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Microeconomics
ECON 100A
Problem Set 4 Solutions [THIS MATERIAL IS NOT ON THE MIDTERM]
Due October 20, 2010 (Solutions Posted October 22, 2010)
1.
Now, let’s see if you can do the general perfect complements problem.
Matt gets utility from X and
Z.
Matt always consumes
α
X with
β
Z.
a.
What type of utility function represents Matt’s preferences?
Write down an expression for
Matt’s utility.
b.
What is Matt’s utility maximizing combination of X*(P
x
, P
z
, Y) and Z*(P
x
, P
z
, Y)?
c.
What is the Matt’s indirect utility function,
i.e., V(P
x
, P
z
, Y)=U(X*(P
x
, P
z
, Y), Z*(P
x
, P
z
, Y))?
d.
Show that Roy’s identity holds for good x.
e.
What share of his budget does Matt spend on X*?
What share of his budget does Matt spend
on Z*?
(Note: check that these two shares sum to one.)
2.
Now, let’s see if you can do the general perfect substitutes problem.
Toni gets utility from X and Z.
Toni thinks that
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 Fall '08
 ZAMBRANO
 Microeconomics, Utility

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