%HETEROGENEOUS.M
%Overborrowing in a model with heterogeneous agents

%Parameter Values
y=1; %first period endowment
ya=2; %Agent a future endowemnt
yb=1.5; %Agent b future endowemnt
Rstar = 1.1; %world interest rate
kapa = 0.3;
cbar = 3;

%Present-discounted value of endowments
Ya = y + ya/Rstar;
Yb = y + yb/Rstar;


clc

%Unconstraint equilibriu
disp('Unconstraint equilibriu')
disp('Consumption agent a')
ca1u = Rstar / (1+Rstar) *Ya
ca2u = Rstar / (1+Rstar) *Ya
 
disp('Consumption agent b')
cb1u = Rstar / (1+Rstar) *Yb
cb2u = Rstar / (1+Rstar) *Yb

disp('Individual debt levels')
aau = ca1u-y
abu = cb1u-y

disp('Aggregate debt level')
au = (aau+abu)/2

disp('An Economy with an Individual Debt Constraint')
disp('Individual debt levels')
aai = min(kapa,aau)
abi = min(kapa,abu)

disp('Aggregate debt level')
ai = (aai+abi)/2

disp('Social Planner problem')
disp('Lagrange multiplier')
mu =Rstar/2*(Ya+Yb)-(1+Rstar)*(y+kapa)

disp('Individual consumption')
cas1=Rstar/(1+Rstar)*(Ya-mu/Rstar)
cbs1=Rstar/(1+Rstar)*(Yb-mu/Rstar)

disp('Individual debt levels')
aas = cas1 -y
abs = cbs1 -y

disp('Aggregate debt level')
as = (aas+abs)/2;

disp('Competitive Equilibrium with an Aggregate debt constraint')
dist=1;
Rmin=Rstar;
Rmax=1.2;
while dist>1e-7
%Interest rate
Ra = (Rmax+Rmin)/2;
%Consumption
caa1 = Ra/(1+Ra) * (Ya - (1/Rstar-1/Ra)*cbar);
cba1 = Ra/(1+Ra) * (Yb - (1/Rstar-1/Ra)*cbar);
ca1 = (caa1+cba1)/2;
%debt
aaa = caa1-y;
aba = cba1-y;
aa = ca1-y;
%Interest rate
Rmin = Ra*(aa>kapa)+Rmin*(aa<=kapa);
Rmax = Rmax*(aa>=kapa)+Ra*(aa<kapa);
dist=sign(aa-kapa)*(aa-kapa);


end

disp('Individual consumptions')
caa1
cba1

disp('Individual debts')
aaa
aba

disp('Aggregate debt level')
aa
disp('Interest Rate')
Ra