Derivations of trade balance 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 &quot;A SIMPLE FRAMEWORK FOR INTERNATIONAL MONETARY POLICY ANALYSIS&quot; (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:
Equation 28: 
Equation 29:
Dividing equation 25 by $\gamma$ gives:
$$
Y_t = C_h + \frac{\gamma}{1-\gamma} C_h^\ast.
$$
Then using 7 and 7a to substitute for $C_h$ and $C_h^\ast$, we get:
$$
Y_t = (1-\gamma) \frac{P_t}{P_h} C_t + \frac{\gamma}{1-\gamma}(1-\gamma) \frac{P_t^\ast}{P_h^\ast} C_t^\ast.
$$
Then multiply both sides by $P_h$ and use $C_t^\ast = C_t$ to get:
$$
\begin{align*}
P_h Y_t &amp;= (1-\gamma)P_t C_t + \gamma \left(\frac{P_t^\ast}{P_t}\frac{P_h}{P_h^\ast}\right) P_t C_t,\\
&amp;= P_t C_t \left(1- \gamma + \gamma \left(\frac{P_t^\ast}{P_t}\frac{P_h}{P_h^\ast}\right)\right)
\end{align*}
$$
This is equal to equation 28 if:
$$
\frac{P_t^\ast}{P_t} \frac{P_h}{P_h^\ast} = 1.
$$
Now $\dfrac{P_t^\ast}{P_t} = \dfrac{1}{\varepsilon}$, which would require that:
$$
\frac{P_h}{P_h^\ast} = \varepsilon.
$$
Dividing 7 by 7a gives:
$$
\frac{P_h}{P_h^\ast} \frac{C_h}{C_h^\ast} = \frac{P_t}{P_t^\ast} = \varepsilon.
$$
So this means that $C_h$ has to equal $C_h^\ast$. I don't know if this makes sense (as I don't know the meaning of all these variables).
Similarly, you can show that 29 is satisfied if $C_f = C_f^\ast$.