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Econ 100A  Worksheet #9
Demand Functions
Exercise 1
Consider the utility function
U
(
x
1
, x
2
) =
x
1
(
x
2

1)
.
Let
p
1
be the price of good 1,
p
2
the price of good 2 and
I
the income. We assume that
I > p
2
.
1)
Find the equation of the indiﬀerence curves and draw a couple with precision.
2)
Find the demand functions
3)
Solving for
I
in the demand for good 1 and substituting into the demand for good 2, ﬁnd the equation of the incomeconsumption
path and plot it on the graph for
p
1
=
p
2
= 1
.
4)
Assume
I
= 1000
. Find the optimal bundles when
p
1
=
p
2
= 10
and when
p
1
= 5
and
p
2
= 10
.
5)
Compute the substitution and income eﬀects.
5)
Are these goods gross substitutes?
Exercise 2
The recipe for the Margarita cocktail speciﬁes the following proportions for one glass:
•
1 1/2 oz tequila
•
1/2 oz premium triple sec (preferably Cointreau)
•
1 oz lime juice
Let us ignore the lime juice and focus only on tequila and Cointreau. Let
T
be the quantity of tequila and
C
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This note was uploaded on 07/09/2010 for the course ECON 100A taught by Professor Woroch during the Fall '08 term at University of California, Berkeley.
 Fall '08
 Woroch
 Microeconomics, Utility

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