The problem is the pie, despite capped, is still incredibly large.
100 million satoshis in 1 BTC means 21 million BTC = Two quadrillion, one hundred trillion satoshis.
If every satoshi was worth 1 penny the total BTC supply would be worth $21 trillion dollars.
Comparing to US dollars, current estimate is $2.38 trillion worldwide circulation.
I fail to see how $21 trillion dollar cap is better than $2.38 ? Actually the US dollar wins here in this example; it appears there are less dollars than Bitcoin thus dollars are actually more scarce.
What do you mean? The size of every pie is 1, which, being the multiplicative identity (https://en.wikipedia.org/wiki/Identity_element), is neither large nor small. Your share is a number in [0, 1].
Here are the market caps of fiat currencies: https://fiatmarketcap.com/ . The USD market cap is much higher than what you stated, but it has no relevance whatsoever.
How can dollars be more scarce? A scarce money is a money that's hard to create more of. The nominal values of the circulating supply have no effect on scarcity. The only thing they indicate is the market share, which tells us where we are on the adoption curve and how much upside it still has - which is not the topic being discussed here, but if we are to go into that, Bitcoin is not only a currency, it's also a store of value; it can grab the market share of not only the USD, but also other fiat currencies and assets, including gold, stocks, real estate, etc.
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Duly noted, good points.
However, the main dillemma I'm trying to highlight is the lowest denomination ie- unit is a satoshi and therefore the pie is measured in that unit. Since even this lowest unit can still represent any arbitrary amount of value you have basically an unlimited supply of units.
The premise of this argument is thus Bitcoin's fixed/finite supply is irrelevant when there are multiple trillions available of the base unit. Like saying we have a cap but that cap is equivalent to the number of grains of sand in the world.
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