%-------------------------------------------------------------------------%
% OG model with two countries and perfect competition
%-------------------------------------------------------------------------%

%-------------------------------------------------------------------------%
% Opening Commands
%-------------------------------------------------------------------------%
clear ;
cd('C:\Rick\UT Economics\Paper Ideas\Dissertation\OG two country\MatLab') ;

%-------------------------------------------------------------------------%
% Functional Forms
%-------------------------------------------------------------------------%
% u(C') = (C'^(1-sigma)-1)/(1-sigma) for sigma>=0
%       = log(C')                  for sigma = 1
% g(n) = chi*(n)^xi
% C' = ((C'^h)^theta)*((C'^f)^(1-theta))
% n  = steady state labor supply
% Ch = steady state domestic consumption of domestic goods
% Cf = steady state domestic consumption of foreign goods
% V(x,x*) = max_x u(C'(x,x*)) - g(n(x,x*))
%-------------------------------------------------------------------------%

%-------------------------------------------------------------------------%
% Parameter values and exogenous values
%-------------------------------------------------------------------------%
% sigma = coefficient of constant relative risk aversion
% chi   = cost function scale parameter
% xi    = cost function shape parameter
% theta = home bias parameter
% epsilon = elasticity of substitution among differentiated goods
%-------------------------------------------------------------------------%
sigma = 3 ;
chi   = 0.5 ;
xi    = 2 ;
theta = 0.65 ;
epsilon = 10 ;

if sigma <= 0
    disp('parameter restriction error: sigma <= 0')
    break
elseif chi <= 0
    disp('parameter restriction error: chi <= 0')
    break
elseif xi < 1
    disp('parameter restriction error: xi < 1')
    break
elseif theta < 0.5
    disp('parameter restriction error: theta < 0.5')
    break
elseif theta > 1
    disp('parameter restriction error: theta > 1')
    break
elseif epsilon <= 1
    disp('parameter restriction error: epsilon <= 1')
    break
end

%-------------------------------------------------------------------------%
% State Space
%-------------------------------------------------------------------------%
% xmax  = maximum value that state space of x can be to keep steady
%         state percent of currency portfolio that is domestic currency
%         greater than zero. x must also be greater than 0.
% x     = domestic money growth rate (monetary policy)
% xstar = foreign money growth rate (monetary policy)
% xsize = number of states in the x vectors
%-------------------------------------------------------------------------%
xmax  = 1/(1-theta) - 0.01 ;
x     = [0.5:0.05:xmax]' ;
xstar = [0.5:0.05:xmax]' ;
xsize = length(x) ;

%-------------------------------------------------------------------------%
% Steady state values
%-------------------------------------------------------------------------%
% n_x_xstar       = the steady state value of domestic
%                   employment/production given domestic and foreign
%                   monetary policy (1st dimensionor columns = values of x,
%                   2nd dimension or rows = values of xstar)
% nstar_x_xstar   = the steady state value of foreign
%                   employment/production given domestic and foreign
%                   monetary policy (1st dimension or columns = values of x,
%                   2nd dimension or rows = values of xstar)
% c_h_x_xstar     = the steady state value of domestic consumption of the
%                   domestically produced good given domestic and foreign
%                   monetary policy (1st dimension or columns = values of x,
%                   2nd dimension or rows = values of xstar)
% c_f_x_xstar     = the steady state value of domestic consumption of the
%                   foreign produced good given domestic and foreign
%                   monetary policy (1st dimension or columns = values of x,
%                   2nd dimension or rows = values of xstar)
% cstar_f_x_xstar = the steady state value of foreign consumption of the
%                   foreign produced good given domestic and foreign
%                   monetary policy (1st dimension or columns = values of x,
%                   2nd dimension or rows = values of xstar)
% cstar_h_x_xstar = the steady state value of foreign consumption of the
%                   domestically produced good given domestic and foreign
%                   monetary policy (1st dimension or columns = values of x,
%                   2nd dimension or rows = values of xstar)
%-------------------------------------------------------------------------%
Delta = theta - sigma*theta - xi ;
Sigma = (1 - theta)*(1-sigma) ;
Omega = (epsilon/(epsilon-1))*((chi*xi)/((theta^(theta*(1-sigma)))*((1-theta)^((1-theta)*(1-sigma))))) ;

if sigma == 1 
    disp('I do not have the log version of ss n done yet')
    break ;
else
    n_x_xstar = (Omega^((Delta-Sigma)/(Delta^2-Sigma^2)))...
        .*((repmat(x',xsize,1)).^((Delta)/(Delta^2-Sigma^2)))...
        .*((repmat(xstar,1,xsize)).^((-Sigma)/(Delta^2-Sigma^2))) ;
    nstar_x_xstar = (Omega^((Delta-Sigma)/(Delta^2-Sigma^2)))...
        .*((repmat(xstar,1,xsize)).^((Delta)/(Delta^2-Sigma^2)))...
        .*((repmat(x',xsize,1)).^((-Sigma)/(Delta^2-Sigma^2))) ;
end

c_h_x_xstar     = theta*n_x_xstar ;
c_f_x_xstar     = (1-theta)*nstar_x_xstar ;
C_x_xstar = ((c_h_x_xstar).^theta).*((c_f_x_xstar).^(1-theta)) ;
cstar_f_x_xstar = theta*nstar_x_xstar ;
cstar_h_x_xstar = (1-theta)*n_x_xstar ;
Cstar_x_xstar = ((cstar_f_x_xstar).^theta).*((cstar_h_x_xstar).^(1-theta)) ;

if sigma == 1
    disp('I do not have the log version of ss V done yet')
    break ;
else
    V_x_xstar = (((((c_h_x_xstar).^theta).*((c_f_x_xstar).^(1-theta))).^(1-sigma) - 1)./(1-sigma))...
        - chi*(n_x_xstar).^xi ;
    Vstar_x_xstar = (((((cstar_f_x_xstar).^theta).*((cstar_h_x_xstar).^(1-theta))).^(1-sigma) - 1)./(1-sigma))...
        - chi*(nstar_x_xstar).^xi ;
end

[Vmax_xstar,xmax_xstar] = max(V_x_xstar,[],2) ;
[Vstarmax_x,xstarmax_x] = max(Vstar_x_xstar,[],1) ;

%-------------------------------------------------------------------------%
% 3-D graphics of steady state values
%-------------------------------------------------------------------------%

% figure(1)
% surf(x,xstar,n_x_xstar)
% xlabel('domestic MP')
% ylabel('foreign MP')
% zlabel('employment/production')
% title('Domestic SS Employment as Function of Domestic and Foreign MP','FontSize',12)
% 
% figure(2)
% surf(x,xstar,nstar_x_xstar)
% xlabel('domestic MP')
% ylabel('foreign MP')
% zlabel('employment/production')
% title('Foreign SS Employment as Function of Domestic and Foreign MP','FontSize',12)
% 
% figure(3)
% surf(x,xstar,c_h_x_xstar)
% xlabel('domestic MP')
% ylabel('foreign MP')
% zlabel('c_h')
% title('Domestic SS C_h as Function of Domestic and Foreign MP','FontSize',12)
% 
% figure(4)
% surf(x,xstar,c_f_x_xstar)
% xlabel('domestic MP')
% ylabel('foreign MP')
% zlabel('c_f')
% title('Domestic SS C_f as Function of Domestic and Foreign MP','FontSize',12)
% 
% figure(5)
% surf(x,xstar,cstar_h_x_xstar)
% xlabel('domestic MP')
% ylabel('foreign MP')
% zlabel('c_h')
% title('Foreign SS C_h as Function of Domestic and Foreign MP','FontSize',12)
% 
% figure(6)
% surf(x,xstar,cstar_f_x_xstar)
% xlabel('domestic MP')
% ylabel('foreign MP')
% zlabel('c_f')
% title('Foreign SS C_f as Function of Domestic and Foreign MP','FontSize',12)

figure(7)
surf(x,xstar,V_x_xstar)
xlabel('x, domestic MP')
ylabel('x*, foreign MP')
zlabel('V(x,x*)')
title('Domestic Lifetime U as Function of Domestic and Foreign MP','FontSize',12)

hold on
%Make line for best response function
xmaxval_xstar = ones(length(xstar),1)*x(xmax_xstar(1)) ;
%figure(10)
plot3(xmaxval_xstar,xstar,V_x_xstar(:,xmax_xstar(1))+ones(xsize,1)*0.01,'k','LineWidth',5)
xlabel('x, domestic MP')
ylabel('x*, foreign MP')
zlabel('V(x,x*)')
grid on
%title('Domestic BR function x as function of x^*','FontSize',12)
hold off

% figure(8)
% surf(x,xstar,Vstar_x_xstar)
% xlabel('domestic MP')
% ylabel('foreign MP')
% zlabel('V(x*,x)')
% title('Foreign Lifetime U as Function of Domestic and Foreign MP','FontSize',12)
% 
% figure(9)
% subplot(2,1,1)
% plot(xmax_xstar)
% subplot(2,1,2)
% plot(xstarmax_x)