Economics Dynamics Problems 240

Economics Dynamics Problems 240 - 224 Economic Dynamics...

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224 Economic Dynamics considering the general solution u t = ar t v r + bs t v s where u t = ± x t x y t y ² If | r | < 1 and | s | < 1 then ar t v r 0 and bs t v s 0 as t →∞ and so u t 0 and consequently the system tends to the Fxed point, the equilibrium point. Return to example 5.4 where r = 0 . 7262 and s =− 0 . 8262. The absolute value of both roots is less than unity, and so the system is stable. We showed this in terms of Fgure 5.1, where the system converges on the equilibrium, the Fxed point. We pointed out above that the system can be represented in its canonical form, and the same stability properties should be apparent. To show this our Frst task is to compute the vector z 0 . Since z 0 = V 1 u 0 , then ± z 10 z 20 ² = ± 0 . 5793 5 . 7537 11 ² 1 ± 4 . 4 12 . 8 ² = ± 13 . 3827 0 . 5827 ² and z 1 t = (0 . 7262) t ( 13 . 3827) z 2 t = ( 0 . 8262) t (0 . 5827) Setting this up on a spreadsheet, we derive Fgure 5.4. The canonical form has transformed the system into the ( z 1 , z 2 )-plane, but once again it converges on the
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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.

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