Metcalfe's Law as a Model for Bitcoin's Value

21 Pages Posted: 2 Dec 2017 Last revised: 25 Feb 2018

Timothy Peterson

Cane Island Alternative Advisors

Date Written: January 22, 2018


This paper demonstrates that bitcoin’s medium- to long-term price follows Metcalfe’s law. Bitcoin is modeled as a token digital currency, a medium of exchange with no intrinsic value that is transacted within a defined electronic network. Per Metcalfe’s law, the value of a network is a function of the number of pairs transactions possible, and is proportional to n-squared. A Gompertz curve is used to model the inflationary effects associated with the creation of new bitcoin. The result is a parsimonious model of supply (number of bitcoins) and demand (number of bitcoin wallets), with the conclusion bitcoin’s price fits Metcalfe’s law exceptionally well. Metcalfe’s law is used to investigate Gandal’s [2018] assertion of price manipulation in the Bitcoin ecosystem during 2013-2014.

Keywords: Bitcoin, Metcalfe, Finance, Investment, Economics, Network Economics, Currency

Suggested Citation

Peterson, Timothy, Metcalfe's Law as a Model for Bitcoin's Value (January 22, 2018). Available at SSRN: or

Timothy Peterson (Contact Author)

Cane Island Alternative Advisors ( email )

515A South Fry Rd #191
Katy, TX 77450
United States

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