Suppose there are n number of identical firms in a market. Each firms cost function is given by C = 648 + 8q^2, where q is the amount that an individual firm produces. This means that an individual firm's marginal cost is given by MC = 16q. Also, the market demand is given by P = 306 - 3Q, where Q is the total amount of the good produced by all of the firms combined. Therefore, Q = n * q.
a) How much output will each firm produce?
b) What will be the market price?
c) How many firms will there be in long run equilibrium?