feb 27, 2023

Pages

14

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University of the Witwatersrand
School of Economic and Finance
Advanced Microeconomic Theory (ECON 4036); Test 2
Date: 16
September 2021
Duration: 3 Hours
Instructions
1.
Attempt all the questions.
2.
Make sure that your student number is clearly written on every page of
your script

1.
Define the following concepts (
5 points each
)
i.
Consumption set
Memo
Definition1:
Let
x
=(
x
1
,x
2
x
3
......... x
n
)
be a consumption vector containing
different quantity of
each of
n
commodities. Then the set of
x
denoted as
X
is referred to
consumption set
where
x
∈
X
is represented by a point
R
+
¿
n
x
=
¿
.
ii.
Budget set
Memo
Definition2:
Let
px≤ y
a budget line where
y
is fixed money income of
the consumer and
px
=
∑
i
n
p
i
x
i
is total expenditure on
n
goods. Then the
subset;
R
+
¿
n
, px≤ y
x
∨
x
=
¿
Β
=
¿
is referred to as a budget set.
Alternatively if you draw a graph and shade the area under budget line with
inclusion of the budget line, you will get the full score.
iii.
Axiom
of completeness
Memo
For consumption
vectors
x
and
y
in
X
where
X
consumption set
,
either
x
≽
y
or y
≽
x
. This axiom formalize the notion that the consumer can make

comparison i.e. he has the ability to discriminate and necessary knowledge to evaluate
the alternatives .
iv.
Axiom of continuity
Memo
Continuity
axiom: For all
R
+
¿
n
x
∈
¿
, the 'at least as good as' set
≽
(
x
¿
and
the 'no better than' set
≼
(
x
¿
are closed
v.
Axiom of monotonicity
Memo
Strict Monotonicity; For all
x
1
and
x
0
in
R
+
¿
n
¿
, if
x
0
≥ x
1
, then
x
0
≽
x
1
while
x
0
>
x
1
then
x
0
≻
x
1
.
This axiom
says that if one bundle contains at least as
much of every commodity as another bundle, then the one is at least as good as the other.
vi.
Axiom of transitivity
Memo
For all
x
,
y
and z in
X ,
if
x
≽
y
and
y
≽
z ,then
x
≽
z
This axiom
requires that the consumer pair wise ranking of alternative is consistent. However, recent
experimental results invalidate this assumption (behavioral economics has much to offer
here).

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