9.6. A perfectly competitive painted necktie industry has a of potential entrant

Question

9.6. A perfectly competitive painted necktie industry has a of potential entrants Each firm has an is minimized at an output of 20 units 20). The minimam average cost is $10 per unit. Total market a What is the industry's long-run supply schedule? b. What is the long-run equilibrium price (P) The total industry output (Q) The output of each firm ( The number ofms The profits of each firm c. The short-run total cost curve associated with each firm's long-ran equilibrium output is given by where SMC 9-10. Calculate the short-run aver- age and marginal cost curves. At what necktie out put level does shozt-run average cost reach a d. Cakculate the short-run supply curve for each firm and the industry short-run supply curve. e Suppose now painted neckties become more fash ionable and the market demand function shifts upward to Q 2,000-50P. Using this new demand curve, answer part b for the very short run when firms cannot change their outputs f In the short run, use the industry short-rn curve to recalculate the answers to part b. What is the ew long-run equilibrium for the

Explanation / Answer

Industry demand: Q = 1,500 - 50P

50P = 1,500 - Q

P = 30 - 0.02Q

(a) In perfectly competitive long run equilibrium, average cost is lowest. So, industry long run supply schedule is:

P = 10

(b) Equating industry demand and long-run industry supply,

30 - 0.02Q = 10

0.02Q = 20

Q* = 1,000

P* = 20

q* = 20

Number of firms = Q* / q* = 1,000 / 20 = 50

Firm profit = q* x (P - AC) = 20 x (20 - 20) = 20 x 0 = 0

(c) STC = 0.5q2 - 10q + 200

Short-run average cost (SAC) = STC / q = 0.5q - 10 + (200 / q)

Short-run marginal cost (SMC) = dSTC / dq = q - 10

SAC is minimum when dSAC / dq = 0

0.5 - (200 / q2) = 0

200 / q2 = 0.5

q2 = 200 / 0.5 = 400

q = 20

(d)

Firm supply curve is the firm's MC curve:

P = q - 10

If there are N firms in the industry in short run, then Industry supply (Qs) = q x N

q = Qs / N

From firm supply function,

P = (Qs / N) - 10

Qs / N = P + 10

Qs = NP + 10N [Industry supply function]

Note that number of firms are different in short run and long run, so we cannot assume that N = 50 as derived in part (b).

NOTE: As per Chegg answering guideline, first 4 parts are answered.

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