Question

A perfectly competitive 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 ( P ) = 1 , 500 - 50 P . 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? 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 ) = 0.5 q 2 - 10 q + 200 . Calculate the short-run average and marginal cost function. At what output level does short-run average cost reach a minimum? Calculate the short-run supply function for each firm and the industry short-run supply function. Suppose now that the market demand function shifts upward to Q = D ( P ) = 2 , 000 - 50 P . Using this new demand curve, answer part (b) 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 (b). What is the new long-run equilibrium for the industry?

Here are the answers to the first 4. I ONLY NEED PARTS E,F, & G.

(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]

Answer 1

(a)

In amazing rivalry, since quite a while ago run harmony holds when since quite a while ago run normal expense = since a long time ago run peripheral expense = cost

We have, Q = 1500 - 50p

Or then again, 50p = 1500 - Q

p = 30 - 0.02Q

This is the since quite a while ago run flexibly shcedule.

(b)

Least normal expense = $10

This is the minor cost (MC) in since quite a while ago run.

Since a completely serious firm likens 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 yield of each firm = 20 units [q*] (Given)

(iii) Number of firms = Absolute yield (Q)/20 = 1,000/20 = 50

(iv) Absolute industry benefit = Income - cost = p* x q* - (AVC x q*)

= q*(p* - AVC)

= 0 [Since p* = AVC = 10]

Over the long haul, abundance benefit = 0 for all organizations.

(c)

C = 0.5q2 - 10q + 200

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

Normal cost, air conditioning = C/q = 0.5q - 10 + (200/q)

Air conditioning is least 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, gracefully work is the peripheral cost capacity of the firm:

p = q - 10 [MC of firm]

or then again,

q = p + 10

All out industry gracefully = singular firm flexibly x number of firms

Q = q x 50

= 50(p + 10)

Q = 50p + 500

Or then again,

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

NOTE: Out of 7 sub-questions, the initial 4 are replied.