Question

Problem 1. 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*), and the output of each firm (qi*)? 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 = 0.5q2 – 10q + 200, where SMC = q – 10. Calculate the short- run average cost curve. At what necktie output level does short-run average cost reach a minimum?

Answer 1

a) In the long run,  Long run supply is horizontal at p= min , P=ATC= $10.

(b) At P= 10, Q= 1500-50(10) = 1000.

Therefore number of firms = 1000

Since each firm produces 20 units, there must be 50 firms in order to supply 1000 units.

since P= min ATC, each firm makes zero profit .

Since price equals minimum total cost, each firm’s profit is zero.

(c) Given,

therefore, Average cost is AC= 0.5q - 10 + 200/q.

Average cost attains its minimum when it is equal to marginal cost.

Hence,we set q-10 = 0.5q - 10 + 200/q. This implies that q= 20.