Regarding the setting of relative prices and the inflation rate in steady-state solution

I encountered a problem while solving for the steady state of the model in Eggertsson (2014). In this two-country asymmetric model, since the relative price variables cannot be set to 1, I am unable to obtain the steady-state values of the variables. Could anyone please advise on how to solve for the steady-state values of this model? I would greatly appreciate it! con_041383.pdf