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Unformatted text preview: Fxed point, and these are values that lie on the stable arm of the saddle point. As we shall see in part II, such possible solution paths are important in ratio-nal expectations theory. Under such assumed expectations behaviour, the system jumps from its initial point to the stable arm and then traverses a path down the stable arm to equilibrium. Of course, if this initial jump did not occur, then the trajectorywouldtendtoplusorminusinFnityandbedrivenawayfromequilibrium. 5.6.2 Repeating roots When there is a repeating root, , the systems dynamics is dominated by the sign/value of this root. If | | < 1, then the system will converge on the equilibrium value: it is asymptotically stable. If | | > 1 then the system is asymptotically unstable. We can verify this by considering the canonical form. We have already...
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- Fall '11