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Consumer’s Problem IV
Income, Substitution and Price Effects
Consider the consumer’s problem:
max U=U(x
1
, x
2
)
s.t.
p
1
x
1
+p
2
x
2
=m
We have seen that the optimal solution to the problem leads to the utilitymaximizing
bundle (x
1
*, x
2
*).
Figure 1
x
2
C
m/p
2
A
x
2
**
R
x
2
*
P
O
x
1
*
x
2
**
m/p B
D
x
1
Now suppose that p
1
and p
2
(Figure 1) remain unchanged but m is raised to m’. We know
that the new budget line satisfying
p
1
x
1
+p
2
x
2
=m’
represented by the line CD will be parallel to the old budget line AB. The point of
tangency B of the new budget line with a higher indifference curve represents the new
1
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1
** and x
2
**. The increase in quantity
of x
1
(x
1
**x
1
*) and x
2
(x
2
**x
2
*) is known as the
income effect
. In general, when income
increases, the new optimal point will be towards the northeast of the old point that is the
income effect is positive for both goods. Goods with positive income effect are called
normal goods.
Return to the previous example of
Ux
x
=+
12
We saw that for m=m
0
and price (p
1
, p
2
)
x
mp
pp p
1
02
11
2
*
()
=
+
and
x
2
01
21
2
*
=
+
If m is increased to m
1
we solve the problem
m
a
x
x
p
1
x
1
+p
2
x
2
=m
1
The new optimal bundle is
x
1
2
**
=
+
and
x
2
2
=
+
Thus the income effects are
xx
mm
p
10
2
*
−=
2
−
+
and
2
xx
mm
p
pp p
22
10
21
2
**
*
()
−=
1
−
+
respectively.
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This note was uploaded on 10/19/2010 for the course ECON 1202 taught by Professor Matel during the Fall '08 term at UConn.
 Fall '08
 MATEL
 Economics, Utility

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