Question

In a competitive industry consisting of 5,000 firms, the short-run marginal cost curve for each

firm is given by MC = 100 + 20Q. The demand curve faced by the industry is given as P = 500 –

0.002Q. P and MC are in $/tonne and Q is in tones.

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

b. Find the producer and consumer surpluses at the equilibrium price.

Answer 1

a)

MC curve for each firm is:

$MC=100+Q_s$

In a competitive market, the marginal cost curve is the supply curve.

$\therefore P=100+20Q_s$

$20Q_s=P-100$

$Q_s=\frac{P}{20}-\frac{100}{20}=\frac{P}{20}-5$

There are 5000 firms.

The industry supply curve is:

$Q_s(5000)=(\frac {P}{20}-5)\times 5000=250P-25000$

The demand curve is:

$P=500-0.002Q_D$

$\implies 0.002Q_D=500-P$

$Q_D=250000-500P$

At equilibrium:

$Q_D=Q_S$

$250000-500P=250P-25000$

$\implies P=366.66$

$Q^*=250000-500(366.66)=66670$

Therefore, the total quantity sold is 66670 tones.

Quantity sold by each firm:$=\frac{66670}{5000}=13.33$ tones.

b)

Consumer surplus$=\frac{1}{2}\times( 500-366.66)\times66670$

$=4444888$

Producer surplus$=\frac{1}{2}\times(366.66-100)\times 66670$

$=8889111.1$

Producer surplus for each firm:

$=\frac{8889111.1}{5000}=1777.82$