% 
% mid1.m is a matlab file that solves the 
% ramsey model using kliens method 
% 

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

clear all 
diary mid1.mout 
diary off 
delete mid1.mout 
diary mid1.mout 

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

%format long 
date 
time0 = clock; 

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

alpha = 0.30;
delta = 0.025 ;
beta = 0.99;
abar = 1;
thetabar = 1.05;
psi = 1;
sigma = 2;
phi = 0.90;

% ----- steady states from ch2ex1 ----- %

sol1 = [2.3501 0.4708 0.3731];
kbar = [2.3501];
cbar = [0.4708];
nbar = [0.3731];

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

A = [1, 0, 0, 0;
0,-kbar/(cbar+kbar-((1-delta)/thetabar)*kbar),0,0;
(beta/(cbar*thetabar))*alpha*abar*(kbar/thetabar)^(alpha-1)*nbar^(1-alpha),... 
(beta/(cbar*thetabar))*alpha*(alpha-1)*abar*(kbar/thetabar)^(alpha-1)*nbar^(1-alpha),... 
-(beta/(cbar*thetabar))*(alpha*abar*(kbar/thetabar)^(alpha-1)*nbar^(1-alpha)+1-delta),... 
(beta/(cbar*thetabar))*alpha*(1-alpha)*(kbar/thetabar)^(alpha-1)*nbar^(1-alpha);
0,0,0,0 ] ;

B = [phi, 0, 0, 0;
-1, -alpha-(((1-delta)/thetabar)*kbar)/(cbar+kbar-((1-delta)/thetabar)*kbar),... 
cbar/(cbar+kbar-((1-delta)/thetabar)*kbar), -(1-alpha);
0, 0, -1/cbar, 0;
1, alpha, -1, -sigma*(nbar/(1-nbar))-alpha];

% ----- find solution using kleins solab ----- % 

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

% ----- exit ----- % 

comptime = etime(clock, time0) 
diary off