Jura Liaukonyte
Econ
419
S
pring
200
7
Math Review Questions
(this is not for grades)
1. Find the derivate of the following cost functions with respect to q.
a)
3
(12
)
q
c
q
=
−
23
2
)
3
( 1)
)
dc
q
q
q
dq
q
−−
−
=
−
b)
3
ln )
cq
q
=−
1
ln )3
(
)
dc
qq q
q
dq
+−
c)
q
ce
=
q
dc
e
dq
=
2.
Suppose that y is a function of x
1
and x
2
, find the values of x
1
and x
2
the maximize
the following function:
y=(x
1
1)
2
–(x
2
2)
2
+ 10
It will be easier if you rewrite the function as:
22
11
yx
x
x
x
+
−
+
+
5
now we need to maximize with with respect to x1 and x2.
You need to use partial derivates.
1
1
2
2
1)
2
2
0 (we set it to zero because want to find max)
y
2)
2
4
0
x
y
x
x
x
∂
+ =
∂
∂
∂
You now gave two equations and two unknowns.
Solving equation 1 and 2 we find the values that maximize this function are :
*
1
x
=1
*
2
x
=2
(How do we know that this is max not min?)
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View Full Document3.
Suppose a firm’s total revenues depend on the amount produced (q) according to
the function:
R=70qq
2
Total costs also depends on q:
C=q
2
+30q+100
a)
What level of output should the firm produce in order to maximize profits
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 Spring '07
 jura
 Derivative, Optimization, Fermat's theorem, Liaukonyte Econ

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