Problem Set #3
1
Basics
Consider the utility function
u
=
x
α
y
1

α
. For this utility function, find:
1. Demand functions.
2. Compensated Demand functions.
3. The Expenditure function.
4. The Indirect Utility function.
5. Using your expressions above and the Slutsky equation, develop math
ematical expressions for the size of the income effect and the size of
the substitution effect as functions of prices and income.
2
Applications
Consider a situation in which
p
x
= $5,
p
y

$10,
I
= $100, and
α
=
1
2
. (Note
that if you couldn’t get answers in the previous section, you might be able
to for the case
α
=
1
2
.)
1. Using the indirect utility function, find the consumer’s utility at the
given prices and income level. Using the demand functions, find the
consumer’s consumption level of each good.
2. Suppose that
p
x
rises to $10.
How much of each good is the con
sumer now consuming?
Using the indirect utility function, find the
consumer’s utility at the new price.
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 Spring '09
 Baker
 Utility, $5, $10, Roy, $100, xdpx

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