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 (qi=20). The minimum average cost is $10 per unit. Total market demand is given by Q=1,500-50P.

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 firm?

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 firm's short-run average and marginal cost curves. 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 supply curve.

E) Suppose now painted neckties become more fashionable and the market deman function shifts to Q=2,000-50P. Using this demand curve, answer part B for the very short run when firms cannot change their output.

F) In the short-run use the industry short-run supply curve to recaclulate the answers to part B.

G) What is the new long-run equilibrium for this industry?

...not even really sure where to begin :/ please be very clear with your answers. Thanks!

Explanation / Answer

A) long-run average cost is minimized

qi = 20

B) P*=$10, qi*=20, Q=1500-50*10=1000, no. of firms=1000/20=50, Profit=10*20-10*20=0

C) short-run average cost curve = 0.5q-10+200/q

marginal cost curves = q-10

d(SRAC)/dq = 0.5 - 200/q^2 =0

q = 20

D) qi=20, MC=q-10(supply curve is the marginal cost curve)

E) P*=$10, qi*=20, Q=20000-50*10=1500, no. of firms=1500/20=75, Profit=10*20-10*20=0

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