% regional model for kwrt reg

N=2;    % the number of regions
alpha=[.6;.6];
alpha_= alpha.^(-alpha).*(1-alpha).^(alpha-1);
r=1;
beta=0.8;    % share of income going to consumption instead of housing
L=[3;3];
%w=[0.77185;0.72815];  % this about works for supply/demand
sumK=3;
K=[1;1];
lambda=1;
%A=[1;1];
pens=[3;1];
tau = [1 1.3;1.3 1];
for i=1:N
  pensshare(i,1)=pens(i)/sum(pens);
end
P=pensshare*ones(1,N);
H=[1;1];   % housing stock
Hp=[1;1];  % housing rent flow


% compute equilibrium values
[w,K]=fixk(sumK,w,r,L,alpha,N);

exp_nohouse= L.*w+ pensshare*sum(r*K);
expenditures=inv(eye(N)-(1-beta)*P)*exp_nohouse;
Hp=(1-beta)*expenditures./H;
supply = alpha_.*A.*(L.^alpha).*(K.^(1-alpha));

q=(w.^alpha).*(r.^(1-alpha))./A;

% share: how much of the expenditures in (column) go to (row)?.
for column=1:N 
  for row=1:N
    rawshare(row,column)=supply(row)*exp(-lambda*q(row)*tau(row,column));
  end
end

for column=1:N
  share(:,column)=rawshare(:,column)/sum(rawshare(:,column));
end

p=sum(share.*(tau.*(q*ones(1,2))))';

util_work=log(w)-beta*log(p)-(1-beta)*log(Hp);
util_pens=-beta*log(p)-(1-beta)*log(Hp);

demand=share*beta*expenditures./q;
supply-demand