Imagine you had a closed economy with two people and they both started off with $100 dollars. How would net savings in aggregate ever not be zero? Anything spent, net, by person 1 would be a positive savings for person 2, and a negative savings for person 1. The same is true vice versa.
I understand that if person 1 and person 2 both produced 10 bushels of wheat and then ate only 5 of them, and then ground up the other five and used them as fertilizer (bad example, I know) that they would have 'saved' and 'invested' 10 bushels of wheat in aggregate. However, in monetary terms, the personal savings rate in aggregate would still be zero because they didn't sell the wheat to anyone and thus had no personal income (again, in dollar/monetary terms).
So, to sum up, my first question is, in monetary terms, in a closed economy will aggregate savings always be zero?
Second, how does the BEA get a positive savings rate, and how do we have positive gross national savings, in addition to running a trade deficit?