Consider a Stackelberg competition with one leader and multiple followers. All products are homogeneous.
The inverse market demand function is: P(Q) = 24 Q
Marginal cost for all firms is zero and all products are homogeneous.
Suppose now we have two followers. The leader chooses a quantity, then, taking the leader’s quantity as given, the two followers play a Cournot game with each other.
If the leader produces a quantity of 6 units how much would each of the other two firms produce in equilibrium?
If the leader produces a quantity of 12 units how much would each of the other two firms now produce in equilibrium? Does the leader get higher profit when it produces 12 units?