%Parameters and Discretization of State-Space
alf=.5;
bet=.99;
P=[.45 .55;   %Markov Transition Matrix
   .35 .65];

k=[.05;.1;.15;.2;.25;.3]; %Capital Choce Set (with 6 discrete states)
a=[1;1.5]; %Productivity States

%Utility Matrices

R1=[];R2=[];

for i=1:6
    for j=1:6 
        
        if a(1)*(k(i)^alf)-k(j)>0
            R1(i,j)=log((a(1)*(k(i)^alf))-k(j)); %Logarithmic Utility
        else
            R1(i,j)=-inf; %Weeding out the choices implying non-positive consumption
        end
        
             
        if a(2)*(k(i)^alf)-k(j)>0          
            R2(i,j)=log((a(2)*(k(i)^alf))-k(j));
        else
            R2(i,j)=-inf;
        end
    end
end

%Value Function Iteration

v1=ones(6,1);v2=ones(6,1); %Initial guesses for the value vector
vn=1;vnt=0;

while norm(vn-vnt)>10^(-8)
    vnt=[v1' v2'];
    [tv1,ind1]=max((R1+(bet*P(1,1)*ones(6,1)*v1')+(bet*P(1,2)*ones(6,1)*v2'))');
    [tv2,ind2]=max((R2+(bet*P(2,1)*ones(6,1)*v1')+(bet*P(2,2)*ones(6,1)*v2'))');
    v1=tv1';v2=tv2';
    vn=[v1' v2'];
end