defining functions in equivalent ways but get different results

Hello,

when i run the following code with different ways of defining the function, I got the different results (the graphs produced are so different).

But I see that both ways of defining the function are equivalent. I dont know why the results come out differently?

Really appreciate any comment or answer.

Thank you

Here is the code and 2 function definitions (at the end of the code)

% HW2
% Solve deterministic growth model by value function iteration + linear
% interpolation

% Housekeeping
clc;
clear all;
close all;
tic
% Parameters
global A alpha beta delta kmat k0 kgrid V0

A=1 ;
alpha=0.6;
beta=0.96;
delta=1;

% first solve the stead state value
kstar = (alpha*beta*A)^(1/(1-alpha)); % steady state k

% Grid points
kmin=0.25*kstar;
kmax=2*kstar;
kgrid = 30;
grid=(kmax-kmin)/(kgrid-1);
kmat = kmin:grid:kmax;
kmat=kmat';
[N,n]=size(kmat);

% Iteration parameters
tol=0.0001;
maxits=300;
its=0;
dif=tol+1;

V0 = zeros(N,1); %initial guess of value function

% Iteration
while dif > tol && its < maxits
    for i=1:N
        k0=kmat(i,1);
        k1=fminbnd(@intlinear,kmin,kmax);
        k11(i,1)=k1; %put k' in order in a vector, so it position is ith elment--> it is optimal for k =k(i)
        V1(i,1)=-intlinear(k1);
    end       
    % no longer (i) --> move out of for loop
    dif = norm(V1-V0);
    V0=V1;
    its=its+1;
end
 
Vapp=V0;

% Compute policy function
Papp = k11;


toc;

% True value/policy function
Vtrue = alpha/(1-alpha*beta)*log(kmat) + 1/(1-beta)*(log(1-alpha*beta)+ alpha*beta/(1-alpha*beta)*log(alpha*beta));
Ptrue = alpha*beta*A*(kmat).^alpha;

figure;
kaxis=kmin:grid:kmax;
plot(kaxis, Vtrue, '-', kaxis, Vapp, '--');
title('True vs Approximated Value Function - Linear Interpolation');
legend({'True VF','Approx. VF'},'Location','southeast');

% Plot distance between two functions
distance= Vtrue - Vapp;
distanceP= Ptrue-Papp;
plot(kaxis, distance, '--');
title('Difference between true and approximated VF');

plot(kaxis, distanceP, '--');
title('Difference between true and approximated PF');

% first way of defining function

function val=intlinear(k)
global A alpha beta delta kmat k0 kgrid V0
% v = ln(k0^alpha +(1-delta)*k0 - kmat) + v0, do not need to take this, we
% have it, as zero vector initially, and update everytime
g = interp1(kmat,V0,k,'linear');
c = A*k0^alpha  - k;
if c <= 0
val = -9999999 - 999*abs(c);
else
val = log(c) + beta*g;
end
val = -val; % make it negative since we're maximizing and code is to minimize.

% 2nd way of define function

function val=intlinear(k)
global A alpha beta delta kmat k0 kgrid V0
% v = ln(k0^alpha +(1-delta)*k0 - kmat) + v0, do not need to take this, we
% have it, as zero vector initially, and update everytime
g = interp1(kmat,V0,k,'linear');
c = A*k0^alpha  - k;
c=max(0,c)
val = log(c) + beta*g; % in matlab log(0)=-inf
val = -val; % make it negative since we're maximizing and code is to minimize.

[Stephen23]

They are not equivalent:

>> c = -1;
>> val = -9999999 - 999*abs(c) % 1st function
val = -10000998
>> log(max(0,c))               % 2nd function
ans = -Inf

[heidi pham]

Thanks,

but, both of them assign very small value of "val" for c<=0, and hence, it would not affect the result of the main code; since the only place that the function is used is :k1=fminbnd(@intlinear,kmin,kmax);wich find the argmin of -val(c), which cannot be c which is negative.

Am I wrong somewhere?

% Iteration

while dif > tol && its < maxits

for i=1:N

k0=kmat(i,1);

k1=fminbnd(@intlinear,kmin,kmax);

k11(i,1)=k1; %put k' in order in a vector, so it position is ith elment--> it is optimal for k =k(i)

V1(i,1)=-intlinear(k1);

end

% no longer (i) --> move out of for loop

dif = norm(V1-V0);

V0=V1;

its=its+1;

end

Vapp=V0;