function [v,k]=DCS(a,rint,beta,x,p)
%Discrete Consumption - Savings
%a is a column vector of allowable asset values.
%rint is the gross real rate of interest.
%x is the level of income when employed.
%p is the state transition matrix.

%Solution is obtained by value function iteration.

%The first set of instructions creates a matrix of current period returns.
%R1 for unemployed.  R2 for employed.  R combines the two.
%First R computes consumption values.
%Rows correspond to current asset values.
%Columns correspond to next period asset values, the control variable.
%Then we take log(R) to put in utility terms.
%The use of max prevents the possibility of choosing negative consumption.
%Negative consumption will never be chosen because log(exp(-100))
%is appreximately minus infinity.


%Avoids cluttering output with warning messages about designed log of zero.
z=size(a);
n=z(1);
    for i=1:n
    for j=1:n
        R1(i,j)=max(rint*a(i)-a(j),exp(-100));
    end
    end
R1=log(R1);

    for i=1:n
    for j=1:n
        R2(i,j)=max(rint*a(i)+x-a(j),exp(-100));
    end
    end
R2=log(R2);
R=[R1;R2];

%Now we initialize the value function as all zero's.
v1=zeros(n,1);
v2=zeros(n,1);

%Set initial criterion to assure the process starts. 
iterations=0;
m=10;
v0=[v1;v2];
while m>.000000000001
    v0=[v1;v2];    
    A=R+beta*kron(p,ones(n,1))*[v1';v2'];
    %Calculates posible values of the Bellman equation terms.
    %Columns are indexed by the choice variable.
    %Rows are indexed by the current state variables.
    [v,k]=max(A');
    %Need to take transpose to properly utilize max command.
    v=v';
    m=norm(v-v0,2);
    %Checks for convergence.
    v1=v(1:n);
    v2=v(n+1:2*n);
    iterations=iterations+1;
    %Prepares to restart at top of while statement.
end
%Output variables are defined.
v=[v1';v2']';
z=zeros(n,2);
z(:,1)=k(1:n)';
z(:,2)=k(n+1:2*n)';

%z values tell us the index value of the optimal policy.
%We want to output the asset values of the optimal policy.

k=zeros(n,2);
for j=1:2
    for i=1:n
        k(i,j)=a(z(i,j));
    end
end

iterations
%y value indicates number of iterations completed.
%First column of v gives value function when unemployed.
%Second column of v gives value function when employed.
%First column of k gives optimal controls (a's) when unemployed.
%Second column of k gives optimal controls (a's) when employed.