Preprint · October 2020 doi: 10. 13140/RG

ab initio
that asset will never be widely adopted to serve as 
a medium of exchange.
9
V 
Network Effects Revisited 
If we observe that, despite large swings in value over the past five years, bitcoin retains a 
positive value, now over 60 percent of its all-time high reached in December 2017, does that 
mean that bitcoin truly does have a positive value, or does it mean that a bubble can persist 
indefinitely? There seem to be only two ways to explain this anomalous state of affairs: either I 
have overlooked some material fact about bitcoin that might impart a positive value to them, or 
there is a problem with the theory of valuation that I am using.
I don’t believe that my basic approach is inconsistent with the positive value that the 
bitcoin has maintained for several years. However, that approach does require some adjustment 
8
B
itcoin provides a unique service as a medium of exchange, unavailable to those using fiat money, in facilitating 
anonymity for transactions, payment via bitcoin being more difficult to trace than electronic payments via 
conventional media of exchange. That is a good reason for people to want to use bitcoins in certain kinds of 
transactions. However, the difficulty of tracing transactions via bitcoin does not explain why bitcoins have a positive 
value in the first place, only an argument why, if they do have a positive value, the demand for them might be 
greater than it would have been if not for that advantage. Without an independent explanation for the positive value 
of bitcoin, a positive value of bitcoin cannot be bootstrapped by citing the difficulty of tracing bitcoin transactions.
9
One reader has suggested that the quantity constraint contributes to incentive compatibility by ensuring that 
holders of bitcoin do not form expectations that the value of bitcoin fall to zero as a result of overissue as suggested 
by Luther (2018). But this argument fails to take account of the inherent incompatibility between a fixed supply of a 
medium of exchange and a constant value. 

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13 
to account for the large role that network effects play in the demand for money. Because the 
willingness of people to accept and hold a medium of exchange increases rapidly as the total 
number of people willing to accept and hold that medium of exchange increases, the backward-
induction argument becomes less straightforward than I had earlier made it out to be.
The network externality affecting the demand for a particular money means that your 
demand for that money increases its usefulness to me and that my demand for that money 
increases its usefulness to you. But network effects have another critical consequence: as 
increasing numbers of people use a particular money for an increasing number of their 
transactions, those using that money to mediate their transactions become increasingly locked in 
to its continued use, because as long as those with whom they are transacting use that money it 
will be difficult for them to switch from that money to an alternative money.
If you and I are actual or potential trading partners, your demand for the particular money 
that we both use in transacting adds to the cost I would incur by switching from the common 
medium of exchange that we now use to a different medium of exchange. So, even if backward 
induction and the expectation that the medium of exchange that we now use will lose its value at 
some future date encourages us both to stop using the medium of exchange that we now use, the 
network externality and the lock-in effect encourages, or even compels, us to continue using the 
medium of exchange that we both use. The net effect is unclear, but the more transactions and 
the more trading partners are implicated in switching from one medium of exchange to another, 
the more tightly we will be locked into continued use of the medium of exchange that we both 
use, notwithstanding our expectation that it will eventually lose its value.
At a minimum, these two opposing forces – one encouraging abandonment of the 
currently-used medium of exchange and the other locking traders into its continued use -- 
suggests that even if the equilibrium value of a fiat money or a crypto-currency is positive, the 
equilibrium value may be unstable. A sufficient change in expectations may cause a drop in 
demand for the money beyond the threshold or tipping point at which the decline in demand and 
value becomes self-reinforcing and cumulative. 
Because currency instability derives from subjective expectations and because changes in 
expectations can be self-fulfilling or self-reinforcing, that instability is difficult, if not 
impossible, to control or contain. To be sure, the larger the network and the greater the lock-in to 
the existing medium of exchange, the more stable is the equilibrium value of the currency and 
the less vulnerable it is to sudden change. But even a widely used medium of exchange may be 
subject to instability and a tipping point if people begin migrating to another medium of 
exchange. For a truly dominant currency, like the US dollar, whose dominance is perhaps more 
overwhelming than that of gold during the heyday of the international gold standard, there is 
little likelihood of a sudden shift to another currency standard, absent some cataclysmic event, 
like the outbreak of world war in August 1914.
How does this discussion relate to bitcoin? I have described three potentially opposing 
forces bearing on the value of a pure medium of exchange. On one side there is backward 
induction, which tends to drive the value of a pure medium of exchange to zero once its future 
loss of value becomes clear enough that it is no longer accepted in exchange. Against backward 

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14 
induction, at least for a fiat currency issued or sponsored by a government with the power to levy 
and collect taxes, the value of the fiat currency can be maintained, despite the logic of backward 
induction, because acceptability in payment of taxes by the government creates a demand for a 
fiat currency as long as the issuing government is expected to remain in power and to impose tax 
liabilities that can be discharged by the currency it issues. And finally, aside from acceptability 
in discharging tax payments, the switching cost borne by current users of a currency in switching 
to another currency increases as the number of people using that currency increases.
For bitcoin and other cryptocurrencies, which are not accepted in discharging tax 
liabilities, only the network effect locking existing users of a currency into its continued use that 
can support a continuing positive quasi-equilibrium value. The question, then, is whether the 
network effects generated by bitcoin or other cryptocurrencies are large enough to maintain their 
value above zero for an extended period of time?
I will try to offer two tentative answers to that question in the next section. I offer two 
answers, because the underlying architecture of bitcoins render it inherently unsuitable as a 
medium of exchange. If I am right in regarding bitcoin as unsuitable to serve as a medium of 
exchange, a different kind of cryptocurrency, based on an alternative architecture might have a 
better chance than bitcoin to establish itself as an alternative medium of exchange, though, under 
almost any conceivable set of circumstances, the chances that any cryptocurrency could expand 
its reach beyond a niche of regular users seems to me very low. 
VI 
Network Effects and Bitcoin 
In the previous section I argued that bitcoins and other cryptocurrencies, providing no 
service other than their anticipated future resale value to their holders, are at risk of losing their 
resale value. Despite their vulnerability to extreme loss of value, bitcoin and other 
cryptocurrencies may avoid such an outcome by gaining sufficient early acceptance as a media 
of exchange. Acceptance as a medium of exchange triggers network effects that increase demand 
for the medium of exchange and promotes lock-in among existing users. If sufficiently strong, 
that lock-in may support continued use of the medium of exchange, thereby preventing what 
would otherwise be an inevitable loss of value.
Despite a seemingly predictable future loss of value, bitcoin has gained acceptance as a 
medium of exchange by providing medium-of-exchange services not provided by other 
currencies, even the dominant currency: the dollar. Bitcoin has also attracted a coterie of 
libertarian and anarchist ideologues who, on principle, prefer using a non-governmentally 
supplied medium of exchange, though it is far from clear how widely such ideologues actually 
use bitcoin in transactions that are not the type for which bitcoin actually enjoys a competitive 
advantage.
Promoters of bitcoin extol the blockchain technology that is designed to render trading 
with bitcoins anonymous and secure. But the decentralized character of bitcoin transactions 
slows down, and increases the cost of, transacting with bitcoins. In fact, most users cannot easily 
access the blockchain directly, relying instead on bitcoin accounts managed by intermediaries 
who access the blockchain on their behalf. There are recurring reports of hacking into the bitcoin 

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15 
accounts managed by intermediaries to effectuate fraudulent transactions, casting doubt on the 
purported security and anonymity of bitcoins.
10
For discussion purposes, let me stipulate that bitcoin does provide enhanced privacy and 
anonymity in performing transactions, which, for some transactions, more than compensates for 
the added cost of transacting with bitcoins or other blockchain-based cryptocurrencies. But the 
number of transactions for which bitcoins or cryptocurrencies might be preferred by transactors 
is a tiny fraction of the total number of transactions mediated by conventional currencies. Still, a 
plausible argument could be made that a niche market for a medium of exchange designed for 
secure anonymous transactions would suffice to make a secure and anonymous medium of 
exchange viable. But a niche currency is a shaky platform upon which to challenge the dominant 
international currency entrenched by extreme network effects and high switching costs.
11
It is therefore seems implausible to imagine that its base of illegal transactions and 
transactions of a small subculture of political extremists could ever provide bitcoin with a 
transaction volume comparable to that currently mediated even by the fiat currency of a small 
economy, say, the Uruguayan peso.
12
Nevertheless, the advantages of using bitcoin to mediate 
illegal exchanges enable bitcoin to provide a service that cannot be duplicated by any established 
fiat currency, enabling bitcoin to maintain a positive value notwithstanding a likely loss of value 
at some point in the indefinite future. 
The small size of the potential market accessible to bitcoin casts doubt on whether other 
cryptocurrencies can be viable. It a niche market characterized by network effects, it is unlikely 
that more than one supplier could be viable. As the first, and still the largest, cryptocurrency, 
bitcoin will not be easily displaced as the primary cryptocurrency, the hype surrounding the 
surge in initial cryptocurrency offerings notwithstanding. However, the structural defect 
mentioned above does create a potential market opportunity for an alternative differentiated 
cryptocurrency to displace bitcoin as the leading cryptocurrency. 
In the previous section, I drew attention to the defect in the bitcoin architecture that, by 
imposing increasing costs on the creation of additional bitcoins as the total quantity created 
10
If bitcoin did gain wide acceptance among a broad range of users, economies of scale might support the 
emergence of efficient, transparent and trustworthy intermediaries to manage personal bitcoin accounts. But the 
inherent limitations of bitcoin militate against the expansion of its usage and acceptance necessary for such 
intermediaries to emerge.
11
One reader has suggested that the success of Ripple in competing with SWIFT in executing international transfers 
shows that cryptocurrencies using blockchain technology can effectively compete with fiat currencies in providing 
transaction services. But the limited success of Ripple in competition with SWIFT actually highlights the limitations 
of blockchain. Blockchain capacity is not sufficient to allow Ripple to handle all international bank transfers, and the 
cost of holding XRP, the volatile cryptocurrency used in making transfers on the Ripple blockchain, adds to the 
transactions costs of using Ripple. SWIFT, a monopolistic supplier of international bank transfer services, has 
responded to Ripple by speeding up and reducing the cost its services. 
12
It has been suggested that there is also a demand by other blockchain users for bitcoins to be used as collateral in 
mediating blockchain transactions using other cryptocurrencies such as the ether. However, recent statistics 
indicated that the amount of bitcoin collateral held by ether is less than a half of one percent of total bitcoin 
capitalization. Another suggested source of potential demand for bitcoins is that people in unstable regimes are 
likely to demand bitcoins despite the high cost of transacting with bitcoins because of the instability of their own 
currencies. However, residents in countries with unstable regimes in power already use dollars as their primary 
alternative to their local regimes and bitcoins are unlikely to replace dollars as the main alternative to unstable 
domestic currencies. 

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16 
approaches a fixed upper bound, undermines its potential for expansion. The architectural defect 
stems from a misguided ideological commitment to making an inflationary increase in the total 
quantity of bitcoins impossible. 
The problem with this architecture is that insofar as bitcoin attracts new users that hold, 
and execute transactions with, bitcoins, the consequent increase in the demand to hold bitcoins 
causes the price of bitcoin would increase. The early growth in the use of bitcoin did indeed 
cause an increase in both its price and the total outstanding quantity. But the rising price of the 
bitcoin, which fueled expectations of further price increases, had an unanticipated effect; to 
undermine the usefulness of bitcoin as a medium of exchange.
It may seem paradoxical that a rapid increases in the value of an asset – or more precisely 
the expectation of a rapid increase in its value – impairs its suitability to serve as a medium of 
exchange, but the tendency for any asset being used as a currency to disappear from circulation 
as a result of an expectation of a rapid increase in its value has long been recognized in the 
literature on money. The phenomenon has both a name (Gresham’s Law) and a pithy epigram 
(bad money drives out the good) attached to it. 
Already commented on by Aristophanes in one of his plays, the phenomenon was a 
commonplace in early writings on metallic coinage. It typically occurs when two moneys – one 
of them having more valuable material content than the other – circulate concurrently. For 
example, if a coinage consists of both full-bodied and clipped coins with equal face value, people 
hoard the more valuable full-bodied coins, offering only the clipped coins in exchange. 
Similarly, if some denominations of the same currency are gold coins and others are silver coins, 
so that the relative values of the coins are legally fixed, a substantial shift in the relative market 
values of silver and gold causes the relatively undervalued (i.e., the “good”) coins to be hoarded, 
disappearing from circulation, leaving only the relatively overvalued (“bad”) coins in circulation. 
I note in passing that a fixed exchange rate between the two coins or currencies is not, as has 
often been suggested, necessary for Gresham’s Law to operate when the rate of appreciation of 
one of the currencies is sufficiently rapid.
13
The fixed exchange rate that equates the values of 
two assets is what creates the expectation of rapid adjustment of the relative value of the two 
assets should the fixed exchange rate be changed, leading to the disappearance from circulation 
of the asset expected to appreciate.
14
If I can use dollars with a stable or even purchasing to obtain the goods and services that I 
seek, why would I instead use an asset that I expect to appreciate rapidly to buy the same goods 
13
The maximum rate of expected appreciation consistent with continued use of an asset as a medium of exchange is 
given by the Fisher equation: