In a competitive industry consisting of 10000 firms the shor

In a competitive industry consisting of 10,000 firms, the short-run marginal cost curve for each firm is given by MC = 200 + 30Q. The demand curve faced by the industry is given as P = 400 – 0.002Q. P and MC are in $/tonne and Q is in tones.

Find the equilibrium price and quantity sold, for the industry and for each firm.

Find the producer and consumer surpluses at the equilibrium price.

Solution

a.

Calculate the equilibrium price and quantity sold, for the industry and for each firm

Equating supply = demand

400 .002Q = 200 + .003Q

           200= .005Q:

Q = 200/.005 = 40,000 for the industry

Q for firm = 40,000/10,000 = 4

       P = 200 + 30(4) = 320

b.

Calculate the producer and consumer surpluses at the equilibrium price

Producer surplus (PS):

PS = 1/2(320 200)[40,000] = 2,400,000

Consumer surplus (CS):

   CS = 1/2(400 320)[40,000] = 1,600,000