//SOE, in order to pin down ss, add cost of holding bonds into budget
//deterministic, closed fixed endownment economy, fixed interest rate
//only decide consumption and bonds

close all;
var lambda, c, b, byratio;
varexo y bbar;

parameters sigma, beta, r, psi;
sigma=1;
beta=0.99;
r=1/beta;
//y = 1;
psi=0.01;
//bbar=0.2;

model;
c^(-sigma) - lambda = 0;
-lambda*(1+psi*(b-bbar)) + beta*lambda(+1)*r = 0;
c + b + 0.5*psi*(b-bbar)^2 = y + r*b(-1); 
byratio = b/y;
end;

//initial bonds
initval;
y = 0.9;
bbar = 0;
b = (beta*r - 1)/psi + bbar;
c = y + (r-1)*b -  0.5*psi*(b-bbar)^2;
lambda = c^(-sigma);
byratio = b/y;
end;
steady;

endval;
y=1;
bbar = 0.2;
b = (beta*r - 1)/psi + bbar;
c = y + (r-1)*b -  0.5*psi*(b-bbar)^2;
lambda = c^(-sigma);
byratio = b/y;
end;
steady;

simul(periods=100,maxit=30);
dsample 100;
rplot c;
rplot b;