5. A competitive industry has the following demand curve: P = 220-a, where a is
ID: 1127080 • Letter: 5
Question
5. A competitive industry has the following demand curve: P = 220-a, where a is the total output produced. All the firms in this industry face the same cost curve: C(q) = 20 + 16q + q, where q is the output of the individual firm. There are 10 firms in the industry. a. Derive the supply curve for a typical firm in this industry. b. Derive the industry supply curve. c. Find the equilibrium price and quantity. d. How much profit is the typical firm making? e. Is this a short-run or long-run equilibrium? Explain.Explanation / Answer
(a) Individual firm's supply function is its Marginal cost (MC) curve:
MC = dC/dq = 16 + 2q
Therefore, firm supply function is: P = 16 + 2q
(b) Since there are 10 firms, Market supply (Q) = 10 x q
q = Q / 10
P = 16 + (2Q / 10)
P = 16 + 0.2Q [Industry supply function]
(c) In market equilibrium, quantity demanded equals quantity supplied.
220 - Q = 16 + 0.2Q
1.2Q = 204
Q = 170
q = Q / 10 = 170 / 10 = 17
P = 220 - 170 = $50
(d) When P = $50 and q = 17,
Total revenue (TR) = P x q = $50 x 17 = $850
TC = 20 + (16 x 17) + (17 x 17) = 20 + 272 + 289 = $581
Profit = TR - TC = $850 - $581 = $269
(e) Since firms are making positive economic profit, this is not a long run equilibrium because in perfect competition, firms earn zero economic profit in long run equilibrium.
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