Question

A typical firm in​ long-run equilibrium in an industry with identical firms has a cost function given by

​C(q)=4,900+2q2.

What is the equilibrium​ price?

Answer 1

In long run equilibrium, Price = Average cost (AC) = Marginal cost (MC)

$AC =\frac {C(q)} {Q} = (\frac {4,900} {Q} ) + 4q$

$MC =\frac {dC(q)} {dq} = 4q$

Equating AC & MC,

$(\frac {4,900} {Q} ) + 2q = 4q$

$2q = \frac {4,900} {q}$

$2q2 = 4,900$

$q2 = 2450$

$q=49.5$

Price = MC = 4q = 4 x 49.5 = 198