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Microeconomics
Problem Set 7 Solutions
Due March 3rd, 2010
Winter 2010 ECON 100A
1.
(This question is from a practice midterm)
Ralph consumes only two goods, potatoes (good
1) and yams (good 2). He is not as particular with his portion sizes and has a utility function
given by
2
1
2
1
)
,
(
q
q
q
q
U
=
, where q
1
is the number of potatoes and q
2
is the number of yams
he consumes in a day. He wishes to maximize utility. The price of a potato is p
1
and the price
of a yam is p
2
. Ralph owns a farm that produces only potatoes and yams and selling these
crops are Ralph’s only source of income. Therefore his income, which depends on the prices
of potatoes and yams and on Ralph’s endowment of potatoes and yams, is given by Y =
p
1
q
1
0
+p
2
q
2
0
, where q
1
0
is Ralph’s endowment of potatoes (i.e. what he harvests) and q
2
0
is his
endowment of yams (i.e. what he harvests).
a.
(5) Solve for Ralph’s Marshallian demand function for potatoes and his Marshallian
demand function for yams. Your solution should be a function only of prices and
endowments. However, if you prefer, you
may
still use the notation “Y” in place of
p
1
q
1
0
+p
2
q
2
0
to keep the equations clean. If you do this, though, don’t forget that Y is still
a function of prices, that will matter!
Also solve for the indirect utility function.
Usual Cobb Douglas in the usual way.
q
2
/q
1
= p
1
/p
2
Y = p
1
q
1
+ p
2
q
2
q
1
= Y/2p
1
= (p
1
q
10
+ p
2
q
20
)/2p
1
q
2
= Y/2p
2
= (p
1
q
10
+ p
2
q
20
)/2p
2
V= (
Y/2p
1
)(
Y/2p
2
)
b.
(5) Solve for Ralph’s Hicksian demand function for potatoes and his Hicksian demand
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 Winter '08
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 Microeconomics

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