ECON 331 Final Exam
Saturday, April 12, 1997
K. Wainwright
Name
Instructions.
•
— Put you name on the EXAM and the Booklets you use for your answers.
— The Exam Sheet must also be handed in as proof you wrote the test.
—
Time allowed is
2.5 HOURS. Total marks = 100
Part One: Shorter problems, 10 marks each
1. Minimize
z
= 3
x
2
−
xy
+ 2
y
2
−
4
x
−
7
y
+ 12
subject to the inequality constraint
x
+
y
≥
15
. Is the constraint binding or nonbinding?
2. Given the utility function
u
=
x
a
y
b
,
show that both
u
and the monotonic transforma
tion,
v
= ln(
x
a
y
b
)
have the same
MRS.
3. Given
y
= 4
xe
3
x
(a) Find the critical point.
(b) Check to see if the function is at a maximum or minimum.
4. A $100 bar of gold is appreciating in value according to the formula
V
= 100
e
√
t
How long should the gold bar be kept to maximize the present value if under continuous
compounding (a)
r
= 0
.
08?
(b)
r
= 0
.
12?
5. Suppose an industry has two
fi
rms which have identical cost functions of the form
C
(
q
i
) =
K
+
cq
i
(where
i
= 1
,
2
and
0
< c <
1
).
The market demand function is
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 Spring '09
 KelvinKwainger
 Economics, Myrtle

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