Econ/ARE 5201
Subhash Ray
Fall 2010
Homework Problem Set #2
1.
John consumes two goods: good 1 and good 2 and has the utility function
2
1
2
1
4
x
x
x
x
U
+
=
where
x
1
and
x
2
are the quantities of the two goods consumed. The prices of the two
goods are
p
1
and
p
2
, respectively. He spends his entire income on these two goods.
(a)
Obtain his Marshallian demand functions
and
)
,
,
(
2
1
1
1
m
p
p
x
x
d
=
).
,
,
(
2
1
2
2
m
p
p
x
x
d
=
(b)
Obtain his indirect utility function
U
*
= V (p
1
, p
2
, m).
(c)
For
)
60
,
find his optimal consumption bundle.
1
,
4
(
2
1
=
=
=
m
p
p
(d)
Now consider a new situation with
).
64
,
4
,
1
(
2
1
=
=
=
m
p
p
Is John better or worse
off in the new situation?
(e)
Obtain his optimal consumption bundle directly from
V(p
1
, p
2
, m)
for the new
prices and income.
2.
Bill derives utility from the consumption of apples and bananas. He has an
endowment of 8 apples and 12 bananas. His utility function is
b
a
x
x
U
+
=
)
ln(
4
where
x
a
and
x
b
are, respectively, the quantities of apples and bananas consumed by
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 Fall '08
 MATEL
 Economics, Utility

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