%SIMU.M
function [pai,R, tau, m,mf, v, vf, y, yf, c, h, d, g, S, sd, la, THETA, BETTA, A, B, fval] =  simu(debt_target,yf,A,B);
%[pai,R, tau, m,mf, v, vf, y, yf, c, h, d, g, S, sd, la, THETA, BETTA, A, B, fval] =  simu(debt_target,yf,A,B); computes the steady state of the Ramsey equilibrium in the  model of  Schmitt-Grohe, Stephanie and Martin Uribe, 
%``Foreign Demand for Domestic Currency and The Optimal Rate of Inflation'' %Journal of Money, Credit and Banking, forthcoming. 
%
%(c) Stephanie Schmitt-Grohe and Martin Uribe
% Date: January 5,  2011


if nargin<1
debt_target = 0.20;
end
if nargin<2
yf = 0.06;
end


if nargin < 3
A = 0.0111/2;
end


if nargin<4
B = 0.07524;
end


BETTA = 1/1.04; %subjective discount factor


g = 0.04; %government spending

THETA = 2.90;  %preference parameter U=log c + THETA log(1-h)


OPTIONS = OPTIMSET('tolx',1e-15,'tolfun',1e-15);


la_min = 0.01;
la_max = 1;

dist = 1

while dist>0.0001

la = (la_min+la_max) / 2;


[vh,fval] = fsolve('findvh',[0 1/3],OPTIONS,la,yf,A,B,THETA,BETTA,g);

Vs = sqrt(B/A); %satiation velocity

Vmax = sqrt((1+B)/A);

v = Vs + (Vmax-Vs) * abs(vh(1)) / (1+abs(vh(1))); 

h = abs(vh(2)) / (1+abs(vh(2)));


vf = v;
S=A*v+B/v-2*sqrt(A*B);
Sv = A-B/v^2;
GAMA = 1 + S + v*Sv;

%Solving the feasibility constraint in the steady-state yields
c = (h - g + yf / vf * (1-(1-v^2*Sv) / BETTA)) / (1+S);

R = 1/ (1- v^2*Sv);

pai = BETTA * R;

m = c / v;

mf = yf / vf;

Uc = 1/c;
Uh = -THETA / (1-h);
tau = 1+Uh/Uc*GAMA;

%Real government debt
d = ((1+S)*c + m * (1-1/pai) - (1-tau)*h ) / (R/pai-1);


%Output
y = h;

%Debt to GD ratio
sd = d/y;

if sd>debt_target
la_max = la;
else 
la_min = la
end

dist = abs(sd-debt_target);

[R tau sd]

fval

pause(1)

end