Question

A perfect competitive industry faces a demand curve represented by Q = 25,000 – 1000P.

Also suppose that an individual firm belonging to that industry faces a total cost function given by TC (q) = 40q – q2 + 0.01q3 Here q represents quantity of output produced by an individual firm, Q is the total industry output and P is the price. What would be the equilibrium market price? How much does each firm produce in equilibrium? and also find how many firms would be there in the industry in the long run?

Answer 1

Solution

$Q=25000-1000$

$ATC(q)=P$ $MC(q)=P$

$40-q^{2}+0.01^{3}=40-2q+0.03q^{2}$

q=50

$p=40-2(50)+0.03(50)^{2}=15$

$Q=25000-1000(15)=10000$

$nq=Q$

Q=10000

and q= 50 units

n=no of firms

$n=\frac{10000}{50}=200 firms$