%
% mid2en.m is a matlab file that solves the 
% ramsey model using kleins method
%

% ----- save output to file ----- %

clear all
diary mid2e.mout
diary off
delete mid2e.mout
diary mid2e.mout

% ----- display date and time of computation ----- %

format long

% ----- define the parameters ----- %

alpha = 0.2443;
delta = 0.025 ;
beta  = 0.9902;
phi   = 1.5;
psi   = .3531;
rho   = 0.9;

% ----- steady states  ----- %

cbar = 0.5159;
kbar = 4.3775;
nbar = 0.3333;
zbar  = 1;

% ----- define the parameters of the model ----- %

% - evolution of state - %

om1z1 = -rho;
om1k1 = 0;
om1c1 = 0;
om1n1 = 0;

om1z2 = 1;
om1k2 = 0;
om1c2 = 0;
om1n2 = 0;

% - budget - %

om2z1 = 1;
om2k1 = alpha + (1-delta)*kbar/(cbar+ kbar-(1-delta)*kbar) ;
om2c1 = -cbar/(cbar+kbar-(1-delta)*kbar) ;
om2n1 = (1-alpha);

om2z2 = 0;
om2k2 = -kbar/(cbar+kbar-(1-delta)*kbar) ;
om2c2 = 0;
om2n2 = 0;

% - intratemp - %

om3z1 = -1;
om3k1 = -alpha;
om3c1 = 1;
om3n1 = alpha+nbar/(1-nbar);

om3z2 = 0;
om3k2 = 0;
om3c2 = 0;
om3n2 = 0;

% - intertemp - %

lambda = psi*(1-phi)-1;
mu = (1-psi)*(1-phi);

om4z1 = 0;
om4k1 = 0;
om4c1 = lambda*cbar^lambda*(1-nbar)^(mu);
om4n1 = -mu*cbar^lambda*(1-nbar)^(mu-1)*nbar;

om4z2 = -beta*cbar^lambda*(1-nbar)^mu*alpha*kbar^(alpha-1)*nbar^(1-alpha);
om4k2 = -beta*cbar^lambda*(1-nbar)^mu*alpha*(alpha-1)*kbar^(alpha-1)*nbar^(1-alpha);
om4c2 = -beta*lambda*cbar^lambda*(1-nbar)^mu*(alpha*kbar^(alpha-1)*nbar^(1-alpha)+1-delta);
om4n2 = beta*cbar^lambda*mu*(1-nbar)^(mu-1)*nbar*(alpha*kbar^(alpha-1)*nbar^(1-alpha)+1-delta)-...
         beta*cbar^lambda*(1-nbar)^mu*(alpha*kbar^(alpha-1)*(1-alpha)*nbar^(1-alpha));

% ----- find solution using kleins solab ----- %
A = [om1z2 om1k2 om1c2 om1n2;
     om2z2 om2k2 om2c2 om2n2;
     om3z2 om3k2 om3c2 om3n2;
     om4z2 om4k2 om4c2 om4n2] ;
     
B = -1*[om1z1 om1k1 om1c1 om1n1;
     om2z1 om2k1 om2c1 om2n1;
     om3z1 om3k1 om3c1 om3n1;
     om4z1 om4k1 om4c1 om4n1]  ;   


[f1,f2]=solab(A,B,2)

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