Suppose you are given the following information about a particular perfectly com

Question

Suppose you are given the following information about a particular perfectly competitive idustry:

Qd = 6500-100P Market demand

Qs= 1200P Market supply

C(Q) = 722+(Q^2)/200 Firm's total cost function

Assume all firms in this perfectly competitve industry are identical

A) Find the equilibrium price and quantity for the entire industry, the output supplied by the firm, and the profit of each firm.

B) Would you expect to see entry into or exit from this industry in the long run?Explain. What effect will entry or exit have on market equilibrium?

C) Suppose the long run total cost function is given by C(Q) = 6Q - 3Q^2 + Q^3. What will the price be in long run equilibrium in this industry? Is profit positive, negative, or zero? Explain

Explanation / Answer

(A) In market equilibrium, Qd = Qs

6500 - 100P = 1200P

1300P = 6500

P = 5 (Market price)

Q = 1200 x 5 = 6000 (Market output)

Total cost for firm, C(Q) = 722 + (Q2 / 200)

Marginal cost (MC) = dC(Q) / dQ = 2Q / 200 = Q / 100

Each firm will equate market price with its MC:

Q / 100 = 5

Q = 500 (Firm output)

For each firm,

Toal revenue (TR) = P x Q = 5 x 500 = 2500

Total cost (C) = 722 + (500 x 500 / 100) = 722 + 2500 = 3222

Profit = TR - TC = 2500 - 3222 = - 722 (Loss)

(B) Since firms are making short run loss, in the long run some firms will exit the market. As a result, market supply will fall and market price will rise, lowering firm profits. This process will continue until long run equilibrium is established when each firm earns zero economic profit, with higher market price and lower market quantity.

(C) C(Q) = 6Q - 3Q2 + Q3

In long run equilibrium, Price = AC = MC

AC = C(Q) / Q = 6 - 3Q + Q2

MC = dC(Q) / dQ = 6 - 6Q + 3Q2

Equating AC and MC,

6 - 3Q + Q2 = 6 - 6Q + 3Q2

2Q2 = 3Q

Q = 1.5 [Assuming Q is non-zero, dividing by 2Q]

Price = AC = 6 - (3 x 1.5) + (1.5 x 1.5) = 6 - 4.5 + 2.25 = 3.75

At this price and quantity,

TR = 3.75 x 1.5 = 5.625

TC = (6 x 1.5) - (3 x 1.5 x 1.5) + (1.5 x 1.5 x 1.5) = 9 - 6.75 + 3.375 = 5.625

Profit = TR - TC = 5.625 - 5.625 = 0

Therefore profit is zero, as is expected in long run equilibrium.

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