global alpha

% DEFINE THE GRID FOR K

kmin = 1; % The minimum value for k
kmax = 20; % The maximum value for k
nk = 25; % The total number of grid points
kstep = (kmax - kmin)/(nk-1); %Define the step length of the grid
K = kmin:kstep:kmax; % Define the grid for K

% SET PARAMETERS
alpha = .33; % A production function parameter
beta = .95; % The Discount factor
tol = 1e-5; % The convergence tolerance
maxit = 1000; % The maximum number of iterations



% SOLUTION USING FASTEST VFI SOLUTION METHOD

% Initialize miss difference and iteration counter
dd = 1;
it = 1;

% Provide initial guess for value function
V = zeros(nk,1);


% Define the matrix R
KS = repmat(K',[1 nk]);
KC = repmat(K',[1 nk])';
R = KS.^alpha + KS - KC;

while (dd > tol)
OBJ = R + beta*ones(nk,1)*V';% Define the objective function
[Vnew,gi] = max(OBJ,[],2); % maximize the objective function
dd = max(abs(Vnew-V)); % Calculate the miss distance
V = Vnew;
if (it >= maxit);
    break;
end

if (max(gi) == nk)
    disp('Warning: Potential Corner Solution.  Increase kmax');
end;

if (min(gi) == 1 && it>1)
    disp('Warning: Potential Corner Solution.  Decrease kmin');
end;
it = it+1;

end;