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Economics Dynamics Problems 31

Economics Dynamics Problems 31 - Introduction exceptions...

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Introduction 15 exceptions, been content to investigate the local stability of the fixed points to a nonlinear system. The fact that a linear approximation can be taken in the neighbourhood of a fixed point in no way removes the fact that there can be more than one fixed point, more than one equilibrium point. Even where we confine ourselves only to stable equilibria, there is likely to be more than one. This leads to some new and interesting policy implications. In simple terms, and using figure 1.2(a) for illustrative purposes, the welfare attached to point x 1 will be different from that attached to x 3 . If this is so, then it is possible for governments to choose between the two equilibrium points. Or, it may be that after investigation one of the stable equilibria is found to be always superior. With linear systems in which only one equilibrium exists, such questions are meaningless. Multiple equilibria of this nature create a problem for models involving per- fect foresight. If, as such models predict, agents act knowing the system will
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