# Solving N non-linear equations using fsolve. How do I pass these equations into my function without typing them out individually?

3 views (last 30 days)
Ethan Goode on 29 Jun 2020
Commented: Celestine Siameh on 21 Aug 2021
Hello all,
I am currently working with the Eaton-Kortum Trade Model in MATLAB. In this model we have N countries, and wish to solve 2N + N^2 non-linear equations for equilibrium outcomes. I am working currently on an example with four countries, which means I will need to use fsolve to solve 24 equations. I understand that I could type all 24 equations individually, but what happens when we allow N to grow in the model (to better reflect what the world looks like)? If I wanted to consider trade between 10 countries I would have to type 120 equations seperatley! Luckily these equations take one of three forms.
N of the equations take the form: (gam.*((sum(Ti.*(dni.*(w(i).^(beta)).*(p(i))).^(1-beta)).^(-theta)).^(-1./theta))) - p(n);
N^2 of the equations take the form: Ti.*(gam.*dni.*(w(i).^(beta))*(p(i).^(1-beta))*(1./p(i))).^(theta) - (x(i));
N of the equations take the form: ((beta).*(sum(Ti.*(gam.*dni.*(w(i).^(beta))*(p(i).^(1-beta))*(1./p(i))).^(theta)*x(i)))) - (w(i).*Li)
Where our unknowns are w's, p's, and x's and everything else is given.
Is there a way for me to iteratively feed these equations into fsolve?
For example:
F(1) = (gam.*((sum(Ti.*(dni.*(w(i).^(beta)).*(p(i))).^(1-beta)).^(-theta)).^(-1./theta))) - p(1);
F(2) = (gam.*((sum(Ti.*(dni.*(w(i).^(beta)).*(p(i))).^(1-beta)).^(-theta)).^(-1./theta))) - p(2);
F(3) = (gam.*((sum(Ti.*(dni.*(w(i).^(beta)).*(p(i))).^(1-beta)).^(-theta)).^(-1./theta))) - p(3);
F(4) = (gam.*((sum(Ti.*(dni.*(w(i).^(beta)).*(p(i))).^(1-beta)).^(-theta)).^(-1./theta))) - p(4);
If there is not a way to do what I suggest how should I attempt to implement this?
Celestine Siameh on 21 Aug 2021
Thanks Walter. Let me check with him then. Hello Ethan Goode, did the code worked for you.

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