Economics Dynamics Problems 226

Economics Dynamics Problems 226 - 210 Economic Dynamics and...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 210 Economic Dynamics and we can find a and b for t = 0 from u0 = avr + bvs where u0 is known. This can either be done by direct substitution, or using the fact that avr + bvs = vr i.e. or (4) V vs a = u0 b a = u0 b a = V−1 u0 b Write the solution ut = art vr + bst vs But we can do this whole process in one step. First we note ut = art vr + bst vs = vr = VDt vs rt 0 0 st a b a b But a = V−1 u0 b Hence ut = VDt V−1 u0 which is the result we proved above. The gain, if there is one, in doing the four steps is the need to solve for a and b. Since this can often be done by direct substitution, then the four steps involve no inverse matrix computation. Example 5.4 Let xt+1 = −8 − xt + yt yt+1 = 4 − 0.3xt + 0.9yt setting xt+1 = xt = x∗ and yt+1 = yt = y∗ for all t, the fixed point is readily shown to be (x∗ , y∗ ) = (6.4, 20.8). Now consider the system in terms of deviations from equilibrium, then xt+1 − x∗ = −(xt − x∗ ) + ( yt − y∗ ) yt+1 − y∗ = −0.3(xt − x∗ ) + 0.9( yt − y∗ ) or ut = Aut−1 ...
View Full Document

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.

Ask a homework question - tutors are online