%
% ex4 is a matlab file that solves for 
% the 'steady-state' for a simplified Kydland and Prescott model
% using the ex4F.m file 
%

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

clear all
diary ex4.mout
diary off
delete ex4.mout
diary ex4.mout

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

%format long
date
time0 = clock;

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

alpha    = 1/3;
thetabar = 1;
delta    = 0.10;
beta     = 0.99;

% ----- dfine fsolve options ----- %

options = optimset('Display','iter','MaxIter',1000);

% ----- solve for steady states ----- %

x = fsolve(@ex4F,[1 1],options,alpha,delta,beta,thetabar)


% ----- linearized eulers coeffs ----- %

h0 = 1/x(1) - 1/x(1)*beta*( alpha*x(2)^(alpha-1) + 1-delta  )

h1 = -(alpha*x(2)^alpha + (1-delta)*x(2))/(x(1)^2) 

h2 = x(2)/(x(1)^2) + (alpha*x(2)^alpha+(1-delta)*x(2))/(x(1)^2)*beta*(alpha*x(2)^(alpha-1)+1-delta) - ...
      1/x(1)*beta*(alpha*(alpha-1)*x(2)^(alpha-1)   ) 

h3 = x(2)/(x(1)^2)*beta*(alpha*x(2)^(alpha-1)+ 1-delta   )

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

comptime = etime(clock, time0)
diary off