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.