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ECON 400
Hartman
Winter 2011
Problem Set VIII
(for Wednesday, March 2)
1.
A person's preferences over two goods can be represented by the utility function
( , )
ab
Uxy xy
where
0
a
and
0
b
are given parameters and
0
x
and
0
y
denote the quantities of the two goods.
Let
p
and
s
denote the prices of goods
x
and
y
, respectively, and let
M
denotes the individual's wealth.
a.
Solve for the individual's Marshallian demand functions for the two goods,
*
(,, )
x
xp
sM
and
*
y
yp
.
Hint:
*
x
does not depend on
s
, and
*
y
does not depend on
p
.
b.
Verify that these demand functions are homogeneous of degree zero in ( , ,
)
psM
.
c. Let
ij
denote the elasticity of demand for good
,
ix
y
with respect to price
,
j
ps
, and let
iM
denote the elasticity of demand for good
i
with respect to income.
(i) Verify that
0
xp
xs
xM
and that
0
yp
ys
yM
.
(ii) Verify that
0
xp
yp
px
sy
px
MMM
, that
0
xs
ys
px
sy
sy
, and that
1
xM
yM
px
sy
MM
.
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 Spring '08
 Ellis,G
 Utility

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