Discrete dynamic systems131Hencesyt=kt(1+n)−(1−δ)kt−1or(1+n)kt−(1−δ)kt−1=sf(kt−1)which can be expressedkt=(1−δ)kt−1+sf(kt−1)1+ni.e.kt=h(kt−1)With constant returns to scale and assuming a Cobb–Douglas production function,thenyt=f(kt−1)=akαt−1a>0,0<α<1Example 3.20This can be investigated by means of a spreadsheet, where we assumea=5,α=0.25,s=0.1,n=0.02,δ=0and letk0=20.Alternatively, using a Taylor expansion aboutk∗>0, thenkt=h(k∗)+(1−δ)(kt−1−k∗)+αsa(k∗)α−1(kt−1−k∗)1+n=h(k∗)+±(1−δ)+αsa(k∗)α−11+n²(kt−1−k∗)=k∗+±(1−δ)+αsa(k∗)α−11+n²(kt−1−k∗)The situation is illustrated in Fgure 184.108.40.206 Solving recursive equations withMathematicaandMapleBothMathematicaandMaplecome 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.