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ECON 331 Sample Midterm Exam
Spring 1998
Selected Answers and Hints:
1. Given the matrix
A
=
2
6
6
6
6
6
4
1
0
4
3
3
0
1
0
6
9
0
0
1
1
2
0
0
2
1
1
0
0
0
1
0
3
7
7
7
7
7
5
The determinant:
j
A
j
= 3
2. Consider the following two market model
Q
d
1
= 20
P
1
+ 2
P
2
Q
s
1
= 2
P
1
2
Q
d
2
= 18
2
P
2
+ 3
P
1
Q
s
2
= 2 + 4
P
2
(a) HINT: Look at the signs of the cross partials
@Q
i
=@P
j
(b) Use Cramer&s rule to ±nd the inverse demand func
tions
P
1
=
P
1
(
Q
1
;Q
2
)
P
2
=
P
2
(
Q
1
;Q
2
)
:
Solution
"
P
1
P
2
#
=
"
1
2
Q
1
+
1
2
Q
2
19
3
4
Q
1
+
1
4
Q
2
39
2
#
3. Consider the following:
(a) Let
q
=
f
(
L
)
be the short run production function
where L represents labour, the only input. use cal
culus to show that when
MP
L
> AP
L
,
AP
L
is
rising and
MP
L
< AP
L
,
AP
L
is falling.
HINT:
See Chapter 7
(b) When
MP
L
=
AP
L
,
AP
L
is assumed to be at a
maximum and not a minimum. What assumption
about the second derivative of
f
(
L
)
ensures this
result? What is the economic expression for this
result?
HINT: Look at a graph of
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This note was uploaded on 09/13/2009 for the course EOCNOMICS Econ 331 taught by Professor Kelvinkwainger during the Spring '09 term at Simon Fraser.
 Spring '09
 KelvinKwainger

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