A world only with two contries (net exporter) We assume that we have two and only two contries: Albania and Bulgaria. There is complete free trade between the two countries.
The aggregate investments in Albania are given by:
$$I^A=A-ar$$
where $A, a &gt;0$ and r real interest rates.
The aggregate investments in Bulgaria are given by:
$$I^B=B-br$$
where $B, b &gt;0$ and r real interest rates.
They have total savings $S^A$ and $S^B$ who are independent of the interest rate.
Now I have to derive the condition that Albania is a net exporter.
My though so far is that I have to use that BNP(Y): $$Y=C+I+G+NX$$ and $$S_A=publicsavings+privatesavnings=(T-G)+(Y-T-C)=Y-C-G$$ and that $NX&gt;0$. But when I use these can only find an expression of the form $S_A&gt;f(A,a,r)$. But I think I have to find an expression of the form $S_A&gt;f(A,a,B,b,r)$. Can someone help me?
So we have
$$S^A = I^A + NX^A $$
$$S^B = I^B + NX^B $$
where $S^A$ and $S^B$ are exogenous constants. And since there are only two countries we have
$$NX^A = -NX^B $$
which leads to
$$S^A - I^A = -( S^B - I^B ) $$
Use that last equation to solve for r (after plugging in the I formulas). Then solve the first equation and require that $NX^A$ be positive.