SOE with Tradables and Non Tradabless

Dear all,
I want to model a SOE with Tradables and Non-Tradable goods.
I have started from [this code]
(Dropbox - SOE2Gzip - Simplify your life), but I get 1 colinear relation.
I am not sure what could be the missing equation, so I was wondering if anybody could help me.
Thank you very much for your help and advice.
nk_open.mod (3.8 KB)
console_nkopen.m (1.6 KB)

It’s hard to tell without going through all of the derivations. But


are identical. So there is clearly an equation missing.

I have tried introducing the UIP, as the missing equation, but I still get a collinearity problem.
Do you have any tip on what might be the probem?
Thank you very much in advance.
nk_open_2.mod (3.9 KB)