A lot of investors think that the main purpose is payments, so they invest in diverse bitcoin related services companies. I think payments in itself does not drive the price, only the urge to hold bitcoins. Fortunately, that is a future side effect of creating many new payment customers, so I am happy with that.
... and we're back to the quantity of money formula !
The "side effect of holding bitcoins with the purpose of doing payments" is *exactly* what that formula expresses !
Of course the payments in itself do not drive price. The payments (Q) plus the "holding" (1/V) that goes with it, does.
But this was also my worry: if bitcoin payments are going to be:
1) acquire bitcoins on an exchange
2) do your payment immediately with it (after a few blocks)
3) the seller receives the payment
4) after a few blocks, converts them back into fiat
Then this corresponds to a very high velocity (a very low time to hold) and you can buy *a lot* of stuff with a few bitcoins at a relatively low price that way.
It's hard to tell from this post whether or not your explanation is correct.
In your scenario, "you can buy *a lot* of stuff with a few bitcoins at a relatively low price" is true if by "price" you mean the price of a bitcoin in terms of stuff. A higher velocity means a higher P in the quantity theory of money formula, where P is the price of stuff in terms of money.
Ok, I'm still reasoning in a fiat-dominated world, so the "price of bitcoin" is the exchange price in dollars. The $380 something of today.
On re-reading, I understand my phrase could lead to confusion. "a few" means: the relatively small amount of existing bitcoins (the 13 million or so today).
The point is that the price of a bitcoin (which is the inverse of P in the formula, if we express Q in dollar) can still be very low ($300 or so like today) and still buy a lot of stuff, if the velocity is high enough, which could be the case if the typical scenario is the one I described, and where bitcoins served to buy something and were only held for a third of a day for doing so.
If a bitcoin can be used 3 times a day to buy its value in goods, then the velocity is 1000 (per year), and the total value of stuff bought with bitcoin is then about 1000 times the market cap. (Q expressed in dollars is then 1000 times the market cap M / P).
So the commercial adoption of bitcoin would not sustain a high bitcoin price (in $$) if the typical way of doing that would be the indicated way, and if all bitcoins were used that way, even if a large amount of stuff were bought each year with bitcoin.
It would be totally different if people were actually paid in bitcoin, and held their pay for half of a month in order to buy stuff. Then the velocity would rather be something like 24 (holding time half a month on average). The price of bitcoin (in $$) would then be 40 times higher than in the previous gedanken experiment for the same amount of stuff bought.