A perfectly competitive painted necktie industry has a large number of potential

Question

A perfectly competitive painted necktie industry has a large number of potential entrants. Each firm has an identical cost structure such that long-run average cost is minimized at an output of 20 units (q_i = 20). The minimum average cost is $10 per unit. Total market demand is given by Q^d = 1500 - 50P 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 (q_i*)? The number of firms? The profits of each firms? c) The short-run total cost curve associated with each firm's long-run equilibrium output is given by STC = 0.5q^2 - 10q + 200 where SMC = q - 10. Calculate the short-run average. At what necktie output level does short-run average cost reach a minimum? d) Calculate the short-run supply curve for each firm and the industry short-run supply curve.

Explanation / Answer

A) Long run supply cure is horizontal p=min ATC=$10

B) P=$10, QD=1500-50(10)= 1000. Since each firm produces 20 units there must be 50 firms to supply 1000 units.

P=Min ATC Hence firms makes zero profits.

C) MC= Q-10

AC= .5Q-10 + 200/Q

MC=MIN AC

Hence q-10=5Q-10 + 200/Q or q=20

D) MC=P hence short run supply will be

q=p+10. in the short run firms cannot enter or exit hence hence 50 identical producers make up the market.

market supply = q=50q= 50p+500

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