Economics Dynamics Problems 160

Economics Dynamics - 144 Economic Dynamics Figure 4.1 with solutions t 9e2t 1 4 2 y(t = 3et x(t = which clearly satisfy the initial conditions

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144 Economic Dynamics Figure 4.1. with solutions x ( t ) = 9 e 2 t 1 4 t 2 y ( t ) = 3 e t which clearly satisfy the initial conditions. Eliminating e t , we can express the relationship between x and y as y = 1 + 4 x + 2 tx 2 , y 3 which clearly depends on t . This means that where a system is at any point in time in the ( x , y )-plane depends on precisely the moment the system arrives at that point. For instance, in ±gure 4.1(b) we draw the system for three points of time, t = 0 , 5 , 10 . There is no longer a single trajectory in the ( x , y )-plane, but a whole series of trajectories, one for each point in time. The system is clearly
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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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