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Unformatted text preview: 204 Economic Dynamics with solution u t = A t u (5.3) where u is the initial values of the vector u . Given u and the matrix A , then we could compute u 100 = A 100 u , or any such time period. Similarly, with the first-order nonhomogeneous linear equation system we have u t = Au t 1 + b = A ( Au t 2 + b ) + b = A 2 u t 2 + Ab + b = A 2 ( Au t 3 + b ) + Ab + b = A 3 u t 3 + A 2 b + Ab + b . . . with solution u t = A t u + ( I + A + A 2 + . . . + A t 1 ) b (5.4) Although solution (5.3) and (5.4) are possible to solve with powerful computers, it is not a useful way to proceed. We require to approach the solution from a different perspective. It will be recalled from our analysis of differential equation systems in chapter 4 that a linear nonhomogeneous system can be reduced to a linear homogeneous system by considering deviations from equilibrium. Thus for u t = Au t 1 + b , with equilibrium vector u we have u = Au + b . Subtracting we obtain u t...
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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.
- Fall '11