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 industry:

QD= 6500-100P .....Market demand

QS= 1200P .....Market Supply

C(Q)=722+(Q2)/200 ......Firm's total cost function

Assume all firms in this perfectly competitive industry are identical.

a) Find the equillibrium price and the equilibrium 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-3Q2+Q3. What will the price be in long run equilibrium in this industry? Is profit positive, negative or zero? Explain.

Explanation / Answer

a) The equillibrium price and the equilibrium quantity for the entire industry can be computed by equating Qd = Qs

6500 - 100P = 1200P

6500 = 1300P

P = 5, Q = 6000

For the output supplied by the firm, Note that each firm faces the following production condition in the short run:

MC = MR = P

From the cost function C(Q)=722+(Q2)/200, Marginal cost, the derivative of total cost is Q/100. Marginal revenue 5

This suggests that

5 = Q/100

Q = 500

Hence the profit maximizing quantity produced by each firm is 500 units

Profit is the difference between TR and TC, so

Profit = 500*5 - (722 + 500*500/200)

= 2500 - 1972

= $528

So the profit of each firm is $528

b) There would be entry of new firms since the industry is earning profit. Entry will continue to happen as long as firms will be making an economic profit. Such entry will increase the supply so the supply curve of the industry so that its shifts out, reducing the price and increasing the quantity.

c) In the long run, a typical firm in perfectly competitive market operates at the minimum level of AC where minimum of LRAC = LRMC where there are no fixed costs. LRAC = LRTC/Q = 6 - 3Q + Q2.

minimum of LRAC can be found by using its derivative and setting it equal to zero.

d(6 - 3Q + Q2)dQ= 0

3 = 2Q

Q = 1.5

The long run profit maximizing output produced by each firm is 1.5 units. At this level of output, firm earns no economic profit.

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