The Money Regression and Emergence of Money from the Barter Economy
The entire purpose of the regression theorem was to help explain an apparent paradox of money: how does money have value as a medium of exchange if it is valued because it serves as a medium of exchange?  Menger and Mises helped break this apparent circularity by explaining the essential time component missing from the phrasing of the paradox.

As Rothbard explains in Man, Economy, and State (p 270),
“…a money price at the end of day X is determined by the marginal utilities of money and the good as they existed at the beginning of day X. But the marginal utility of money is based, as we have seen above, on a previously existing array of money prices. Money is demanded and considered useful because of its already existing money prices. Therefore, the price of a good on day X is determined by the marginal utility of the good on day X and the marginal utility of money on day X, which last in turn depends on the prices of goods on day X – 1. The economic analysis of money prices is therefore not circular. If prices today depend on the marginal utility of money today, the latter is dependent on money prices yesterday.” [all emphasis added]

Rothbard then goes on to explain that in order for money to emerge from a barter economy, it must have a preexisting commodity value.  This commodity value arises from barter demand for the potential money in direct consumption (i.e. ornamentation).  This value seeds future estimations of the value of the money as a medium of exchange.  The natural market emergence of money is thus fully explained.

The Monetary Economy
However, once an economy has been monetized and a memory of price ratios for goods and services has been established, a money may lose its direct commodity value and still be used as a money (medium of indirect exchange).  Rothbard explains (p 275):
“On the other hand, it does not follow from this analysis that if an extant money were to lose its direct uses, it could no longer be used as money. Thus, if gold, after being established as money, were suddenly to lose its value in ornaments or industrial uses, it would not necessarily lose its character as a money. Once a medium of exchange has been established as a money, money prices continue to be set. If on day X gold loses its direct uses, there will still be previously existing money prices that had been established on day X – 1, and these prices form the basis for the marginal utility of gold on day X. Similarly, the money prices thereby determined on day X form the basis for the marginal utility of money on day X + 1. From X on, gold could be demanded for its exchange value alone, and not at all for its direct use. Therefore, while it is absolutely necessary that a moneyoriginate as a commodity with direct uses, it is not absolutely necessary that the direct uses continue after the money has been established.”

This explains the history of fiat currencies.  They originally started off as simple names for weights of commodity money (silver) that developed out of the pre-monetary barter economy.  Despite later losing their ties to direct commodity value through state interference, paper currency retained status as money because of memory of previous money prices.  This factor is so strong that the relationship between gold and the USD, for example, is somewhat inverted.  Gold no longer circulates as a common medium of exchange.   Prices are set in USD, not in gold.  Most individuals wishing to trade in gold do so based on their knowledge of USD/gold price ratios.  (“Hey, let me buy that $100 couch from you in gold?”  “Ok, USD/gold is $1000/oz. Give me 1/10oz of gold.”)  Legal tender laws, state taxation, and the entire financial regulatory environment maintain this inertia of USD prices and make it challenging to return to gold money directly, despite the destructive inflationary nature of fiat currencies.

The Emergence of the Bitcoin Economy
The very first businesses in the Bitcoin economy were exchangers (NewLibertyStandard, BitcoinMarket, BitcoinExchange,….).  This is not an accident, but flows from the analysis above.  In order for Bitcoins to serve as a medium of exchange without commodity value for uses besides indirect exchange, there must be a translated knowledge of money prices.  Market exchangers fill this gap and give Bitcoin users access to this knowledge.  Bitcoins may therefore currently serve as a money intermediary for paypal dollars\pecunix\euros.  But why is there demand for Bitcoin over USD??  This is a subjective valuation arising from properties such as anonymity, decentralized system of clearance, cryptographic trust, predetermined and defined rate of growth, built in deflation, divisibility, low transaction fees, etc…. inherent to the Bitcoin system.

The essential point is that once exchange can occur between a money (USD) and Bitcoins, providers of goods have a means by which to value Bitcoins as a potential medium of exchange.  The money regression is satisfied, because taken back far enough we reach traditional commodity money: BITCOINS -> USD -> MONETIZED GOLD & SILVER [start monetary economy] -> [end barter economy] COMMODITY GOLD & SILVER.

Of course, if a major meltdown occurred and knowledge of all price ratios was wiped out, Bitcoin probably would NOT directly emerge as a money (assuming Bitcoins have limited value outside of exchange).  Fiat currencies with zero direct barter value certainly would not.  Commodities such as gold and silver that have widely recognized direct value in barter would likely emerge first.  The economy would then be monetized with price ratios in gold and silver.  Bitcoins then, being valued for intrinsic properties amenable to exchange, might then become prevalent in trade.  Initially, creators of value would continue to make their price value ratios in terms of the true money (gold oz/BTC ratio), but with time Bitcoin prices (BTC) can emerge (see vekja.net as example).  We are in this initial phase now.

Therefore, so long as exchange of BTC and USD/Euros/etc… occurs, knowledge of existing price ratios can be utilized in the Bitcoin economy.  In time as Bitcoins become increasingly marketable, these fiat<->BTC price ratios will seed direct BTC price ratios.  The Bitcoin Economy thus emerges.  The Misean regression theorem is satisfied.

XC

edit: clarified possibility of direct emergence of bitcoin as money from barter economy.

As a thought experiment, imagine there was a base metal as scarce as gold but with the following properties:
– boring grey in colour
– not a good conductor of electricity
– not particularly strong, but not ductile or easily malleable either
– not useful for any practical or ornamental purpose

and one special, magical property:
– can be transported over a communications channel

If it somehow acquired any value at all for whatever reason, then anyone wanting to transfer wealth over a long distance could buy some, transmit it, and have the recipient sell it.

Maybe it could get an initial value circularly as you’ve suggested, by people foreseeing its potential usefulness for exchange.  (I would definitely want some)  Maybe collectors, any random reason could spark it.

I think the traditional qualifications for money were written with the assumption that there are so many competing objects in the world that are scarce, an object with the automatic bootstrap of intrinsic value will surely win out over those without intrinsic value.  But if there were nothing in the world with intrinsic value that could be used as money, only scarce but no intrinsic value, I think people would still take up something.

(I’m using the word scarce here to only mean limited potential supply)

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