Suppose there are n identical firms in an oligopoly who compete in quantities. The inverse market demand is given by p = 2520 - Q, where Q = Sigma n, i = 1, qi. Each fir's cost function is given by ci(qi) = 0.5qi2 + 32400, where 32400 is fixed cost of entering market.
(a) Calculate the output, q* produced by a typical firm in a symmetric NE as a function of n. Calculate an expression for the NE profit, profit* as a function of n.
(b) If there are no barriers to entry, firms will enter the market until a typical firm earns zero profit. How many firms will there be in this market in the long run?