Unformatted text preview: Consider the following general Frst-order linear nonhomogeneous equation y t + 1 = ay t + c (3.10) Asimplewaytosolvesuchequations,andoneparticularlyusefulfortheeconomist, is to transform the system into deviations from its Fxed point, deviations from equilibrium. Let y denote the Fxed point of the system, then y = ay + c y = c 1 a Subtracting the equilibrium equation from the recursive equation gives y t + 1 y = a ( y t y ) Letting x t + 1 = y t + 1 y and x t = y t y then this is no more than a simple ho-mogeneous difference equation in x x t + 1 = ax t with solution x t = a t x Hence, y t y = a t ( y y )...
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- Fall '11
- Economics, Elementary algebra, linear homogeneous equation, initial population size, homogeneous difference equation