Economics Dynamics Problems 166

Economics Dynamics Problems 166 - = x − 3 y = − 2 x + y...

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150 Economic Dynamics Figure 4.4. Figure 4.5. or Maple. 2 Such a solution path to the system in the ( x , y )-plane is illustrated in fgure 4.5. This is a specifc solution since it satisfes the initial conditions. But we want to know what is happening to the path in relation to the fxed point, the equilibrium point, oF the system. We already know that a fxed point is established by setting ˙ x = 0 and ˙ y = 0. The fxed point is readily established by solving the simultaneous equations
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Unformatted text preview: = x − 3 y = − 2 x + y which has solution x ∗ = 0 and y ∗ = 0. Another way to view the fxed point is to note that 0 = x − 3 y is the equilibrium condition For the variable x ; while 0 = − 2 x + y is the equilibrium condition For the variable y . The fxed point is simply where the two equilibrium lines intersect. The equilibrium lines are y = x 3 (˙ x = 0) y = 2 x (˙ y = 0) 2 See section 4.12....
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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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