%------------------------------------------------------------------
% This script shows how to solve the RBC model by Taylor projection
%------------------------------------------------------------------

clear,clc

%-----------------------------------------
% Define symbolic variables and parameters
%-----------------------------------------

syms k kp c cp z zp epsp real
syms BETA GAMMA ALPHA RHO DELTA SIGMA real

%-------------------------------------------------
% Function f (Euler condition) in a unit-free form
%-------------------------------------------------

f_fun=BETA*(c/cp)^GAMMA*(ALPHA*exp(zp)*kp^(ALPHA-1)+1-DELTA)-1;

%-------------------------------------------------------
% Function Phi (law of motion of capital and technology)
%-------------------------------------------------------

Phi_fun=[exp(z)*k^ALPHA+(1-DELTA)*k-c;
         RHO*z+SIGMA*epsp];

%--------------------------
% Vector of state variables
%--------------------------

x=[k,z]; % current period
xp=[kp,zp]; % future period

%----------------------------
% Vector of control variables
%----------------------------

y=[c]; % current period
yp=[cp]; % future period

%-----------------
% Vector of shocks
%-----------------

shocks=[epsp];

%---------------------
% Vector of parameters
%---------------------

symparams=[BETA,GAMMA,ALPHA,RHO,DELTA,SIGMA];

%--------------------
% Approximation order
%--------------------

order=4; % fourth order is the maximum possible

%----------------
% Call prepare_tp
%----------------

model=prepare_tp(f_fun,Phi_fun,yp,y,xp,x,shocks,symparams,order);

%-----------
% Save model
%-----------

save('model') % you will need this later