Perfect Competition and Monopoly Problems
4)
Q (Thousand)
9
10
11
12
13
14
15
16
17
18
19
20
a)
AVC
41.10
40.00
39.10
38.40
37.90
37.60
37.50
37.60
37.90
38.40
39.10
40.00
AC
52.21
50.00
48.19
46.73
45.59
44.74
44.17
43.85
43.78
43.96
44.36
45.00
MC
30.70
30.10
30.10
30.70
31.90
33.70
36.10
39.10
42.70
46.90
51.70
57.10
Market Structure
60
50
profit
P($)
40
AVC
30
AC
20
MC
10
0
9
10
11
12
13
14
15
16
17
18
19
20
Q(thousands)
b) Yes. If P=$50, the company should produce 18 thousand. It is because at the price of
$50, the company will have profit if they enter the market. There the profit when the
MC is higher than AC.
c) At this time, the production has to decrease to around 14 thousand. However, the profit
of the firm also will be negative; in other word the firm will experience huge loss of
$136.36. It is happen because the marginal cost is lower than average cost. It would be
the best option if the firm decides to pull out from the market.
5)
Q (Thousand)
0
1
2
3
4
5
6
7
8
9
10
Price
1650
1570
1490
1410
1330
1250
1170
1090
1010
930
850
MR
AVC
AC
MC
Profit
1570
1410
1250
1090
930
770
610
450
290
130
1281
1134
1009
906
825
766
729
714
721
750
2281
1634
1342.33
1156
1025
932.67
871.86
839
832.11
850
1281
987
759
597
501
471
507
609
777
1011
289
423
491
493
429
299
103
-159
-487
-881
a. The price the firm should charge if it wants to maximize its profit in a short run is
$1,330.
b. If charging a price higher than $1,330, it is plausible until the price of $1,490. At the
price $1,490, the profit still high at $423 and if it increased a bit higher at $1,570, the
profit decreased nearly half.
c. If charging a price lower than $1,330, it can only until $1,250 where the profit at $429. If
lower than $1,250, the profit will have huge decrease.
6)
a. Given functions as follows
TC = 500,000 + 0.85Q + 0.015Q2
Q = 14,166 – 16.6P
So, P = 853.37 - 0.06Q
TR = PQ = Q(853.37 – 0.06Q) = 853.37Q - 0.06Q2
MR = δTR/δQ = δ(853.37Q - 0.06Q2)/δQ = 853.37 - 0.12Q
MC = δTC/δQ = δ(500,000 + 0.85Q + 0.015Q2)/δQ = 0.85 + 0.03Q
Short run profit maximizing rule is MR = MC, So we can write
853.37 - 0.12Q = 0.85 + 0.03Q
Q* = 5683.466 (Profit maximizing output level)
P = 853.37 - 0.06(5683.466)
P* = $512.36 (profit maximizing price)
b.
7)
𝑃𝑄 = 100𝑄 − 8𝑄 2
𝑇𝐶 = 50 + 80𝑄 − 10𝑄 2 + 0.6𝑄 3
a) Max f(Q)
= PQ – TC(Q)
= 100Q - 8Q2 – (50 + 80Q – 10Q2 + 0.6Q3)
= 20Q + 2Q2 – 0.6Q3 – 50
𝑑𝑓
𝑑𝑄
= 20 + 4Q – 1.8Q2
= 20 + 4Q – 1.8Q2 = 0
Q1 = -2.40
Q2 = 4.62
Thus maximize profit = 20Q + 2Q2 - 0.6Q3 - 50
= 20 (4.62)2 – 0.6 (4.62)3 – 50
= 317.72
b) PQ
= 100Q – 8Q2
= 100 (4.62) – 8(4.62)2
= 291.24