%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 14.461 Blanchard-Kahn for Open Economy Dynamics                         %
%        FIXED EXCHANGE RATE                                              %
% ----------------------------------------------------------------------- %
% Suman Basu, September 2005                                              %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

tic

% Starting the program
clear

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Parameter values                                                        %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
alpha = 0.5;
beta = 0.1;
gamma = 10;
pstar = 0;

% Set matrix and stochastic steady state
a11 = 1 + beta/alpha + 1/(alpha*gamma);
a12 = -1/(alpha*gamma);
a21 = 1;
a22 = 0;
M = [a11 a12; a21 a22];
yss = 0;
pss = pstar;
X = [0; 0];

%Decompose matrix and solve for price level;
[V, J] = jordan(M)
Z = inv(V);
X(2) = 0;
xstable = -(Z(1,2)/Z(1,1))*X(2);
X(1) = xstable;                      % Here xstable = 0.
                                     % PSet 1 Problem 2 Part 1: Change X(1)

% No. of periods
T = 10;

% Set up grid for graphing
price = zeros(1, T);
price(1,1) = X(2);
price(1,2) = X(1);

% Generate impulse response
for i = 1:T-2
    X = M*X;
    price(1, i + 2) = X(1);
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Graph time series                                                       %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
plot(1:T, price); grid
title('Evolution of price level in FIXED exchange rate economy, mbar = m')

toc