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

V. In the price leadership model, assume there are only to firms: firm 1 and firm 2. Firm 1 is the leader and chooses the price. Then firm 2, assuming that the price will remain at the level chosen by firm 1, chooses its quantity. Finally firm 1 produces the quantity that makes up the difference between the total demand and the quantity produced by firm 2. The aggregate demand curve is Y = 10 p and the firms' cost functions are as in Question IV above.

1.Find the equilibrium of this model. What are firm 1's profits?

2.Assume firm 1 produces the quantity you found in 1 above, what would firm 2 produce in the model of Question IV above?

3. Here, does firm 1 prefer to be a quantity leader or a price leader?