I our “Is Cryptocurrency Real?” blog we described the interesting example of how an Italian telephone token (the gettone) behaved like currency, even though it had limited use and no intrinsic value. The gettone analogy is important because Metcalfe’s law, upon which our work is based, originated from a description of telephone networks. The holders of gettoni and the payphones themselves are a network. The value of a gettone to someone in that network, when spending the coin, is one of convenience and the value of the information relayed over the network. If we assume a growing number of pay telephones and callers, and then apply the constraint of a limited number of gettoni, we have mirrored the key elements of cryptocurrency’s supply and demand characteristics.
Network economics is a new field, and so much of the economics around cryptocurrency is foreign to most. The network economy is the emerging economic order within the information society. The name stems from a key attribute−products and services are created and value is added through social networks operating on large or global scales. This is in sharp contrast to industrial-era economies, in which ownership of physical or intellectual property stems from its development by a single enterprise. Examples of network effects can be found in internet websites, mobile phone proliferation, and social media applications like Facebook, Twitter, LinkedIn, SnapChat, and Instagram.
Metcalfe’s Law is regarded as the first and most reliable explanation of the network effect. It is a calculation of the maximum number of connections a network can make, based on the number of nodes (or users). The value of any network, be it currency, internet, telephone, or social, is dependent upon the number of users. Here is an example of the calculation:
"If only one person has a telephone, then the device is obviously quite useless. If two people have telephones, it is possible to make one connection between two people. As the number of people (n) rises in a linear fashion, the number of possible connections increases exponentially. Thus, if 5 people have telephones, letting n in the equation equal 5 will produce 10 possible connections. If n were equal to 10, there would be 45 possible connections. In other words, a doubling of n, or a doubling of the nodes so to speak, increases the number of possible connections by a factor of 4.5. If one then further increases the number n to 12, the number of possible connections increases to 66. Hence, a 20% increase in n produces a 46.67% increase in possible connections."
 Reed E. Hundt, then the chairman of the U.S. Federal Communications Commission, declared that Metcalfe’s Law and Moore’s Law “give us the best foundation for understanding the Internet.” Marc Andreessen, who created the first popular Web browser and went on to co-found Netscape, attributed the rapid development of the Web—for example, the growth in AOL’s subscriber base—to Metcalfe’s Law.
 From the FRMO Corporation Annual Meeting of Shareholders, September 15, 2017.
In 2017, we performed a comparison of Facebook’s growth to that of Bitcoin. Facebook is uniquely suited for comparative study because it shares with Bitcoin many similar circumstances:
Both have characteristics of networks.
Both have observable market values.
Both have observable values for nodes (wallets and accounts).
Both had nearly identical early growth rates, averaging 100% per year (doubling).
Both were banned in China.
Facebook was the subject for proof of Metcalfe’s law in two papers.
At the time, Bitcoin was 8 years into existence; Facebook IPO’d in its 8th year.
Facebook, for its first 8 years, did not have an observable market value. But using data on the number of accounts, we can derive the value from Metcalfe’s law. Likewise, we can derive a value for Bitcoin from a projected growth rate and apply Metcalfe’s law. We can also compare Facebook’s actual market capitalization to the value predicted by Metcalfe’s law.
Both Facebook and Bitcoin doubled the number of network nodes (user accounts and wallets) early on. Since its initial public offering, Facebook has grown its users at a rate of about 16% per year. Using Metcalfe’s law, we can impute a value for Facebook pre-IPO using actual users . Using Facebook’s post-IPO growth rate of 16%, and Metcalfe’s law, we projected a value for Bitcoin going forward.
 These Metcalfe values have been scaled by a coefficient so as to better visually align with the subject price/market capitalization under scrutiny. The underlying Metcalfe value itself is not modified, it is only adjusted by an order of magnitude.
Despite its rapid growth, people could not declare Facebook to be a bubble in its early years because, unlike Bitcoin, its market value was not visible. Had Facebook users been co-owners of the company, they would have experienced Bitcoin-like returns. However, its early growth rate in user accounts of 100% was not sustainable in the long run. Likewise, Bitcoin’s adoption-stage growth rate of 100% is also not sustainable.
We don’t know what Bitcoin’s future annual growth rate will be, but 16% is not unreasonable. If Bitcoin ceased is supernormal growth today, and grew at 16% for the next five years, a reasonable expectation of return based on Metcalfe value would be just over 50% per year. By comparison, Facebook’s post-IPO growth in market cap was 31% per year.
There is one glaring problem with an analysis that only considers number of users: the value of networks cannot go up forever. An incomplete application Metcalfe's law measures only the potential number of contacts, i.e., the technological side of a network. However the utility of a network depends upon the number of nodes actually in contact (transactions) and the quality of information transacted. Metcalfe said that, over time, this utility declines. In other words, the effect of growth in users on value is subject to the Law of Diminishing Marginal Returns.
Practical examples of this degradation in network value include things like spam, excessive advertising, and other bits of false, irrelevant, or uninteresting pieces of information.
Imagine you throw a party. Only a few people show up, and it’s pretty boring. There is some opportunity to interact with the people who are there, but there just isn’t much potential for interaction in general. As more people show up, the party gets better. But then consider a party where too many people show up. It’s too noisy, and people can’t hear each other clearly. Most people are strangers to you, and some behave badly. Drinks are spilling everywhere. It’s so crowded, people can’t move around or dance. This is an example of diminishing marginal returns. We call this the Goldilocks effect: the network cannot be too big or too small, it must be just right to maximize value.
Metcalfe expressed this concept in his formula with a term he called “Affinity,” dimensioned as value-per-user, and labeled as A in his equation. As n goes up, A goes down. This puts a limit on the network effect.
In our experience, most cryptocurrency models do not account for diminishing marginal returns. As a result, they generate values that are too high for cryptocurrency.
To date we have been able to use Metcalfe’s law to explain prices in dozens of cryptocurrencies We believe Metcalfe’s Law explains a large number of economic and financial phenomenon.These include social media applications like Facebook and LinkedIn; payment systems like PayPal and Square; and mobile phone companies like Apple, Samsung, and Google. We also believe that Metcalfe’s law has been a predominant factor in the most successful economies throughout history:
The Roman Empire with its network of roads;
The British Empire with its network of shipping routes; and
The United States with its network of navigable rivers; transcontinental rail, telegraph and telephone; electrical grids; interstate highway; air transport; internet; and communications satellites.