Cannot get rid of Price levels in two goods sector and having rank condition problem

Hello everyone! I am new to Dynare. I have been reading lots of posts to solve my problem but I could not find an answer.

I have created a NK model with two goods, non-homothetic preferences, and two agents with different productivity levels in production.

My problem is that when I solve for budget constraints, the price levels remain in the model.

Here Z_L and Z_H are the composite goods of household L and H. When I write the model in the dynare and run it I get the following error:

There are 8 eigenvalue(s) larger than 1 in modulus
for 9 forward-looking variable(s)

The rank condition ISN’T verified!

I checked timing of the equations and since it is similar to the textbook example I do not believe it is related to the timing.
These two sectors are almost completely identical except the first good’s demand is nonhomothetic.
As far as I understand, in stochastic models, I cannot use nonstationary variables. So, I tried to define a new variable called k = P_1/P. But I guess this is not stationary as well since P_2 and P can behave differently due to shocks. If you know how can I solve the rank condition problem it would be great!
noC1.mod (3.5 KB)

Thank you!

Looking at the mod-file, it may just be a timing issue. The model currently features indeterminacy, not a fundamental singularity.