For some reason I just noticed your post now. It sounds like via various lending arrangements and contracts, M1 gets converted onto M2, and M1 and M2 get converted into M3. In the bitcoin economy I understand that if I set up a Bitcoin credit card company and you take out one of my credit cards and I give you a 20 BTC line of credit, that 20 BTC has moved into M3. Bit it's also 20 BTC that I can't spend simultaneously, so it is removed from M1, no? M3 still contains only 21 million bitcoins right?
Exactly, that's what you'd think. The main issue with this theory though is that its wrong.
You see, say Citibank comes over to you and says "hey, here's a Bitcoin. Ok I lied, its not a dollar, but its going to be a Bitcoin tomorrow. But y'know, here's my signature and all, and I'll give you a few extra satoshis tomorrow and all... please let me buy a coffee." And then you say OK because you were probably just going to deposit your Bitcoins into Citibank anyway, to get your few free satoshis, and its not as if Citibank has ever lost any of your money before, so why not just accept his note. After all, there's this guy you know that Citibank lent money to about a week ago, and if he doesn't pay me back Citibank will get his house, and they'll just sell that to pay you back instead. So you accept Citibank's note, because he'll give you a few extra satoshis.
Presto, now M3 contains more than 21 million bitcoins.
Well you might say that isn't really how its going to work out, and that nobody will actually accept those notes, however it already happens, its just you don't notice it as much. Like, take Mt. Gox. People are always depositing bitcoins, you're depositing your real Bitcoins and they're just upping a number in a table. Now there's two bitcoins: Gox has access to the first, and the second Bitcoin, the one you see in your Mt. Gox account, you can use to buy stuff: USD. As we all know, what happens when you use a Bitcoin to buy USD? It contributes some selling pressure to push the price down. In other words, that's inflation. Because there are now TWO bitcoins.
Secondly, it doesn't need to work exactly like the above, although from a bank's perspective, that's ideal. Traditionally (and if things were fair, the way things would work) would be that the bank gets this contract, saying that a person owes them such and such amount of money, suddenly they get a huge urge to spend some of that money they just lent away. So they go to some market somewhere and sell it, and get some money, and spend the proceeds of that sale. And each successive link in that chain, the moment he wants to spend some money, goes back to the market, and somebody else will buy it from him, because they know, they'll get some of that money that was originally owed to Citibank, and they'll give him real Bitcoins, to spend right away, in return for that debt. The debt functions exactly like a Bitcoin in your wallet: It can be spent (although you have to go to the market to do so) and it serves as a store of value.
The only real difference is that that money actually can't move through the blockchain. But I highly doubt that theres going to be 21 Million Bitcoins waiting for confirmation at the same time, so what does it matter?
Regardless of the above, I think my formula about is still correct for valuing bitcoins based only on their use in transactions (this it gives a correct lower bound on their real world price). It does not try to estimate the value of M3 in bitcoin. It's just saying: "if this much value is transacted using bitcoins, then each bitcoin must be worth at least X." For reference, this is the statement I'm saying must always be true:
(price of 1 BTC) >= [(World GDP in dollars)*(fraction of economic transactions using bitcoin)]/[(supply of bitcoins)*(fraction of bitcoins used in transactions)*(bitcoin velocity)]
Not true. What you're saying is if Bitcoin was at its point of maximum deflation (when there is no debt), then you'd be right. Otherwise, M3 is bigger than M0 and you're quickly getting screwed.
