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Econ 501
Homework Assignment 3
Due January 29, Tuesday
1.
BB 4.3
This question cannot be solved using the usual tangency condition. However, you
can see from the graph below that the optimum basket will necessarily lie on the
“elbow” of some indifference curve, such as (5, 3), (10, 6) etc. If the consumer
were at some other point, he could always move to such a point, keeping utility
constant and decreasing his expenditure. The equation of all these “elbow” points
is 3
x
= 5
y
, or
y =
0.6
x
. Therefore the optimum point must be such that 3
x
= 5
y.
The usual budget constraint must hold of course. That is,
220
10
5
=
+
y
x
.
Combining these two conditions, we get (
x
,
y
) = (20, 12).
2.
BB 4.7
See the graph below. The fact that Helen’s indifference curves touch the axes
should immediately make you want to check for a corner point solution.
To see the corner point optimum algebraically, notice if there was an interior
solution, the tangency condition implies (
S
+ 10)/(
C
+10) = 3, or
S
= 3
C
+ 20.
Combining this with the budget constraint, 9
C +
3
S =
30, we find that the optimal
number of CDs would be given by
30
18
−
=
C
which implies a negative number
of CDs. Since it’s impossible to purchase a negative amount of something, our
(5,3)
(10,6)
y
x
(20,12)
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View Full Document assumption that there was an interior solution must be false.
Instead, the optimum
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This note was uploaded on 07/17/2008 for the course ECON 501.02 taught by Professor Yang during the Winter '08 term at Ohio State.
 Winter '08
 YANG
 Microeconomics

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