How does your model deal with services?
This is a good question, and I recognize that "services" are included in "economic production." I do not know the details of how they are evaluated as a contribution to an economy.
If you pay someone to cut your hair, then the "product" is an (allegedly) prettier head, which would be valuable to the person receiving the haircut.
As noted in the previous discussion, the GDP (as a measurement of economic growth) in fact evaluates exchanges, but in a way that is designed for them to represent production. Therefore, only exchanges involving the purchases of "final products" (and, I think, only
new products), are counted, and not the mere transfer of things, or their components, from one person to another.
WRT banks, the initial deposit would represent an exchange value having been received by the depositor, for something that he had produced. The lending would not represent any final product, and it would therefore presumably not be counted as economic growth (although the salary of the banker, would represent his service and would likely be counted as being a thing of value). The interest/profit would represent the source of funding for new production.
So, the money would not simply multiply without production of anything of value, as you describe. Instead, the original, deposited money represents previous production, and the interest/profit represents new production. In real terms (excluding a consideration of monetary inflation, which devalues money by increasing its supply beyond that which would account for new products), money "grows" through interest,
because it represents a potential for new production, and the eventual repayment of the loan's interest, would ultimately represent the exchange value of new products (or perhaps valuable services, which can be regarded as new, desirable conditions' being produced from the raw materials of undesirable conditions - such as excessively long hair, as in your haircut example).
In a way, the charging of interest for a loan, represents a request for advance payment for new products. As the loan is eventually repayed, with interest, the money for the payment of that interest, will have come from, and represents, the value of the new products/services created and sold by the borrower.
And of course, a failure to repay a loan, demonstrates a miscalculation/misrepresentation of value - on account of which, the participants in the loan procedure, suffer disappointment of their expectations - an "economic failure," although perhaps without any change in the real value of things.
As a kind of side note, it has been stated by economists, that every economic transaction represents a sort of "profit" for both sides of the transaction. The seller profits because the buyer's money is more valuable to him, than his own product (this is why he is willing to give away his product, in order to get the buyer's money), and the buyer profits because the seller's product is more valuable to him than his own money (this is why he is willing to give away his money, in order to get the seller's product). Objectively, the transaction represents an exchange of equivalent value, but subjectively, the trade represents an improved condition for both participants.