notes: math_sci_tech

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The minimum Cost of Production Price of #Bitcoin

Summary: I present a bitcoin price indicator based on cost of production. It is constructed from hash, issuance and energy efficiency data that is available in the open. Only electricity price is (additionally) assumed. The indicator provides a potential alternative to the power law for estimating the fair value price of bitcoin.

The current network hash rate of bitcoin is a whopping 650EH/s! Thats about 650000000000000000000 SHA256 int32 operations per second! This spectacular feat was achieved through the combined effort of a network of miners spread across the world. This has brought tremendous value to bitcoin by making it the most secure ledger ever created.

At present, the cost of this global operation is paid for mainly by the block subsidy (i.e. by newly created bitcoin). One can express the relation between the total hash and the cost of producing it by a simple formula:

Hash = Efficiency . (breakeven) Price . Revenue (in BTC).
or,
H = E.P.R

Here, the breakeven price of bitcoin is the price at which mining is just profitable. Henceforth, I refer to this as the (minimum) Cost of Production or CoP Price. Efficiency (or dollar price of hash) represents the amount of hash that the network can produce per dollar of cash spent.

Since H, E and R can be determined independently, the above formula can be used to estimate CoP price:

CoP Price = H / (ER)

https://m.primal.net/KQey.png
https://m.primal.net/KQfB.png

Related work/Further reading:
[1]. https://x.com/IIICapital/status/1547953224555999233
@IIICapital

[2]. https://medium.com/@paulewaulpaul/bitcoin-difficulty-per-issuance-a-pow-pricing-model-452cd8a3017b
@paulewaulpaul

[3]. https://x.com/moneyordebt/status/1814322194354471081 by
@moneyordebt
for more insight.

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 2/ Determining H, E and R

Obtaining data for hash and revenue is straightforward. I downloaded it from http://blockchain.com. The data for efficiency was more tricky to derive.  I was only able to find efficiency data in terms of energy i.e. TH/J, from https://ccaf.io/cbnsi/cbeci.  Converting from TH/J to TH/$ requires an assumption on the electricity costs of mining.

Fortunately, electricity price does not scale as much as energy efficiency of the mining rigs themselves, so it is not too critical a parameter for modeling the overall trend. Only a small correction is needed to account for the improved price of electricity secured by the miners over time. 

To this end, I propose two heuristic models for electricity price:

Model 1: Electricity price is fixed at 0.1 dollar per kWhr
Model 2: Electricity price is modeled as 0.24/sqrt(year-2009) dollars/kWhr*

*This model is only applicable for years >2010.

https://m.primal.net/KQfc.png

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 3/ Results and Discussion

The chart with the two models is shown below. It can be seen that even when assuming constant electricity price, the CoP price strongly correlates to the actual price over a long time period. However, at 10 cents per kWhr, it ends up sightly overestimating the absolute breakeven price (given by the price floor) during the more recent period. The varying price model corrects for this aspect. I used the later model in all the other charts in this post.

https://m.primal.net/KQfj.png

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