Equilibrium:
Diagrammatically this is shown in Figure. The equilibrium is obtained where the two reaction functions intersect each other i.e., at point E corresponding to which we have the two equilibrium output levels as qA* and qB*
Stability:
For stability analysis, let us consider Figure 10. 3 where MN and SP represent the reaction functions of firms A and B respectively. To see if point E is a stable equilibrium, we would start from an arbitrary point and see if the inbuilt dynamics of the model would take us to point E. In the diagram, ON is the monopoly output of firm A and OS represents that of firm B. Suppose firm A enters the market first and produces the monopoly output ON. Next, firm B enters and assuming that firm A would continue producing at ON chooses to produce Ob from it's reaction function SP. Therefore, the two firms end up at point 1 on B's reaction function. As at point 1 firm A is off it's reaction function, it would not be maximising it's profit. Hence, A would not choose to be at 1. Assuming that firm B would continue producing at Ob, firm A would choose to be at point 2 on it's reaction function whereby it would be producing Oa amount of output. From the point of view of firm B, point 2 is not a desirable one because given that A produces Oa, Ob is no more the profit maximising level of output. Hence, B would move from point 2 to point 3 on it's own reaction function. Finally, such actions would take both the firms to point E. This movement towards E would occur if we start from a point like OS above the equilibrium point. Thus, we see that point E is a stable equilibrium point because any disturbance from point E would take us back to E.
