3. Equilibrium n a competitive industry Suppose you are given the following info
ID: 1124335 • Letter: 3
Question
3. Equilibrium n a competitive industry Suppose you are given the following information about a particular industry CP-6500-100P Qs= 1200P C(q) 784 q- 400 Market demand Short run market Supply Firm total cost function by perfect competition. Using the demand and supply curves above find the short run equilibrium price and quantity in the industry. Using the total cost function derive the marginal cost function for firms in the industry. 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. a) b) c) 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 indusry in the long run? Explain. What effect will entry or exit have on market equilibrium (market price and quantity)? Given the cost curve above, what is the long run equilibrium price in the industry? f)Explanation / Answer
(A) In market equilibrium, Quantity demanded equals quantity supplied (QD = QS).
6500 - 100P = 1200P
1300P = 6500
P = 5 (Market price)
Q = 1200 x 5 = 6000 (Market output)
(b) Total cost for firm, C(Q) = 784 + (q2 / 400)
Marginal cost (MC) = dC(q) / dq = 2q / 400 = q / 200
(c) Each firm will equate market price with its MC:
q / 200 = 5
q = 1000 (Firm output)
For each firm,
Toal revenue (TR) = P x q = 5 x 1000 = 5000
Total cost (C) = 784 + (1000 x 1000 / 400) = 784 + 2500 = 3284
Profit = TR - TC = 5000 - 3284 = 1716
(d) Number of firms = Market output / Firm output = 6000 / 1000 = 6
(e) Since firms are making short run profit, in the long run new firms will enter the market. As a result, market supply will rise and market price will fall, lowering firm profits. This process will continue until long run equilibrium is established when each firm earns zero economic profit, with lower market price and higher market quantity.
(f) C(q) = 784 + (q2 / 400)
In long run equilibrium, Price = AC = MC
AC = C(q) / q = (784 / q) + (q / 400)
MC = q / 200
Equating AC and MC,
(784 / q) + (q / 400) = q / 200
784 / q = (q / 200) - (q / 400) = q / 200
q2 = 156800
q = 396 (Assuming output is integer)
Price = MC = 396 / 200 = 1.98
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