Ch 5:
5.7, 5.10, 5.15, 5.17
Ans: 5.7
a)
Denoting the level of income by
I
, the budget constraint implies that
I
y
p
x
p
y
x
=
+
and the tangency condition is
y
x
p
p
x
=
2
1
, which means that
2
2
4
x
y
p
p
x
=
. The demand for
x
does not depend on the level of income.
b)
From the budget constraint, the demand curve for
y
is,
x
y
y
y
x
p
p
p
I
p
x
p
I
y
4

=

=
.
You can see that the demand for
y
increases with an increase in the level of
income, indicating that
y
is a normal good. Moreover, when the price of
x
goes
up, the demand for
y
increases as well.
5.10
a)
The budget constraint is
240
2
8
=
+
y
x
and the tangency condition is
4
2
8
2
=
=
x
y
. Solving, the optimal bundle is (
x
,
y
)=(20, 40) with a utility of 20
2
(40)=16,000.
b)
Now
p
y
=8. We need to calculate
p
x
such that, with the new prices, Ginger reaches
exactly the same indifference curve as before. The new optimal bundle (x,y) must
be such that:
16000
and
,
240
8
2
=
=
+
y
x
y
x
p
x
. The tangency condition now
implies that
8
2
x
p
x
y
=
that is,
.
16
y
x
p
x
=
Substituting this into the budget
constraint we find that y=10. Using the condition
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 Summer '10
 Raven
 Px, tangency condition, PFF

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