solution to a single nonlinear equation with a parameter

Question

msh am 10 Nov. 2016

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https://de.mathworks.com/matlabcentral/answers/311589-solution-to-a-single-nonlinear-equation-with-a-parameter

Bearbeitet: Matt J am 10 Nov. 2016

I want to get the solution to a nonlinear single equation, that carries a parameter the functional form is complicated:

the function that I want to solve is:

w  = (1-alpha)*A*x^alpha;
r  = alpha*A*x^(alpha-1);
xs = d2*(1+r);
d1*(w-(r-n)*b)/(1-xs)=(1+n)*(x+b);  % this is the function I looking

The parameter that I want to experiment in order to find different solutions is the b,

I have created this function

function y = f(x,b)
global alpha A d1 d2 n
   w  = (1-alpha)*A*x^alpha;
   r  = alpha*A*x^(alpha-1);
   xs = d2*(1+r);
   y  = d1*(w-(r-n)*b)/(1-xs)-(1+n)*(x+b);
  end

where the other parameters of the equations are:

global alpha d1 d2 n debt

beta  =0.3;   % discount factor
delta =0.10;  % altruism 
A     =9.37;  % TFP 
alpha =0.3;   % income share of capital 
n     =1.81;   % growth rate of population
d1 =(1+delta)*beta/(1+(1+delta)*beta);  % MPS 
d2 =delta/(1+n)*(1+delta);              % degree affecting altruism

Can someone assist me with how to call fzero, in order to look for solutions at different values of b ? As guidance, b is between (0,0.10)

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Answer 1

Matt J am 10 Nov. 2016

1
Verknüpfen

Direkter Link zu dieser Antwort

https://de.mathworks.com/matlabcentral/answers/311589-solution-to-a-single-nonlinear-equation-with-a-parameter#answer_242766

Bearbeitet: Matt J am 10 Nov. 2016

In MATLAB Online öffnen

Get rid of the global variables (because they're just bad) and redefine the function as follows

function y = f(x,b, alpha, A, d1, d2, n)
   w  = (1-alpha)*A*x^alpha;
   r  = alpha*A*x^(alpha-1);
   xs = d2*(1+r);
   y  = d1*(w-(r-n)*b)/(1-xs)-(1+n)*(x+b);
end

Then to use fzero,

beta  =0.3;   % discount factor
delta =0.10;  % altruism 
A     =9.37;  % TFP 
alpha =0.3;   % income share of capital 
n     =1.81;   % growth rate of population
d1 =(1+delta)*beta/(1+(1+delta)*beta);  % MPS 
d2 =delta/(1+n)*(1+delta);              % degree affecting altruism 
xsol = fzero(@(x) f(x,b, alpha, A, d1, d2, n) , x0)

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msh am 10 Nov. 2016

I just make random guess, x= should be nearly 0.5 to 1.5. So I play with values in this interval.

Matt J am 10 Nov. 2016

Bearbeitet: Matt J am 10 Nov. 2016

x= should be nearly 0.5 to 1.5. So I play with values in this interval.

Did you plot your function to verify if this is true? When I plot it, I see that it comes nowhere near zero in the interval [0.5,1.5] and in fact appears to decrease monotonically in [0.5,inf] starting from a value of about -0.8 at x=0.5.

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