A perfectly competitive industry consists of many identical firms, each with a l

Question

A perfectly competitive industry consists of many identical firms, each with a long-run average total cost of LATC = 800 – 10Q + 0.1Q 2 and long-run marginal cost of LMC = 800 –20Q + 0.3Q 2 . a. In long-run equilibrium, how much will each firm produce? b. What is the long-run equilibrium price? c. The industry's demand curve is Q D = 40,000 – 70P. How many units do consumers buy in long-run equilibrium? How many firms are in the industry? d. Suppose the industry's demand curve rises to Q D = 40,600 – 70P. How many new firms will enter this constant-cost industry in the long run?

Explanation / Answer

(a) In long run equilibrium, LATC = LMC

800 - 10Q - 0.1Q2 = 800 - 20Q + 0.3Q2

0.4Q2 - 10Q = 0

Q x (0.4Q - 10) = 0

Assuming Q is non-zero,

0.4Q = 10

Q = 25

(b) P = LMC = 800 - (20 x 25) + (0.3 x 25 x 25) = 800 - 500 + 187.5 = 487.5

(c) QD = 40,000 - 70P = 40,000 - (70 x 487.5) = 40,000 - 34,125 = 5,875

Number of firms = 5,875 / 25 = 235

(d) QD = 40,600 - (70 x 487.5) = 40,600 - 34,125 = 6,475

New number of firms = 6,475 / 25 = 259

Number of new firms entered = 259 - 235 = 24

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