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When any unit of trade has no activity, it's by definition worthless.

It could be argued that the opposite is also true; a unit of trade with activity (let's call it its "velocity") has value, because (also by definition) it must carry the value that it's being traded for. The precise relationship I have no idea, but I think it could follow. I feel like I read a paper about this idea back when Bitcoin was new, but it escapes me now.

EDIT: Found it, dates from 2013 which puts things into interesting perspective: https://bitcoinsurvey.wordpress.com/2013/04/08/what-is-the-r...




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