Economics Dynamics Problems 104

Economics Dynamics Problems 104 - one equilibrium point....

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88 Economic Dynamics Figure 3.1. 3.4 Equilibrium and stability of discrete dynamic systems If y t + 1 = f ( y t ) is a discrete dynamic system, then y is a Fxed point or equilibrium point of the system if f ( y t ) = y for all t (3.7) A useful implication of this deFnition is that y is an equilibrium value of the system y t + 1 = f ( y t ) if and only if y = f ( y ) ±or example, in the cobweb model (3.6) we have, p = a c b ± d b ² p Hence p = a c b + d where p 0if a c With linear demand and supply curves, therefore, there is only one Fxed point,
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Unformatted text preview: one equilibrium point. However, such a Fxed point makes economic sense (i.e. for price to be nonnegative) only if the additional condition a ≥ c is also satisFed. As with Fxed points in continuous dynamic systems, a particularly important consideration is the stability/instability of a Fxed point. Let y ∗ denote a Fxed point for the discrete dynamic system y t + 1 = f ( y t ). Then (Elaydi 1996, p. 11)...
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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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