PlanB recently published a fantastic publication on Medium, exploring Bitcoin’s Value models in the context of scarcity.
Satoshi’s (true) Vision
By creating the bitcoin genesis block on 3rd January 2009, Satoshi Nakamoto created the world’s first ‘scarce digital object’. Unlike gold or silver, which can only be virtually transferred as token reserves, actual bitcoin can be ‘sent’ over the internet, creating true peer-to-peer value.
” 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 [..], not useful for any practical or ornamental
purpose .. and one special, magical property: can be transported over a
communications channel” — Nakamoto 
This scarcity, and genuine representation of the asset creates value. PlanB explores this very scarcity and stock-to-flow modeling.
Definitions of Scarcity and Stock-to-Flow
Nick Szabo defines scarcity as ‘unforgeable costliness’. Due to PoW and the electricity/computational required to process transactions, bitcoin qualifies for unforgeable costliness. Security of the network, via hash rate difficulty, guarantees the veracity of bitcoin.
Saifedean Ammous discusses scarcity in reference to stock-to-flow (SF) ratio. Gold and bitcoin are different to other consumable commodities, such as copper and zinc, because they have high SF.
“The existing stockpiles of Bitcoin in 2017 were around 25 times larger than the
new coins produced in 2017. This is still less than half of the ratio for gold, but
around the year 2022, Bitcoin’s stock-to-flow ratio will overtake that of gold” —
Gold currently has an SF of 62. Silver 22. Bitcoin currently has an SF of 25. Due to its fixed (and deflationary supply) this SF will only increase with time.
Interestingly, as scarcity, measured by SF, ‘directly drives value’. Therefore bitcoin’s halving events, and increased ‘scarce’ total supply, will have a dramatically positive effect on the speculative price. Plotting of both logarithmic values or axis for SF demonstrates a clear linear relationship between SF and market value. Extrapolating bitcoin’s future SF with the same model gives an SF of 50 after the May 2020 halving. This would equate to a price of $55,000.
There is clearly some very interesting research and modeling to be done regarding the correlation between scarcity, stock-to-flow, and bitcoin’s potential future speculative price. PlanB’s efforts a clear and their conclusions sound. Further peer review needs to be conducted to verify their findings.