Economics Dynamics Problems 84

# Economics Dynamics - 68 Economic Dynamics Figure 2.18 Hence f(k =(n(1(k k Since 0 < < 1 and n and are both positive then this has a negative slope

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68 Economic Dynamics Figure 2.18. Hence f ( k ) =− ( n + δ )(1 α )( k k ) Since 0 <α< 1 and n and δ are both positive, then this has a negative slope about k 2 and hence k 2 is a locally stable equilibrium. The situation is shown in fgure 2.18. The frst-order linear approximation about the non-zero equilibrium is then ˙ k = f ( k ) =− ( n + δ )(1 α )( k k ) with the linear approximate solution k ( t ) = k 2 + ( k (0) k 2 ) e ( n + δ )(1 α ) t As t →∞ then k ( t ) k 2 . What we are invoking here is the Following theorem attributed to Liapunov THEOREM 2.1 If ˙ x = f ( x ) is a nonlinear equation with a linear approximation
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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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