SD&ZY_20102011/9
ISL233M
İ
KRO
İ
KT
İ
SATUYGULAMA DERS
İ
9
1314.12.2010
50.
The following table contains information for a price taking competitive firm.
Complete the table and
determine the profit maximizing level of output (round your answer to the nearest whole number).
Output
Total
Cost
Marginal
Cost
Fixed
Cost
Average
Cost
Total
Revenue
Average
Revenue
Marginal
Revenue
0
5
0
1
7
10
2
11
20
3
17
30
4
27
40
5
41
50
6
61
60
Solution:
Output
Total
Cost
Marginal
Cost
Fixed
Cost
Average
Cost
Total
Revenue
Average
Revenue
Marginal
Revenue
0
5
–
5
–
0
–
–
1
7
2
5
7
10
10
10
2
11
4
5
5.5
20
10
10
3
17
6
5
6
30
10
10
4
27
10
5
7
40
10
10
5
41
14
5
8
50
10
10
6
61
20
5
10
60
10
10
The profit maximizing level of output is either 3 or 4.
Note that at Q=4 the profitmaximizing
condition
MR=MC is satisfied.
Since this problem is discrete, the profit at Q=3 happens to be the
same as the profit at Q=4, so either of these answers is correct.
51.
Homer's Boat Manufacturing cost function is:
( )
4
75
10,240
128
=
+
C q
q
.
The marginal cost function is:
( )
3
75
.
32
=
MC q
q
If Homer can sell all the boats he produces for $1,200, what is his optimal output?
Calculate Homer's profit or loss.
Solution:
The profit maximizing output level is where the market price equals marginal cost (providing
the price exceeds the average variable cost).
To determine the optimal output level, we need to
first equate marginal cost to the market price.
That is,
( )
3
75
1,200
8.
32
=
=
=
⇔
=
MC q
q
P
q
The average variable cost at this output level is:
( )
( )
( )
3
75 512
75
8
8
300.
128
128
=
=
=
AVC
Since
( )
8 ,
>
P
AVC
Homer
will
maximize
profits
at
8
units.
Homer's
profits
are:
( ) ( )
( )
4
75 8
1,200 8
10,240
3,040.
128
=

=

+
= 
Pq C q
π
Homer will produce and make a
loss as losing $3,040 is better than not producing and losing $10,240.
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52.
Sarah's Pretzel plant has the following shortrun cost function:
( )
3
3
2
,
50 ,
1000
=
+
wq
C q K
K
K
where
q
is
Sarah's output level,
w
is the cost of a labor hour, and
K
is the number of pretzel machines Sarah leases.
Sarah's
shortrun marginal cost curve is
( )
2
3
2
3
,
.
100
=
wq
MC q K
K
At the moment, Sarah leases 10 pretzel machines, the
cost of a labor hour is $6.85, and she can sell all the output she produces at $35 per unit.
If the cost per labor
hour rises to $7.50, what happens to Sarah's optimal level of output and profits?
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 Spring '11
 Meonk
 Economics, Supply And Demand, Sarah, Leann

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