Economics Dynamics Problems 74

Economics Dynamics Problems 74 - system, for any initial...

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58 Economic Dynamics of the attractor, the differential equation has a negative slope. In fact, this is a typical feature of instability/stability. A Fxed point is unstable if the slope of the differential equation in the neighbourhood of this point is positive; it is stable if the slope of the differential equation in the neighbourhood of this point is negative. If there is only one Fxed point in a dynamic system, then such a Fxed point is either globally stable or globally unstable. In the case of a globally stable system, for any initial value not equal to the Fxed point, then the system will converge on the Fxed point. ±or a globally unstable
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Unformatted text preview: system, for any initial value not equal to the Fxed point, then the system will move away from it. Consider example 2.4, a simple continuous price-adjustment demand and supply model with the differential equation dp dt = α ( a − c ) + α ( b − d ) p α > ±or a solution (a Fxed point, an equilibrium point) to exist in the positive quadrant then a > c and so the intercept is positive. With conventional shaped demand and supply curves, then b < 0 and d > 0, respectively, so that the slope of the differential equation is negative. The situation is illustrated in Fgure 2.16(a). Figure 2.16....
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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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