The particular type of stability that is exemplified by the model is called saddlepoint stability: there is exactly one stable adjustment path (called the saddle path)

that re-establishes equilibrium after a shock. Technically speaking, the requirement that the economy be on the saddle path has more justification than just convenience:

ultimately, an exploding solution is seen by agents not to be in their own best interests, so that they have good reason to restrict attention to the saddle-path solution. The remainder of this chapter will be used to demonstrate the remarkable predictive content of models incorporating saddle-point stability.

Consider the case of an unanticipated and permanent increase in the investment subsidy.

This means that at some time tA the government announces that s, will be increased "as of today". In other words, the policy change is implemented immediately.