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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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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
 Dr.Gwartney
 Economics

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