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Introduction
15
exceptions, been content to investigate the local stability of the Fxed points to a
nonlinear system.
The fact that a linear approximation can be taken in the neighbourhood of a
Fxed point in no way removes the fact that there can be more than one Fxed
point, more than one equilibrium point. Even where we conFne 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 Fgure 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
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This note was uploaded on 12/14/2011 for the course ECO 3023 taught by Professor Dr.gwartney during the Fall '11 term at FSU.
 Fall '11
 Dr.Gwartney
 Economics

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