Revenue Maximization. Consider the following single-period duopoly quantity competition game. Two firms face an inverse demand function for their homogeneous product of the form p = 100 Q. Firms a and b have a constant marginal cost of c = 10 and no fixed costs, but firm a's manager maximizes profit while firm b's manager maximizes revenue.

(a) Given these different objectives, find the best-response curves for each firm. Give your answer both algebraically and graphically. What is the Nash equilibrium in this game? How does it compare to the one that would obtain if the managers of both firms maximized profit? What are the profits of both firms?