How do I create an iterated or recursive formula that includes the product of a sequence?

I am new to matlab, so I apologize if my code is quite poor, but that's why I'm here!

I'm attempting to create the recursive formula below (it is formatted for LaTeX, which I don't think renders on this site, but I have attached an image of it as well):

$k_{T+1}=(1-\delta)k_T+k_{T}^\alpha-\beta^(T/\gamma)g^Tc_0\prod\limits_{t=1}^{T}R_t$\ where $R_t=\alpha k_t^{\alpha-1}+1-\delta$

The code I have attempted is below, but it is clearly incorrect as it does not like what I've tried (I have defined the variables being referred to with specific values, but I did not include those in this code sample):

t=1;

k(1)=kyratio^(1/(1-alpha));
R(1)=alpha*k(1)^(alpha-1)+1-delta

for t=2:105 j=1:105;
k(t+1)=(1-delta)*k(t)+k(t)^alpha-(beta^(1/gamma)*symprod(R(j+1),j,1,t))*czero*gstar^(-(t-1)) ;
R(j)=alpha*k(t)^(alpha-1)+1-delta ;
end

Thanks in advance for any resources you can point me towards, or any advice you give me!

[Walter Roberson]

Please explain what you intended by

for t=2:105 j=1:105;

[jlpva]

I want to iterate k_t about 100 times, so I wish to run this for those values of t (and j for R). Thanks!

Answer 1

[Dennie]

Hello,

there are a number of errors in this code, but all easy enough to fix. I can see that you tried to make 2 loops in 1, one for the k(T+1), and one for R(t). In matlab coding you can do it with just one loop since you use the same variable t. You fill the array of R with the calculation for each t and then you take the product of array R.

Also it looks to me that you define first R(t+1) before defining R(t).

Also beta^(1/gamma) should be beta^(t/gamma) judging from your formula. and gstar should be gstar^(t)

try like this:

k(1)=kyratio^(1/(1-alpha));
R(1)=alpha*k(1)^(alpha-1)+1-delta

for t=1:105
     R(t)=alpha*k(t)^(alpha-1)+1-delta ;
     R_prod=prod(R);
     k(t+1)=(1-delta)*k(t)+k(t)^alpha-beta^(t/gamma)*czero*gstar^(t)*R_prod) ;
end

Hope this helps,

Kind regards, Dennie

[jlpva]

Thanks for your help!