Economics Dynamics Problems 147

Economics Dynamics Problems 147 - Discrete dynamic systems...

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Discrete dynamic systems 131 Hence sy t = k t (1 + n ) (1 δ ) k t 1 or (1 + n ) k t (1 δ ) k t 1 = sf ( k t 1 ) which can be expressed k t = (1 δ ) k t 1 + sf ( k t 1 ) 1 + n i.e. k t = h ( k t 1 ) With constant returns to scale and assuming a Cobb–Douglas production function, then y t = f ( k t 1 ) = ak α t 1 a > 0 , 0 <α< 1 Example 3.20 This can be investigated by means of a spreadsheet, where we assume a = 5 = 0 . 25 , s = 0 . 1 , n = 0 . 02 = 0 and let k 0 = 20. Alternatively, using a Taylor expansion about k > 0, then k t = h ( k ) + (1 δ )( k t 1 k ) + α sa ( k ) α 1 ( k t 1 k ) 1 + n = h ( k ) + ± (1 δ ) + α sa ( k ) α 1 1 + n ² ( k t 1 k ) = k + ± (1 δ ) + α sa ( k ) α 1 1 + n ² ( k t 1 k ) The situation is illustrated in Fgure 3.21. 3.13 Solving recursive equations with Mathematica and Maple Both Mathematica and Maple come with a solver for solving recursive equations.
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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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