5. A competitive industry currently has 1000 identical firms. Each firm has cost
ID: 1116603 • Letter: 5
Question
5. A competitive industry currently has 1000 identical firms. Each firm has costs TC(q) = 8 + 4q + q2 and MC-q + 4, minimum AC-8, and is reached when the firm produces q 4. Please answer the following a. Find the individual firm's supply curve b. Find the industry short-run supply curve c. Currently, the industry demand is Q 20,000 1,000P. Find the short-run equilibrium price P, market quantity Q, and individual firm quantity q. d. What is the profit of an individual firm? e. Suppose there are thousands of similar firms outside of the market and ready to enter Find the long-run equilibrium price P, market quantity Q, individual firm quantity q, and number of firms n.Explanation / Answer
(a) Individual firm's supply curve is its MC function.
Individual supply function: P = q + 4
(b) Industry supply Q = 1,000 x q
q = Q / 1,000
From firm supply function,
P = (Q / 1,000) + 4
Q / 1,000 = P - 4
Q = 1,000P - 4,000 [Industry supply function]
(c) In equilibrium, Industry demand equals Industry supply.
20,000 - 1,000P = 1,000P - 4,000
2,000P = 24,000
P = 12
Q = 20,000 - (1,000 x 12) = 20,000 - 12,000 = 8,000
q = 8,000 / 1,000 = 8
(d) When q = 8,
Total revenue (TR) = P x q = 12 x 8 = 96
TC = 8 + (4 x 8) + [(1/2) x 8 x 8] = 8 + 32 + 32 = 72
Individual Firm profit = TR - TC = 96 - 72 = 24
(e) In long run equilibrium, Price = ATC = MC
ATC = TC / q = (8 / q) + 4 + 0.5q
Equating with MC,
(8 / q) + 4 + 0.5q = 4 + q
0.5q = 8 / q
q2 = 16
q = 4
P = MC = 4 + 4 = 8
Q = 20,000 - (1,000 x 8) = 20,000 - 8,000 = 12,000
Number of firms = Q / q = 12,000 / 4 = 3,000
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