micro-fall2007-6 - Households Preferences An important...

Households Preferences
An important property of the utility function
The indi/erence curves remain unchanged under any monotonic
transformation of the utility function.
Let
f : R
!
R
be a strictly increasing function. Then,
(
i
)
f
(
u
(
x
)) =
f
(
u
(
z
))
()
u
(
x
) =
u
(
z
)
.
(
ii
)
MRS
(
x
)
:
= °
dx
2
dx
1
=
f
0
( ± )
∂ u
( ± )
∂ x
1
f
0
(
±
)
∂ u
( ± )
∂ x
2
=
∂ u
( ± )
∂ x
1
∂ u
( ± )
∂ x
2
Ani Guerdjikova Fall 2007 74 / 80

Households Preferences
Properties of the preference relation
A representation of preferences by means of a utility function is
possible if following assumptions are satis°ed:
1
Completeness
For all x , z
2
X
° either x
%
z
° or z
%
x
° or x % z and z % x
Ani Guerdjikova Fall 2007 75 / 80

Households Preferences
Properties of the preference relation
A representation of preferences by means of a utility function is
possible if following assumptions are satis°ed:
1
Completeness
For all x , z
2
X
° either x
%
z
° or z
%
x
° or x % z and z % x
2
Transitivity
For all x , y , z
2
X ,
x
%
y and
y % z
imply
x
%
z .