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, λ , the system’s dynamics is dominated by the sign/value of this root. If | λ | < 1, then the system will converge on the equilibrium value: it is asymptotically stable. If | λ | > 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
- Economics, Rational expectations, Canonical form, Stability theory, Economic Dynamics