# 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 $$A, a >0$$ and r real interest rates.

The aggregate investments in Bulgaria are given by: $$I^B=B-br$$ where $$B, b >0$$ 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 $$NX>0$$. But when I use these can only find an expression of the form $$S_A>f(A,a,r)$$. But I think I have to find an expression of the form $$S_A>f(A,a,B,b,r)$$. Can someone help me?

• Question: Is total savings defined as S = Y - C - G ? Jan 12 at 5:41
• Yes spot on. While we have that $S_A=publicsavings+privatesavning=(T-G)+(Y-T-C)=Y-C-G$. But when I use this I also just get an expression of the form $𝑆_𝐴>𝑓(𝐴,𝑎,𝑟)$. Can you help me to find the right expression? Jan 12 at 9:37

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.
• Nice. Thank you that makes sense. So when I have found r I just plug the expression for r in, in: $$NX^A>0 \Leftrightarrow S^A-I^A>0 \Leftrightarrow S^A>I^A=A-ar$$. And then I have found the condition that Albania is a net exporter? Jan 12 at 17:19