Suppose you are given the following information about a particular industry: QD

Question

Suppose you are given the following information about a particular industry: QD = 6500-100P Market demand QS = 1200P Short run market Supply C(q) = 784 + q2 /400 Firm total cost function Assume that all firms are identical and that the market is characterized by perfect competition. a) Using the demand and supply curves above find the short run equilibrium price and quantity in the industry. b) Using the total cost function derive the marginal cost function for firms in the industry. c) Using your answers to parts a) and b) find the quantity produced by each firm in a short run competitive equilibrium. Find the profit of each firm in the short run equilibrium. d) Using your answers to parts a) and c) find the number of firms in a short run equilibrium. e) Would you expect to see entry into or exit from the industry in the long run? Explain. What effect will entry or exit have on market equilibrium (market price and quantity)? f) Given the cost curve above, what is the long run equilibrium price in the industry?

Explanation / Answer

(a) In equilibrium, QD = QS

6500 - 100P = 1200P

1300P = 6500

P = 5

Q = 1200 x 5 = 6000

(b) TC = 784 + (q2 / 400)

Marginal cost (MC) = dTC / dq = 2q / 400 = q / 200

(c) Each firm maximizes profit by equating market price with its MC:

5 = q / 200

q = 5 x 200 = 1000

TC = 784 + (1000 x 1000 / 400) = 784 + 2500 = 3284

Revenue (TR) = P x q = 5 x 1000 = 5000

Firm profit = TR - TC = 5000 - 3284 = 1716

(d) Number of firms = Market output (Q) / Firm output (q) = 6000 / 1000 = 6

(e) Since short run profit is positive, this will attract new entry in long run, which will increase market supply, therefore increasing market quantity and decreasing market price.

(f) In long run equilibrium, P = MC = ATC

ATC = TC / q = (784 / q) + (q / 400)

Equating with MC,

(784 / q) + (q / 400) = (2q / 400)

784 / q = q / 400

q2 = 784 x 400 = 313600

q = 178 (Considering integer value for output)

P = MC = q / 200 = 178 / 200 = 0.89

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