%
% ch2ex2.m is a matlab file that solves the 
% ramsey model using kliens method
%

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

clear all
diary ch2ex2.mout
diary off
delete ch2ex2.mout
diary ch2ex2.mout

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

%format long
date
time0 = clock;

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

alpha = 0.36;
delta = 0.025 ;
beta  = 0.99;
abar  = 1;

phi = 0.95;

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

sol1 = [37.9893 2.7543];
kbar = [37.9893];
cbar = [2.7543];

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

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

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

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

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

comptime = etime(clock, time0)
diary off