UCLA
Economics 11 – Fall 2006
Professor Mazzocco
Problem Set 5
Due by November 9 before 11:30am.
1)
A consumer has utility:
5
.
0
5
.
0
y
x
U
+
=
.
The Marshallian demands are given by:
)
(
)
(
y
x
y
U
y
x
x
y
U
P
P
P
PxI
Y
P
P
P
I
P
X
+
=
+
=
And that the Hicksian demands are given by:
2
2
+
=
+
=
y
x
x
C
y
x
y
C
P
P
U
P
Y
P
P
U
P
X
a) Find the Indirect Utility Function
V
.
b) Find the Expenditure Function
E
.
c) Using the Slutsky equation, find the expressions for the substitution effect and the
income effect on X generated by an increase in
P
x
.
d) Derive the Slutsky equation for the good X for a change in the price
P
y
. [Hint:
follow the method that we used in class to derive the Slutsky equation for the good X
for a change in the price
P
x
. But instead of computing the derivatives of the starting
equation with respect to
P
x
, you have to compute the derivatives with respect to
P
y
.]
f) Using the Slutsky equation derived in part d) find the expressions for the
substitution effects and the income effect on X generated by an increase in
P
y
.
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 Spring '08
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 Utility

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