A perfectly competitive industry has a large number of potential entrants. Each

Question

A perfectly competitive industry has a large number of potential entrants. Each firm has an identical cost structure such that the long-run average cost Is minimized at an output of 20 units. The minimum average cost is $10 per unit. Total market demand is given by Q = 1,500- 50p. What is the industry's long-run supply schedule? What is the long-run equilibrium price p*? The total industry output Q*? The output of each firm q*? The number of firms active in the market? The profits of each firm? The short-run total cost function associated with each firm's long-run equilibrium output is given by C(q) = 0.5q^2 -10q + 200. Calculate the short-run average and marginal cost functions. At what output level does short-run average cost reach a minimum? Calculate the short-run supply function for the firm and for the industry. Suppose now that the market demand function shifts upward to Q = 2,000 - 5Op. Using this new demand curve, answer part for the very short run when firms cannot change their outputs. In the short-run, use the industry short-run supply function to recalculate the answers to What is the long-run equilibrium for the industry?

Explanation / Answer

(a)

In perfect competition, long run equilibrium holds when long run average cost = long run marginal cost = price

We have, Q = 1500 - 50p

Or, 50p = 1500 - Q

p = 30 - 0.02Q

This is the long run supply shcedule.

(b)

Minimum average cost = $10

This is the marginal cost (MC) in long run.

Since a perfectly competitive firm equates P with MC:

p = 30 - 0.02Q = 10

0.02Q = 20

(i) Q = 1,000 [Q*]

(ii) p = 30 - (0.02 x 1000) = 10 [p*]

Since output of each firm = 20 units [q*] (Given)

(iii) Number of firms = Total output (Q) / 20 = 1,000 / 20 = 50

(iv) Total industry profit = Revenue - cost = p* x q* - (AVC x q*)

= q*(p* - AVC)

= 0 [Since p* = AVC = 10]

In the long run, excess profit = 0 for all firms.

(c)

C = 0.5q2 - 10q + 200

Marginal cost, MC = dC / dq = q - 10

Average cost, AC = C / q = 0.5q - 10 + (200/q)

AC is minimum when dAC / dq = 0

0.5 - (200/q2) = 0

(200/q2) = 0.5

q2 = 200 / 0.5 = 400

q = 20 [Output when AVC is minimum]

(d)

In the short run, supply function is the marginal cost function of the firm:

p = q - 10 [MC of firm]

or,

q = p + 10

Total industry supply = individual firm supply x number of firms

Q = q x 50

= 50(p + 10)

Q = 50p + 500

Or,

p = (Q - 500) / 50 [Industry short run supply function]

NOTE: Out of 7 sub-questions, the first 4 are answered.

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