Algorithmic stablecoins are provably impossible without continuous funding

Alice trusts Bob, who trusts Charlie. Alice has no idea who Charlie is.

Now Charlie gets $10 dollars as credit (not the same as cash) from Alice (mediated through Bob) and wants to buy $10 items from David and Eve. He shows the letter saying that Alice is good for the cash. Without a distributed consensus method, how can David or Eve confirm that they will be able to go to Alice to collect the cash? How can they even know that Alice has the cash in the first place? What if something happens to Bob?

The only way to do this without a blockchain would require something like Paxos, but Paxos only works if the participants are selected a priori. Every new participant would have to be vetted by everyone else, or everyone else would have to follow some central authority that can grant access to the system. If you are going this route, you are just re-inventing a credit cooperative.

I don't think you understood. The scenario I presented Charlie is malicious by making a double-spending attack against David and Eve, separately.

You can remove Bob from the scenario and the problem still stands. Say that Charlie gets the IOU directly from Alice, David and Eve are left with duplicate IOUs. Alice has trusted Charlie with $10, not $20, so she can not re-pay both of the creditors. If you say "David and Eve should not have trusted Charlie then, so too bad if they lost each $10", consider the systemic issue if the double spending is made against with thousands of participants.

Without a way to control for double-spending, everyone can mint IOUs freely and any credit note is essentially worthless. And if remove the idea of IOU and try to make all transactions "cash-based", you just turned a fungible-currency into a non-fungible one (are these $10 coming from Alice-the-good-creditor or are they coming from Dick-the-double-spender?)

Charlie doesn't give Alice's IOU to David and Eve, he gives his own IOUs. He can default on those, but that's implied by David and Eve interacting with Charlie directly.

I doubt money supply has much to do with the issue at hand, since we're looking at the real world and money is just a tool for managing it.

I think you're correct in that everything is very expensive, possibly close to the most expensive it can be. Salaries paid are essentially just what is enough to keep yourself alive nowadays, often not even enough to keep yourself in decent mental health. I doubt your average worker is capable of purchasing everything they create in a month with their monthly salary.

It's certainly not the first time this has been observed either. Let me give you a classic criticism. Take the old but reliable labour theory of value. We ignore price fluctuations for this analysis because they are considered nothing but representative of true value – a method of making trade easier. Work is what people value, specifically the time used for labour. Creating something in one minute gives it one minute of value, it would be more valuable if it took more effort to create. For the purposes of markets, it's also obvious that what matters to us is not the individual value per se but the socially necessary labour time, the average value taken to create something. Therefore a man who creates a spoon in one minute and a man who creates one in 20 will make an equally valuable object in the societal context. Creating an object from materials will have the value of those materials plus the value you create through your work, so $2 bread from $1 wheat will have $1 of additional work done by the baker.

With this in mind, let's investigate farming. A farmer works land, they create $1 worth of wheat and sell it. That $1 is the full reimbursement for their work and if they want to buy their wheat back they will pay that $1 for it.

Adding in an agricultural conglomerate, lets say that a bunch of farmers work the land of this conglomerate as employees. As a large oversimplification, we once again say that a farmer creates $1 worth of wheat for the company. The company sells it and returns to pay the farmer a salary: ¢80. The ¢20 missing is the profit of the company and it has to be larger than zero for the company to keep existing at all, profit being their singular reason for existence.

This is fine and all, and it's how most companies work, the issue arises when you think about the farmer being a consumer. The farmer is not reimbursed in full for their work, in other words, they become incapable of purchasing back their own labour in full. If the farmer the goes home and to the store, they cannot purchase the wheat they themselves created, it will cost more than what they were paid. This repeats itself in every company, the employees simply cannot be fully reimbursed for their work, not now and not ever. Yet, the workers also form the base of consumers, they are the vast majority of people who must be relied upon to consume these products. The end result is that everything seems expensive relative to salaries and you will, at some point, have to have a violent economic event to correct the markets as consumers simply run out of money.

Now that's not accurate in its entirety and it's a critique from the 19th century, but it goes to show that we have always recognised this being an issue. We just deal with it by accepting that some people will be unjustly hurt in regular recessions in the boom and bust cycle and move on – there's no just way of doing things without entirely removing companies from the picture. That's the way our economy is doomed to work, and we just have to accept it and move on unless we want to literally outlaw companies and organise production on a national level.

This only works at a minuscule scale, where people could actually get to meet face-to-face. On a global network, Alice can still create an attack against Charlie. She just needs to get more intermediaries. Even if the intermediaries thought "surely Alice won't put the relationship at risk over a small amount", no one in their right mind would be doing large scale, automated transactions based on "friend-of-a-friend" connections.

Another thing, if you want to make transactions like the one you described, you don't need to pass IOUs around, you just pass money. Alice gives the IOU to Bob, Bob gives her money and then she can buy from Charlie, David, Eve or anyone else.