Economics Dynamics Problems 219

Economics Dynamics Problems 219 - Discrete systems of...

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Discrete systems of equations 203 Example 5.1 x t = 2 x t 1 + 3 y t 1 y t =− 2 x t 1 + y t 1 or ± x t y t ² = ± 23 21 ²± x t 1 y t 1 ² i.e. u t = Au t 1 where I A = ± 1 3 20 ² and ( I A ) u = ± 1 3 x y ² = ± 0 0 ² the only values for x and y satisfying this system are x = 0 and y = 0. Example 5.2 x t = 4 x t 1 + 2 y t 2 y t 1 3 x t 1 + 3 i.e. ± x t y t ² = ± 40 3 2 x t 1 y t 1 ² + ± 2 3 ² Then u = ( I A ) 1 b = ± 30 33 ² 1 ± 2 3 ² = ± 2 / 3 5 / 3 ² i.e. x 2 / 3 and y = 5 / 3. Having established that an equilibrium exists, however, our main interest is establishing the stability of such systems of equations. In establishing this we
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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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