Question #41416

The market demand for woozles is given by: Qd = 2,400 – 20p
There is only one available technology, and it is employed by all producers actual and potential. It implies the following average cost function:
AC = 625q–1 + 0.25q
Currently, 20 firms serve the market.
a. Find the individual firm’s supply curve.
b. Find the industry supply curve.
c. Determine the short run competitive price and output.
d. How much profit is the typical firm making?
e. Determine the long run competitive market price and quantity and how many firms will operate.

Expert's answer

The individual supply curve is the part of marginal cost (MC) curve after the intercection with average variable cost (AVC) curve.

MC is the derivative of TC curve.

MC = TC' = (AC*q)' = (625 + 0.25q^2)' = 0.5q, so Ps = 0.5q or qs = 2p

b. Find the industry supply curve.

Answer:

The industry supply curve is the sum of 20 individual firm's supply curves, so Qs = 20*2p = 40p

c. Determine the short‐run competitive price and output.

Answer:

The short‐run competitive equilibrium price and output is in the point, where Qs = Qd, so:

40p = 2,400 – 20p

60p = 2,400

Pe = $40

Qe = 40*40 = 1,600 units

Individual competitive output is q = 1,600/20 = 80 units.

d. How much profit is the typical firm making?

Answer:

Total profit will be:

TP = (P – AC)*q = (40 – (625/80 + 0.25*80))*80 = (40 – 27.8125)*80 = $975

e. Determine the long‐run competitive market price and quantity and how

many firms will operate.

Answer:

As in the short-run firms receive profits, the new firms will enter the market until the profits become zero (normal profit) in the long-run, so P = AC.

We calculate P from the demand curve, so p = 120 – q/20 = 120 – 0.05q, AC = 625q^–1 + 0.25q

120 – 0.05q = 625/q + 0.25q

0.3q + 625/q – 120 = 0

0.3q^2 + 625 – 120q = 0 (q > 0)

q1,2 = (120 +- (14400 – 144)^0.5)/0.6

q1 = 399 (q2 < 1 and is not available in our case)

So, total market output will be 399 units.

Equilibrium market price in the long-run will be Pe = 120 – 399/20 = $100.05

There will be next amount of firms in the market in the long-run:

n = Q/q = 399/80 = 4.99 or 5 firms.

MC is the derivative of TC curve.

MC = TC' = (AC*q)' = (625 + 0.25q^2)' = 0.5q, so Ps = 0.5q or qs = 2p

b. Find the industry supply curve.

Answer:

The industry supply curve is the sum of 20 individual firm's supply curves, so Qs = 20*2p = 40p

c. Determine the short‐run competitive price and output.

Answer:

The short‐run competitive equilibrium price and output is in the point, where Qs = Qd, so:

40p = 2,400 – 20p

60p = 2,400

Pe = $40

Qe = 40*40 = 1,600 units

Individual competitive output is q = 1,600/20 = 80 units.

d. How much profit is the typical firm making?

Answer:

Total profit will be:

TP = (P – AC)*q = (40 – (625/80 + 0.25*80))*80 = (40 – 27.8125)*80 = $975

e. Determine the long‐run competitive market price and quantity and how

many firms will operate.

Answer:

As in the short-run firms receive profits, the new firms will enter the market until the profits become zero (normal profit) in the long-run, so P = AC.

We calculate P from the demand curve, so p = 120 – q/20 = 120 – 0.05q, AC = 625q^–1 + 0.25q

120 – 0.05q = 625/q + 0.25q

0.3q + 625/q – 120 = 0

0.3q^2 + 625 – 120q = 0 (q > 0)

q1,2 = (120 +- (14400 – 144)^0.5)/0.6

q1 = 399 (q2 < 1 and is not available in our case)

So, total market output will be 399 units.

Equilibrium market price in the long-run will be Pe = 120 – 399/20 = $100.05

There will be next amount of firms in the market in the long-run:

n = Q/q = 399/80 = 4.99 or 5 firms.

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