III. In the quantity leadership or Stackelberg model, firm 1 is the leader and firm 2 the follower. The market demand curve is Y = 10 p. Both firms have the same cost function c (y) = y2. Find the equilibrium of this model. What is the price at equilibrium? At the equilibrium, does firm 1 produce the same quantity it would have produced had it been a monopoly?

IV. Same questions as in III above but assume here that firm 1's cost function is c1 (y1)=2y1 and firm 2's c2 (y2) = y2²