On the use and misuse of the instantaneous speed of adjustment assumption

A commonly used simplifying assumption in dynamics is that one of the variables moves infinitely fast to its equilibrium value, given the current values of the slower variables. If a theorist believes that one of his variables is fast relative to the others, how safe is he in setting the system up as if the relatively fast variable were infinitely fast? How do the dynamics of the simplified system compare with those of the true system? In this paper, the notion of adjustment speed is analysed and a new definition is offered. It is found that the simplified system behaves like the true system only in highly unlikely cases.