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Economics Dynamics Problems 150

Economics Dynamics Problems 150 - 134 Economic Dynamics...

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134 Economic Dynamics Problems (i)–(v) are all recursive equations of the first-order. The same basic form is used to solve higher-order recursive equations. Given the recursive equation y t + 2 = ay t + 1 + by t then this can be solved with the instructions: Mathematica RSolve[y[t+2]==ay[t+1]+by[t],y[t],t] Maple rsolve(y(t+2)=a*y(t+1)+b*y(t),y(t)); But because this is a general recursive equation the output in each case is quite in- volved. Mathematica ’s output even more so, since it involves Binomial equations! What is revealed by the output is the need to know two initial conditions to solve such second-order recursive equations: Solving y t + 2 = y t + 1 + 2 y t with initial conditions y (0) = 5 and y (1) = 4, we have Mathematica RSolve[{y[t+2]==y[t+1]+2y[t],y[0]==5,y[1]==4},y[t],t] with output {{y[t]->2(-1) t + 3 2 t }} Maple rsolve({r(t+2)=y(t+1)+2*y(t),y(0)=5,y(1)=4},y(t)); with output 2(-1) t + 3 2 t Furthermore, there is no difficulty with repeated roots, which occur in solving y t + 2 = 4 y t + 1 4 y t . For initial conditions y (0) = 6 and y (1) = 4, we have solutions Mathematica : {{y[t]->-2
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