I am facing some problems in deriving the two equations for trade balance (from which we derive that the trade balance is zero within each country) in the article "A SIMPLE FRAMEWORK FOR INTERNATIONAL MONETARY POLICY ANALYSIS" (2002) that you can find here. My objective is to derive equations 28 and 29 of that paper. In order to do that, I used the following equations:
Firstly, I tried to substitute the value of given by equation 7a in equation 25, but what I got was not right:
Then I tried to get the value of from equation 25 and substitute in equation 7, but this was not right either:
I also tried to substitute for gamma, but the results were not correct. I cannot think of anything else. How would you do that?
The equations that I am looking for: