Eco11, Fall 2008
Simon Board
Economics 11: Practice Problems 4 (Week 5)
October 16, 2008
1. Expenditure Minimisation with CES demand
A consumer has the utility
u
(
x
1
, x
2
) =
x
1
/
2
1
+
x
1
/
2
2
.
a) Find the Hicksian demand for
x
1
and
x
2
b) Find the expenditure function.
c) Find the Marshallian demand for
x
1
and
x
2
.
d) Find the indirect utility function. Depending on how you approach this question, you may
find it useful to note that:
p
2
p
1
¶
1
/
2
+
p
1
p
2
¶
1
/
2
=
p
1
+
p
2
(
p
1
p
2
)
1
/
2
e) Show that the Slutsky equation holds.
2. Consumption with Endowments: Labour Supply
A particular household consists of two agents who are both potential workers and who pool
their budgets. The households preferences are represented by a single utility function
u
(
x
0
, x
1
, x
2
) = log(
x
0

α
) + log
x
1
+ log
x
2
where
x
1
is the amount of leisure enjoyed by agent 1,
x
2
is the amount of leisure enjoyed
by agent 2, and
x
0
is the amount of the single composite consumption good enjoyed by the
household. The two agents each have
T
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 cunningham
 Utility, P1 P2, Simon Board

Click to edit the document details