The demand function for an oligopolistic market is given by the equation, Q = 180 - 4P. The industry has one dominant firm whose marginal cost function is: MC = 12 + .1Qd, and many small firms, with a total supply function: Qs = 20 + P.
a) Derive the demand equation for the dominant oligopolist.
b) Determine the oligopolist's profit maximizing output and price.
c) Determine the total output of the small firms.