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Figure 7
x
is a substitute for
y
does not imply that
y
is a substitute for
x
original budget line = MN
original optimum = A
When
p
y
"
, hence
y
#
and
x
"
, thus
x
and
y
are substitutes (
x
is a substitute for
y
).
TE = total e/ect =
x
2
±
x
0
>
0
SE = substitution e/ect =
x
1
±
x
0
>
0
IE = income e/ect =
x
2
±
x
1
<
0
SE dominates IE (SE
>
j
IE
j
), hence TE
>
0
When
p
x
"
, the optimum moves from A
to C±, hence
x
#
and
y
#
, thus
x
and
y
are complements (
y
is a complement for
x
).
TE = total e/ect =
y
2
±
y
0
<
0
SE = substitution e/ect =
y
1
±
y
0
>
0
IE = income e/ect =
y
2
±
y
1
<
0
IE dominates SE (
j
IE
j
>
SE), hence TE
<
0
34
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View Full Document3. Net Substitutes and Complements
x
and
y
are net substitutes if
@x
@p
y
U
=
constant
>
0
x
and
y
are net complements if
@x
@p
y
U
=
constant
<
0
@x
@p
y
U
=
constant
>
0
implies that
@y
@p
x
U
=
constant
>
0
(proof not required)
Example:
U
(
x;y;z
) =
1
x
1
y
1
z
:
Then
x
=
I
p
x
+
p
p
x
p
y
+
p
p
x
p
z
,
y
=
I
p
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 Fall '09
 LeungSiuFai
 Microeconomics

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