Sample Paper
Attempt All Questions:
Q # 1:
A company estimates that the demand for its product fluctuates with the price it
char4ges. The demand function is:
=
,

q
280 000 400p
where q equals the number of units demanded and p equals the price in dollars. The cost
function is estimated as:
=
,
+
+ .
C
350 000 300q 0 0015q2
a)
Determine how many units should be produced in order to maximize annual
profit.
b)
What price should be charged?
c)
What is the annual profit expected to equal?
Q # 2:
An individual’s utility function is given by:
=
+ .
+ .
 .
 .
U
10x1 4 5x2 0 05x1x2 0 02x12 0 01x22
a)
Determine the values of
&
MU1
MU2
when
=
.
&
= .
x1
1 3
x2
5
Hence, estimate
the change in utility if the
x1
increases by one unit and
x2
increases by 15
units.
b)
Does the law of Diminishing Marginal Utility hold for this function?
Q # 3:
Verify Euler’s theorem for the Cobb–Douglas production function:
=
Q
AKαLβ
NOTE: this is a homogeneous function of degree
+ .
α
β
1

P a g e
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Q # 4:
a)
The owner of a grocery store purchases 50 glass items, used for decoration, to
sell at $15 each. The owner knows from the past experience that about 6% of
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 Spring '11
 fazli
 Economics, cobb–douglas production function, rade discount series, Diminishing Marginal Ut, ili ty hold

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