As an engineering with an accounting degree, it is rare that I get to point out that this is fairly well understood by the bean counters. I'm not saying that you are wrong, but I think that we can simplify it. Once you get a handle on what accountants do (although I think many people just assume they hide stuff!), the parable becomes a non-problem.

If you take first year accounting in school, you'll find out that balance sheets are simply a static representation of your asset, liabilities, and retained earnings. Retained earnings is basically the difference in what you owe vs what somebody owes you.

In very, very simple language, balance sheets add everything to show your wealth. I think this is a bit simpler than "store of value," but basically says the same thing. Or, as my accounting professor, and probably every accounting professor likes to say, "they are snapshots."

Now you can say "but money can be used as a medium of exchange," but I think this really adds complexity. In accounting 101, we simply say income statements show the path by how those quarterly balance sheet snapshots change. If you balance sheet change, it is because some activity happened. Now we don't normally say "medium of exchange" for income statements.

Instead, we simply write the steps of making money, which is as follows:

Revenue = What you sell
-COGS = What it cost you
-----
=GM =The results in after the sell
-SGA&RDA =What you paid your employees
------
=Net Income = What you made

You then add that profit to the balance sheet (less taxes and one time events). Your income statement bottom line perfectly shows up as a change in your retained earnings. So they are perfectly tied together.

The "classic" parable that you linked simply misses the point of accounting 101. In the parable, they talk about the "debt" that mysteriously goes away because a stranger comes into town and basically lends a $100.

This mystery is not new, and is well understood in accounting, and this is why we have "double entry" bookkeeping. This "paradox" was noticed by various cultures around 800-900 AD. However, the written rules was done by Luca Pacioli, a friar, in 1000 AD. To make it clear what actually happens, Pacioli pointed out that every transaction is both a lending and obligation to payback. Therefore, Pacioli said that all financial transactions have to be recorded twice. So, all of his ledgers recorded transactions on the left side of the T-ledger and on the right side of the T-ledger. Double entry bookkeeping was invented, and a thousand CPAs found lifetime security.

Thus all transactions generated a "owed something" and it was recorded on the left side of the ledger, which was something owed or latin debitum, or what we call "debits" today. Each debit entry must be also recorded on the right side with an offsetting entry of the same amount, or what you believed would be paid back or creditum (trust) at the same time. Both sides need to equal zero.

Thus if you were a bicycle store, and if you had a $800 bicycle (price you paid) on your balance sheet, and if you sold it for $1000, you would debit your cash by $1000 (add it), you would credit your bike inventory by $800 (remove it), and you would add the $200 profit to your retained earnings. (Well sort of. In your bicycle store, you probably had to pay employees, which would have been taken from the $200 profit, but I'm simplifying.)

In the "brain teaser" that you linked, they only do single side entry, which makes it look like everybody is in debt and was down $100. This is not true. Everybody in town both had "owed something" but also an offsetting "trust of being paid back." These two sides equaled zero. Before the $100 was circulated, everybody had a net worth of zero, and afterwards everybody had a net worth of zero.

With double entry, everybody in town would have recognized that everybody had an offsetting credit for the debit. Both before and after the exchange their net worth is zero, thus no change.

But this is an old thread, and I'll be typing this probably to myself and nobody will ever see it. However, I feel better for explaining it.