Unformatted text preview: t = a t − 1 + bY t − 1 Many problems reduce to this kind of relationship. ±or example, population of a species at time t may be proportional to its size in the previous period, but predation may take place each period. Or, human populations may grow proportionally but immigration and emigration occurs in each period. Solving the recursive equation can be achieved by iteration. Let the initial values be Y and a , respectively, then Y 1 = a + bY Y 2 = a 1 + bY 1 = a 1 + b ( a + bY ) = a 1 + ba + b 2 Y Y 3 = a 2 + bY 2 = a 2 + b ( a 1 + ba + b 2 Y ) = a 2 + ba 1 + b 2 a + b 3 Y Y 4 = a 3 + bY 3 = a 3 + b ( a 2 + ba 1 + b 2 a + b 3 Y ) = a 3 + ba 2 + b 2 a 1 + b 3 a + b 4 Y...
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 Fall '11
 Dr.Gwartney
 Economics, 7%, 7.2%, recursive equation, Economic Dynamics

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