Solving capital constraint and optimal labor choice using numerical method - fzero

Function takes important model parameters as inputs and evaluates constrained k and corresponding optimal l, given phi using numerical method - fzero.

Back to full code page https://kritikhanna.github.io/BKS-modified/

Function Inputs : One combination of Asset and entrepreneurial productivity, relevant model parameters required to compute the constraint on capital and labor based on the degree of contract enforceability.

Function Outputs : constrained k and l (scalers)

Contents

function [k,l] = conkl_numerical(varargin)

close all;
profile off;
profile on;

if (~isempty(varargin))

    [fl_a,fl_z,fl_r,fl_w,fl_alpha,fl_theta,fl_kappa,fl_delta,fl_phi,fl_R] = varargin{:};
    bl_display_param      = true;

else

    fl_a          = 50;
    fl_z          = 1;
    fl_r          = 0.0467;
    fl_w          = 1.0667;
    fl_alpha      = 0.36;
    fl_theta      = 0.79-fl_alpha;
    fl_kappa      = 0;
    fl_delta      = 0.06;
    fl_phi        = 0.1;
    fl_R          = fl_r + fl_delta;
    bl_display_param      = true;

end

%s = (fl_w/(fl_theta*fl_z*kbar^(fl_alpha)))^(1/(fl_theta-1));
%lval= z*x(1)^alpha*s^theta-w*s;
%lval=kbar^fl_alpha*fl_z*((fl_w/(kbar^fl_alpha*fl_theta*fl_z))^(1/(fl_theta - 1)))^fl_theta - fl_w*(fl_w/(kbar^fl_alpha*fl_theta*fl_z))^(1/(fl_theta - 1));

Capital renting constraint condition

c = @(kbar)[(1+fl_r)*fl_kappa-fl_z*kbar^fl_alpha*(fl_w/(fl_theta*fl_z*kbar^(fl_alpha)))^(1/(fl_theta-1))^fl_theta;(1-fl_phi)*(kbar^fl_alpha*fl_z*((fl_w/(kbar^fl_alpha*fl_theta*fl_z))^(1/(fl_theta - 1)))^fl_theta - fl_w*(fl_w/(kbar^fl_alpha*fl_theta*fl_z))^(1/(fl_theta - 1))+(1-fl_delta)*kbar)-kbar^fl_alpha*fl_z*((fl_w/(kbar^fl_alpha*fl_theta*fl_z))^(1/(fl_theta - 1)))^fl_theta - fl_w*(fl_w/(kbar^fl_alpha*fl_theta*fl_z))^(1/(fl_theta - 1))+fl_R*kbar+(1+fl_r)*fl_kappa-(1+fl_r)*fl_a];
k = fsolve(c,2);                                          % Solving for constraint k
l = (fl_w/(fl_theta*fl_z*k^(fl_alpha)))^(1/(fl_theta-1)); % Value of corresponding optimal l

if (bl_display_param  == true)
    disp(['k= ' ,num2str(k)]);    % Display contrained k
    disp(['l= ' ,num2str(l)]);    % Display optimal l corresponding to constrained k

profile off;
profile viewer;

end

Warning: Trust-region-dogleg algorithm of FSOLVE cannot handle non-square
systems; using Levenberg-Marquardt algorithm instead. 

No solution found.

fsolve stopped because the last step was ineffective. However, the vector of function
values is not near zero, as measured by the default value of the function tolerance. 



k= 60.8724
l= 2.7212

end

Published with MATLAB® R2018a