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Solutions to Selected Questions from Exam 1
Form A
Finley Edwards
This document contains answers to all Multiple Choice and True False Questions, as well as complete
solutions to all four problems.
Multiple Choice and True False Answers
1. B
2. D
3. A
4. C
5. C
6. D
7. D
8. B
9. D
10. A
11. D
12. E
13. C
14. A
15. C
16. D
17. B
18. B
19. FALSE
20. TRUE
Question 21
Part (a)  5 points
In each case the budget equation takes the form
p
x
x
+
p
y
y
=
m

F
where
F
is the fee associated with that
plan.
Plan A:
x
+ 2
y
= 80
Plan B:
x
+
y
= 60
Part (b)  10 points
I only asked for the optimal amount of
y
, but we’ll need
x
for part (c) so I’ll solve for both. The simplest
way to solve this part is to recognize that this is a CobbDouglas utility function with
c
= 0
.
5 and recall
that the demand function for a CobbDouglas utility function is given by
y
(
m,p
x
,p
y
) =
c
m
p
y
. This gives the
1
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View Full Documentdesired quantities.
Plan A:
y
= 0
.
5
80
2
= 20 and
x
= 0
.
5
80
1
= 40
Plan B:
y
= 0
.
5
60
1
= 30 and
x
= 0
.
5
60
1
= 30
If you did not recognize that this was CobbDouglas utility, you would need to solve for the optimal
choice. Using the
MRS
=

p
x
p
y
condition, we have:
MRS
=

MU
x
MU
y
=

y
x
=

p
x
p
y
Solving for
x
gives
x
=
y
p
y
p
x
. Plugging this result into our budget equation gives the optimal amount of
y
.
Plan A:
Plugging
x
= 2
y
into the budget constraint we have 2
y
+ 2
y
= 80 which gives
y
= 20. This
implies that
x
= 2
*
20 = 40.
Plan B:
Plugging
x
=
y
into the budget constraint we have
y
+
y
= 60 which gives
y
= 30. This implies
that
x
=
y
= 30.
Part (c)  5 points
To choose between the two plans, we need to compare the utility under the two plans.
Plan A:
U
(40
,
20) = 40
*
20 = 800
Plan B:
U
(30
,
30) = 30
*
30 = 900
Since Plan B gives a higher utility, he would choose plan B.
I graded this part of the question based on the amount of
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 Spring '10
 JOSEPHPETRY

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