One Bitcoin contains 100 million Satoshis, the smallest division possible. As I type this, one sat is worth .000264 USD (BTC @26K). Bitcoin's market cap is currently 502,312,545,442 USD (502 billion.)
An estimate of global wealth in 2023 is 272 Trillion USD. If Bitcoin captured 1% of all global wealth then as an asset class, it's a 2.72 trillion market cap ... rough math, that's 139,673 per BTC. A sat at this price is 100 millionth of this, .00139673 US cents.
Let's say then BTC becomes 10% of all (current) global wealth, a market cap of 27.2 trillion. That's a simple 10X to 1.39 million per Bitcoin; this gives us the one cent = one sat equivalence.
Bitcoin would then need to perform a 100X to be a buck a sat, which would exceed current global wealth many times over as we can see.
So it's unlikely but the cent/sat equivalnce is 100% doable.
(The global wealth estimate I've used is different to the M1/M2 money supply amounts which can get us closer to the unicorn of Satbucks but simplistically put it more presupposes all global cash and assets "becomes BTC" if that makes sense.)
Sources:
https://www.statista.com/statistics/915334/global-wealth-value/
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