I was thinking of what would be a good long-run valuation model of Bitcoin. I thought maybe one could use the MV=PY identity to make an estimate.

For those who don't know, MV=PY says that the supply of Bitcoin (M) times the velocity of Bitcoin (V) must equal to the total value of all transactions done in Bitcoin (PY).

So imagine now a world in which all transactions are done in Bitcoin, perhaps through a L2 solution. The total value of all world trade (world GDP) is valued at around $85 trillion in today's US dollar values. So PY=$85 trillion. M, the total supply of Bitcoin, is 21 million. Assuming velocity is the same, around 1.2, we get:

(21 million BTC)*(1.2) = ($85 trillion)

Which means 1 BTC = $3.4 million. So in a hyperbitcoinized world where all trade was done in Bitcoin, one bitcoin would buy about $3.4 million worth of goods, valued in today's dollars.

Of course, velocity may not be the same, and not all world trade may be done in Bitcoin. But still, this model may be useful as a starting point. For example, if you think velocity will be lower, then the value of Bitcoin would actually be higher; if you think share of world trade will be less than 100%, then the value of Bitcoin will be lower.

Thoughts?