Cornell University
Economics 3130
Problem Set 4 Solutions
1. (Question 7.2 from Text) Suppose you have an income of $24 and the only two goods
you consume are applies (
x
1
) and peaches (
x
2
). The price of apples is $4 and the price
of peaches is $3.
(a) Suppose that your optimal consumption is 4 peaches and 3 apples.
i. Illustrate this graphically with a budget constraint and indifference curve.
See panel (a) below.
ii. Now suppose that the price of apples falls to $2 and I take enough money
away from you to make you as happy as you were originally. Will you buy
more or fewer peaches?
Fewer because peaches are now relatively more expensive. The tangency of
the original indifference curve to the new budget constraint occurs further
along it. See panel (b) below.
iii. In reality, I do not actually take income away from you as described in (ii)
but your income stays at $24 after the price of applies falls. I observe that,
after the price of apples fell, you did not change your consumption of peaches.
Can you conclude whether peaches are an inferior or normal good for you?
The fall in the price of apples creates an income and a substitution effect.
As shown in panel (b) and discussed above, the substitution effect results in
fewer peaches being consumed. If the consumption of peaches is unchanged,
there must be a positive income effect. Peaches are a normal good.
(b) Suppose that your tastes can be described by the function
u
(
x
1
, x
2
) =
x
α
1
x
1

α
2
.
i. What value must
α
take in order for you to choose 3 apples and 4 peaches at
the original prices?
The Marshallian demand for good 1 is
x
1
=
αI
p
1
. Substituting in the known
variables gives
α
=
1
2
.
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 Spring '06
 MASSON
 Economics, Microeconomics, indirect utility function

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