(Cournot's duopoly game with linear inverse demand and different unit costs) Find the Nash equilibrium of Cournot's game when there are two firms, the inverse demand function is given by (54.2), the cost function of each firm i is Ci (qi ) = ciqi, where c1 > c2, and c1 α. (There are two cases, depending on the size of c1 relative to c2.) Which firm produces more output in an equilibrium? What is the effect of technical change that lowers firm 2's unit cost c2 (while not affecting firm 1's unit cost c1) on the firms' equilibrium outputs, the total output, and the price?