Question

Consider a perfectly competitive firm with a cost function of
?(?) = 50 + 2? + 2/3 q^{2}

a. Solve for the firm’s supply function.

b. If there are 20 firms in the market and they are all
identical, what is the equilibrium price if market demand is given
by ?_{D}(?) = 1,970 − 25? ?

c. Is the market in long run equilibrium? If not, what changes would you expect? Explain your answer and show your work.

Please show step by . step solutions fora, b and c. Thanks!

Answer #1

(a)

Firm supply function is the MC.

MC = dc(q)/dq = 2 + 2 x (2/3) x q = 2 + (4q/3)

Firm supply function: P = 2 + (4q/3)

(b)

Market supply (QS) = 20q

q = QS/20

P = 2 + [4 x (QS/20)]/3 = 2 + (QS/15)

15P = 30 + QS

QS = 15P - 30

Equating QD and QS,

1,970 - 25P = 15P - 30

40P = 2,000

P = 50

(c)

When P = 50,

Q = 15 x 50 - 30 = 750 - 30 = 720

q = Q / 20 = 720 / 20 = 36

When q = 36,

Firm revenue (TR) = P x q = 50 x 36 = 1,800

c(q) = 50 + 2 x 36 + (2/3) x 36 x 36 = 50 + 72 + 864 = 986

Firm profit = TR - c(q) = 1,800 - 986 = 814

Since firm is making a profit, this is a short run equilibrium. In long run, short run profit will attract entry and this will continue until each firm earns zero profit in long run.

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