CORNELL UNIVERSITY
FINAL EXAM
Wednesday, December 16, 2009
INTERMEDIATE MICROECONOMIC THEORY
ECON 3130
Professor Majumdar
Fall 2009
You have 150 minutes to complete this exam. There are 135 points.
Permitted Materials: Nongraphing calculators only.
WARNING
The exam is divided into two parts, Part A and Part B. You must answer
failure to do so will result in a 10point penalty.
On the cover of each exam booklet, please state whether it includes
Make sure your name is on all exam booklets used.
When time is called, please put your answers to Part A in the box marked
±Part A², and put your answers to Part B in the box marked ±Part B².
No exam booklets will be accepted after we leave the room.
PLEASE DO NOT OPEN THIS EXAM UNTIL INSTRUCTED TO DO SO
Page 1 of 10
ECON 3130
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Question 1
Answer "yes" or "no" with a brief justi±cation of your position
(
a
)
[ 5 points ] No, it is not true in general. As an example, take any smooth utility
function over 2 goods (say, the CobbDouglas utility function
u
(
x;y
) =
x
1
2
y
1
2
).
Then, consider any bundle on one of the axes but outside of the budget set (for
example,
2
m
p
x
;
0
±
). It then follows that
u
(
x
;y
) = (
x
y
)
1
2
> u
2
m
p
x
;
0
±
= 0
.
(
b
)
[ 5 points ] No, both goods
x
and
y
cannot be both Gi/en goods. If both are Gi/en
then by de±nition both must be inferior goods, something we have already proven
cannot hold:
Assume both goods
x
and
y
are inferior. De±ne
(
x
;y
)
to be the optimal bundle
of goods chosen given the budget set
B
(
p
x
;p
y
;m
)
and consider some variation of
income. Since both goods
x
and
y
are inferior, then by de±nition of an inferior
good we have
@x
(
p
x
;p
y
;m
)
@m
<
0
and
@y
(
p
x
;p
y
;m
)
@m
<
0
. By the assumption that "more
is preferred to less" of both goods, we know that the budget constraint has to
bind at the optimum. In other words,
p
x
x
(
p
x
;p
y
;m
) +
p
y
y
(
p
x
;p
y
;m
) =
m:
Di/erentiating implicitly with respect to
m
, we get
p
x
@x
(
p
x
;p
y
;m
)
@m
+
p
y
@y
(
p
x
;p
y
;m
)
@m
=
1
. However, since
p
x
and
p
y
are de±ned to be positive, then
@x
(
p
x
;p
y
;m
)
@m
<
0
and
@y
(
p
x
;p
y
;m
)
@m
<
0
imply that
p
x
@x
(
p
x
;p
y
;m
)
@m
+
p
y
@y
(
p
x
;p
y
;m
)
@m
<
0
6
= 1
:
(
c
)
[ 5 points ] No. Consumer 2 will choose the same commodity bundle
(
x
;y
)
:
v
(
x;y
) = 2
u
(
x;y
) + 3
is a linear transformation of
u
(
x;y
)
, and therefore it is
a monotonic increasing transformation of
u
(
x;y
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 '06
 MASSON
 Economics, Microeconomics, Supply And Demand, Inverse demand function

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