When it gets used on line a little, then bitcoin coffee shops and restaurants popup, what happens? Bitcoin can price, and price in a global unit of exchange that trades into central bank currencies everywhere. So, breaking down its price, scarcity is really ledger fees, and the rest represents purchase power equivalence of the various government currencies, it is an FX exchange definition, not even a trade. The dollar price of yuan in Beijing is exactly the bitcoin cost equivalent of a hamburger in the typical USA or China. Because, the folks in Beijing convert bitcoin into hamburgers as do the folks in Wichita.
Here I assume transaction costs zero, but positive, congestion priced ledger fees. Noe he difference. Transaction costs zero means I can convert all the flow into a complex of two color trade offs. I do not have to worry a third parties in every trade, so my bitcoin model across central bank boundaries is very simple. After transaction costs, the utility of bitcoin is nill, except for transaction accounting, so in a bitcoin one color world, the real banking costs is always the competitively bid local ledger fees. So, simple. If I factor out ledger fees I get the direct scarcity of hamburgers in Wichita and Beijing. Very simple stuff.
Deviations from the formula occur when exchanges are in short supply locally, or when the technology is immature. We want a full spectrum of customers buying hamburgers in both places, to get the closed system. By closed we mean the hamburger supply chain is observable at the cash level; we are computing arrival likelihood everywhere..
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