Microeconomics
ECON 100A
Problem Set 7
Due November 9, 2010 (Solutions Posted November 12, 2010)
1.
From problem set 4 question 3 you already have seen the following utility function:
z
x
z
x
U
2
)
,
(
+
=
a.
Solve for the optimal consumption bundle, x* and z*, as a function of
x
p
,
z
p
, and Y.
b.
What are x*, and z* if Y=100,
2
=
x
p
1
=
z
p
c.
What is the level of utility given x* and z*?
d.
Solve for the Hicksian demand functions X
h
(p
x
, p
z
,
U
) and Z
h
(p
x
, p
z
,
U
).
e.
NOW, Suppose P
x
falls to $1. At this new, lower price of X, what are the ordinary demands,
X* and Z*, and the consumer’s maximum achievable utility?
f.
What are the values of X
h
(p
x
, p
z
,
U
) and Z
h
(p
x
, p
z
,
U
) if U is equal to value you solved for
in part c, and
1
=
x
p
1
=
z
p
g.
What are the income and substitution effects of this lower price of X? Please draw a picture
and label it with the values you solve for.
2.
From problem set 5 question 3 you already have seen the following utility function:
U=Z+4X
a.
Solve for the optimal consumption bundle, x* and z*, as a function of
x
p
,
z
p
, and Y.
b.
What are x*, and z* if Y=100,
2
=
x
p
1
=
z
p
c.
What is the level of utility given x* and z*?
d.
Solve for the Hicksian demand functions X
h
(p
x
, p
z
,
U
) and Z
h
(p
x
, p
z
,
U
).
e.
NOW, Suppose P
x
rises to $5. At this new, lower price of X, what are the ordinary demands,
X* and Z*, and the consumer’s maximum achievable utility?
f.
What are the values of X
h
(p
x
, p
z
,
U
) and Z
h
(p
x
, p
z
,
U
) if U is equal to value you solved for
in part c, and
5
=
x
p
1
=
z
p
g.
What are the income and substitution effects of this lower price of X? Please draw a picture
and label it with the values you solve for.
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3.
True or false. Explain fully. (Hint: the answer if false.)
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 Fall '08
 ZAMBRANO
 Microeconomics, Utility, Sheila, Hicksian demand function, Hicksian demand functions, kangaroo burgers

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