Economics Dynamics Problems 103

Economics Dynamics Problems 103 - Discrete dynamic systems...

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Discrete dynamic systems 87 and so on. Hence, each number in the sequence ultimately depends on two initial values, y t + 1 and y t . This requirement generalises. For an m -order dynamic system m -initial values are generally required for its solution. Let y t + 1 = f ( y t ) y 0 at t = 0 This represents a recursive equation and we can generate a sequence starting from the value y 0 . The sequence would be y 0 , f ( y 0 ) , f ( f ( y 0 )) , f ( f ( f ( y 0 ))) ,... Letting f n ( y 0 ) denote the n th iterate of y 0 under f , then the sequence can be ex- pressed y 0 , f ( y 0 ) , f 2 ( y 0 ) , f 3 ( y 0 ) ,... The set of all (positive) iterates { f n ( y 0 ) , n 0 } is called the (positive) orbit of y 0 . 3.3 The cobweb model: an introduction Tohighlightthefeaturessofaroutlined,andotherstofollow,considerthefollowing typical cobweb model in which demand at time t , q d t , depends on the price now ruling on the market, p t , while the supply at time t , q s t , depends on planting, which in turn was governed by what the price the farmer received in the last period,
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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.

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