Satoshi says: $10,000,000 per Bitcoin!
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Taking research such as
https://mpra.ub.uni-muenchen.de/34778/1/MPRA_paper_34778.pdf (and earlier sources that are no longer available)....
The averaged makeup in 2010 of US currency was (as the nominal Average citizen):
# Face value of note
31 x USD $ 1
7 x USD $ 5
5 x USD $ 10
21 x USD $ 20
4 x USD $ 50
23 x USD $ 100
This provides 91 Notes (as a mean value) with a value of USD $ 3,036 for the (average) person in the US (including the USD amounts held abroad).
Note, this is the value of money. It does not include the value of goods and services. Most of these are transacted only periodically and not all require cash.
Most critically, this is the total value of the cash holdings in USD that is actually held. Since 2010, the amounts used in credit have increased as well as bank holdings, but the reality of this is that there is not an increased cash requirement.
The value of USD in cash format is (at 2010) limited to a global supply of 1.062 Trillion USD.
This extends to the (static) value of USD notes and the M1 supply as (is inflated) by banks. With this, the total comes to USD 20.827 Trillion.
At This level, the expected value in USD for each Satoshi would come to 0.049588 USD.
When the global money market is factored into this, we have a final expected value of 0.1070109 USD per satoshi.
This is why we are seeking to scale Bitcoin. This is the value it was designed for and why there are 21 million BTC.
This, when coupled with a faster settlement and transaction rate, increases the velocity of money even as it caps the amount.
At 10 minute intervals, the maximum velocity of money with Bitcoin is 2.1E15 x 52,560 Blocks/annum = 1.1E20
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And I thought I was crazy with my $1 million prediction.