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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

Microeconomic Theory
Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter2: Mathematics For Microeconomics
Section: Chapter Questions
Problem 2.2P
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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?

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
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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