Economics Dynamics Problems 227

Economics Dynamics Problems 227 - Discrete systems of...

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Unformatted text preview: Discrete systems of equations where A= −1 −0.3 1 0.9 Solving for the eigenvalues from A − λI = −1 − λ 1 −0.3 0.9 − λ we have |A − λI| = −(1 + λ)(0.9 − λ) + 0.3 = λ2 + 0.1λ − 0.6 = 0 giving r = 0.7262 and s = −0.8262. Given r = 0.7262 then (A − 0.7262I)vr = 0 so −1.7262 1 −0.3 0.1738 vr 1 vr 2 = 0 0 vs 1 vs 2 = 0 0 i.e. −1.7262vr + vr = 0 1 2 −0.3vr + 0.1738vr = 0 1 2 Let vr = 1 then vr = 0.5793. 2 1 For s = −0.8262 −0.1738 1 −0.3 1.7262 i.e. −0.1738vs + vs = 0 1 2 −0.3vs + 1.7262vs = 0 1 2 Let vs = 1 then vs = 5.7537. Hence 2 1 0.5793 1 V = [ vr vs ] = ut = V (0.7262)t 0 5.7537 1 and 0 V−1 u0 (−0.8262)t Suppose x0 = 2 and y0 = 8, i.e. u0 = −4.4 −12.8 Then x t +1 − x ∗ yt + 1 − y∗ = 0.5793 1 5.7537 1 0.5793 1 5.7537 1 (0.7262)t 0 −1 −4.4 −12.8 0 (−0.8262)t 211 ...
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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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