6. Each firm in a competitive market has an identical short-run and long-run cos

Question

6. Each firm in a competitive market has an identical short-run and long-run cost function C(q) 144 + q. The market demand function is Q 240 - P, where Q is total output and P is price. The price is currently $40 per unit. a. Find the individual firm's supply function, the short-run profit maximizing output level for the firm and the firm's profits. b. What is the market output and how many firms are in the industry in the short-run. c. What is the condition for this market to be in long-run equilibrium? d. Find the long-run equilibrium price, quantity per firm, and number of firms in this market.

Explanation / Answer

(a) Individual firm's supply function is its Marginal cost (MC) curve:

MC = dC/dq = 2q

Therefore, supply function is: P = 2q

Since P = $40, we get

40 = 2q

q = 40/2 = 20

Total revenue (TR) = P x q = $40 x 20 = $800

Total cost (TC) = 144 + (20 x 20) = 144 + 400 = $544

Profit = TR - TC = $800 - $544 = $256

(b) When P = $40,

Market output (Q) = 240 - 40 = 200

Number of firms = Q / q = 200 / 20 = 10

(c) Condition for long run equilibrium is Price = MC = Average cost (AC)

(d)

AC = C / q = (144 / q) + q

MC = 2q

Equating AC and MC,

(144 / q) + q = 2q

q = 144 / q

q2 = 144

q = 12

When q = 12, P = MC = 2 x 12 = $24

When P = $24, Q = 240 - 24 = 216

Number of firms = Q / q = 216 / 12 = 18

Related Questions

Navigate

• Browse (All)
• Browse 6
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.