A typical firm in long-run equilibrium in an industry with identical firms has a cost function given by TC(g) = 800 + 2q? and has a marginal cost function of MC = 4q. The fixed costs of 800 is avoidable if the firm shuts down. What is the equilibrium price? This is a long-run question and it states finding the equilibirum. This means we're looking for minimum ATC. Here is a truth. MC and ATC intersect at min(ATC). I could use this fact to find the minimum ATC (and hence the equilibrium price). ATC = 800/g+2g where is that equal to MC=4q. Solve, 800/q + 2q = 4g, or 800/q=2q, or 800/2 = q*. So, q = 400, or q = 20. So, the minimum ATC occurs at q = 20 and the price is at MC(20) = 4*20 = 80. ATC MC start skip 'll draw a picture. 5 170 20 1 6 145.3333 7 128.2857 24 28 Find Min(ATC) 116 32 9 106.8889 36 180 10 100 40 160 11 94.72727 44 140 12 90.66667 48 120 13 87.53846 52 100 9 80 ATC 14 85.14286 56 АТС 15 83.33333 60 9 60 MC 16 82 64 40 17 81.05882 68 20 18 80.44444 72 10 15 20 25 30 35 19 80.10526 76 20 80 80 As profisied by the math ATC is at a minum at q = 20 and price (ATC and MC are both megasured in dollars) of 80 21 80.09524 84 22 80.36364 88 23 80.78261 92 24 81.33333 22222 96 25 82 100 26 82.76923 104 27 83.62963 108 28 84.57143 112 29 85.58621 116 30 86.66667 120 MC, AC, dollars
A typical firm in long-run equilibrium in an industry with identical firms has a cost function given by TC(g) = 800 + 2q? and has a marginal cost function of MC = 4q. The fixed costs of 800 is avoidable if the firm shuts down. What is the equilibrium price? This is a long-run question and it states finding the equilibirum. This means we're looking for minimum ATC. Here is a truth. MC and ATC intersect at min(ATC). I could use this fact to find the minimum ATC (and hence the equilibrium price). ATC = 800/g+2g where is that equal to MC=4q. Solve, 800/q + 2q = 4g, or 800/q=2q, or 800/2 = q*. So, q = 400, or q = 20. So, the minimum ATC occurs at q = 20 and the price is at MC(20) = 4*20 = 80. ATC MC start skip 'll draw a picture. 5 170 20 1 6 145.3333 7 128.2857 24 28 Find Min(ATC) 116 32 9 106.8889 36 180 10 100 40 160 11 94.72727 44 140 12 90.66667 48 120 13 87.53846 52 100 9 80 ATC 14 85.14286 56 АТС 15 83.33333 60 9 60 MC 16 82 64 40 17 81.05882 68 20 18 80.44444 72 10 15 20 25 30 35 19 80.10526 76 20 80 80 As profisied by the math ATC is at a minum at q = 20 and price (ATC and MC are both megasured in dollars) of 80 21 80.09524 84 22 80.36364 88 23 80.78261 92 24 81.33333 22222 96 25 82 100 26 82.76923 104 27 83.62963 108 28 84.57143 112 29 85.58621 116 30 86.66667 120 MC, AC, dollars
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
Given the cost information in the previous question and an industry demand function of Q = 2400 - 5p, how many firms are in this industry in the long-run equilibrium?
Transcribed Image Text:A typical firm in long-run equilibrium in an industry with identical
firms has a cost function given by
TC(g) = 800 + 2q?
and has a marginal cost function of MC = 4q. The fixed costs of 800 is
avoidable if the firm shuts down. What is the equilibrium price?
This is a long-run question and it states finding the equilibirum. This
means we're looking for minimum ATC. Here is a truth. MC and ATC
intersect at min(ATC). I could use this fact to find the minimum ATC
(and hence the equilibrium price).
ATC = 800/g+2g where is that equal to MC=4q.
Solve, 800/q + 2q = 4g, or 800/q=2q, or 800/2 = q*.
So, q = 400, or q = 20.
So, the minimum ATC occurs at q = 20 and the price is at MC(20) =
4*20 = 80.
ATC
MC
start
skip
'll draw a picture.
5
170
20
1
6 145.3333
7 128.2857
24
28
Find Min(ATC)
116
32
9 106.8889
36
180
10
100
40
160
11 94.72727
44
140
12 90.66667
48
120
13 87.53846
52
100
9 80
ATC
14 85.14286
56
АТС
15 83.33333
60
9 60
MC
16
82
64
40
17 81.05882
68
20
18 80.44444
72
10
15
20
25
30
35
19 80.10526
76
20
80
80 As profisied by the math ATC is at a minum at q = 20 and price (ATC and MC are both megasured in dollars) of 80
21 80.09524
84
22 80.36364
88
23 80.78261
92
24 81.33333
22222
96
25
82
100
26 82.76923
104
27 83.62963
108
28 84.57143
112
29 85.58621
116
30 86.66667
120
MC, AC, dollars
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