This article will give an insight and demonstrate how market price, miner adoption, mining profitability and transaction fee ratio are linked with each other based on specific rules that have to be fulfilled. First, a specific price model will be used to generate a future model price. Then, the model price and the factors mentioned above will be put into relation to describe relevant key characteristics of the Bitcoin network from the early days with high block rewards until the late stage without any block rewards at all.
Introduction
In the last article it was reasoned why the Bitcoin price will very unlikely follow the output of the regular S2F model because of natural limitations of resources on earth (in each year an upper ceiling value of the Bitcoin price can be estimated based on block reward, miner profitability and limited amount of global electricity). A different model that is also based on S2F but has major adjustments so that the Bitcoin price approaches a limit value within time takes those limitations (especially the limitation and decrease of buy demand within time) into consideration. The output of this model by Medium author QuantMario will be used to link the generated price data to other parameters within the Bitcoin ecosystem and see whether reasonable outputs derived from these data are produced to describe a sustainable state of the Bitcoin network in any given year.
Preliminary remarks
Differences of BTC to a conventional asset following S2F like gold
Whether a basic S2F model or an adjusted version of this model is even suitable to estimate a future Bitcoin price in the long run can still be argued, since there are fundamental differences between Bitcoin and a traditional S2F asset like gold.
Flow / Time - Correlation:
- Flow of gold does not change rapidly within time.
- Flow of Bitcoin halves every four years.
Flow / Mining Effort - Correlation
- Flow of gold is correlated to mining effort.
- Flow of Bitcoin is not correlated to mining effort.
Mining Cost / Global Mining Effort - Correlation
- Mining cost of one gold miner is not correlated to global mining effort.
- Mining cost of one Bitcoin miner is correlated to global mining effort.
Counterfeit Protection / Global Mining Effort - Correlation
- Counterfeit protection of gold is not influenced by global mining effort.
- Counterfeit protection of Bitcoin is correlated to global mining effort.
Based on these facts, in Bitcoin’s case the market “decides” the mining cost per Bitcoin - there is no lower boundary value derived by the technical mining process itself like it is the case for gold. The flow cannot be influenced.
For gold it is generally the other way round - the flow is “decided” by the market participants (miners), the mining cost per ounce can only be optimized within a certain range (scale of production, improved process technology).
Why a basic S2F model cannot hold long term for Bitcoin
The S2F model’s output basically demands a 10x price increase from one cycle to the next cycle. If a constant profitability of miners is assumed (equilibrium of price and miner adoption), then the mining effort has to quintuple every four years - the combination of a tenfold increase of price and a halving of the block reward results in a five-fold increase of reward in fiat currency every four years. There are three reasons why this cannot practically last for a relevant number of cycles:
- After some cycles the mining effort would allocate the majority of the world’s electricity consumption at a reasonable profitability or in extreme case even more than the theoretical 100% that is possible. The table shows that the S2F model price and S2FX model price this early would need a very high global electricity ratio put towards mining Bitcoin to keep up a sustainable equilibrium of price and mining adoption.
2. The buy demand would not only have to increase five-fold every cycle to take out the new daily emission in fiat on the sell side, it would even have to be higher to take out some of the increased sell pressure that is produced by the increased valuation of coins in circulation (market capitalization).
3. The very long term outlook of Bitcoin is a network that is profitably run by miners living off regular transaction fee income only. Based on the regular S2F model’s output the transaction fee ratio would rather decrease than increase (tx fees are constant, block reward goes up in fiat currency), which makes this scenario practically implausible long term. Based on these thoughts, a long term model that describes the equilibrium of price and miner adoption can be thought out. The following three hypetheses must be fulfilled in this model:
- The Tx Fee Ratio increases long term from 0% to 100%.
- The Bitcoin price converges to a value of buy/sell equilibrium.
- Miners always mine with a constant profitability.
Relevant preconditions and derived hypotheses
For easier calculations and visualization the genesis block is set at the beginning of 2008, followed by 32 block reward halvings taking place every four years.
The block reward value (BTC/b) is starting with 50 in the year 2008 and halves every four years. The last halving is taking place in 2136. The block reward is 0 from the year 2140 on.
The daily transaction fee value ($/d) is estimated for every year — the base value is set constant as $1m per day (500k tx/d, 2$/tx) with some exceptions (lower values for tx amount and tx fee) in the first few years based on historical data.
The daily transaction fee ratio (%) is the ratio of the total miner output ($) that is made up by the regular transaction fees ($). Therefore, the following rules must apply: The daily transaction fee ratio (%) is between 0% and 100% from 2008 until 2040 and must be 100% from 2040 on.
The daily total miner reward is the sum of daily transaction fee value and daily total block reward value.
A fundamental hypothesis is that miners are always mining with profit. A total mining profitability is set and held constant. For a mining profitability of 50% the following is valid:
(daily transaction fee value + daily total block reward)/mining cost = 1.5
The ratio of global electricity consumption describes how much percent of the global electricity consumption is used for mining Bitcoin - it is between 0% and 100% by definition.
Based on these assumptions and the known emission schedule of Bitcoin, the daily transaction fee ratio is expected to go long term from 0% to 100% in an S-shaped curve. The price of Bitcoin is expected to increase fast in the beginning and then level out at a specific stable value. A specific model that is taking those assumptions into consideration is used to estimate the price of Bitcoin for every year. From this point on, all required parameters (Bitcoin price, daily emission, daily transaction fee value, profitability) are known and all other parameters and curves can be derived by using only these data.
Values for daily transaction fee value and Bitcoin price are set for each year. Based on these values the daily total block reward is known for every year. Based on these values and the known emission schedule of Bitcoin the daily transaction fee ratio can be derived for every year. Based on the set mining profitability and the known total miner reward the daily mining cost can be derived. By using reference data the daily mining cost can be transformed in a ratio of global electricity consumption.
The yearly inflation rate of fiat currency is existent in all set or derived parameters (transaction fee, market price, mining cost, etc.) and can therefore be taken out of all calculations and equations.
Different Phases of Equilibrium
The miner adoption and therefore energy put towards mining Bitcoin is either constant or increases. This is the current state since the first Bitcoin block. As it was hypothesised that miners must mine with a profit by definition and the block reward halves every four years, the price must at least double every four years for miners to stay profitable. Since this would also result in a duplication of the market capitalization it is not very likely for this scenario to stay reality for a high number of future cycles. Also, this would go against the theory that the daily transaction fee ratio converges long term to 100%. Therefore, this scenario can only be one phase from different phases - Phase I.
As price must consistently increase in order to sustain the constant or increased miner adoption, there will be very likely a point reached where the increased value of early and mid adopters’ holdings will result in an increased selling pressure. The equilibrium of holders (more and more selling pressure) and buyers (less and less buyers because of ongoing adoption) shifts and the price increase will slow down. Since miners need at least a duplication of price every four years to stay profitable at a constant mining effort, the global mining effort must go down if the growth rate of Bitcoin price is lower than 2x per cycle. As a result, there is some transition phase in which an increase of price and decrease of miner adoption will be existent - Phase II.
Based on the assumption that global adoption of Bitcoin will take place, the price will very likely find a ceiling and converge towards this global adoption value. Therefore, the miner adoption has to decrease continuously in order to ensure constant miner profitability. Also, in this phase the transaction fee ratio converges more and more towards 100%. This means, that the miner profitability becomes less and less correlated to the Bitcoin price. This will be the real decoupling - Phase III.
Finally, the miners have to be profitable completely from their income of regular transaction fees. The market price of Bitcoin has become completely uncorrelated from the miner adoption by then - Phase IV.
As a conclusion, on a very long term outlook the current miner adoption can be only sustainable - miners are profitable - held if the daily transaction fee value increases in the future. There are only three possibilities to achieve this:
- A higher average transaction fee ($2 in the model)
- A higher number of transactions per day (500,000 in the model)
- A combination of 1. and 2.
Visualization of the resulting model with set parameters
The graph above shows the Bitcoin price within time based on the output of the LGS-S2F model by QuantMario. For easier fit with the following linked parameters, the genesis block is assumed to have taken place at the beginning of 2008 and each halving is assumed to take place exactly every four years.
The graph depicts the trend of Block Reward and Tx Fee Ratio over time. It can be seen that the ratio is almost zero in the early years of Bitcoin - the block rewards were high, the daily number of transactions and transaction fees were low. The daily transaction fee value is assumed to rise from a very low amount (almost zero dollars) to a constant value ($1MM). Based on the historical transaction fee data, the future estimated transaction fee value, the known block reward schedule and the Bitcoin model price data the Tx Fee Ratio vs. time curve is obtained. The outcome shows that the price model data fulfils the requirement of the Tx Fee Ratio converging to 100% in a smooth transition (S-shaped curve) before the last block reward.
The chart visualizes the dependence of the global electricity consumption on the Bitcoin price. In the beginning, an increase of both Bitcoin price and miner adoption is existent. The global mining effort peaks in the year 2032 - still way below the current mining effort put towards gold - and marks the end of Phase I. A slowed down increase of Bitcoin price and decrease of miner adoption is existent in Phase II. A decoupling of Bitcoin price and miner adoption is existent in Phase III. A complete independence of miner adoption on Bitcoin price and vice versa is existent in Phase IV. Each phase continuously merges into the next one in a smooth transition.
The chart above visualizes how the miner profitability becomes more and more independent from the Bitcoin price in Phase III. It can be seen how the defined miner profitability (50%) is less and less affected by a duplication or triplication of the Bitcoin price.
The chart above demonstrates how the smooth transition from a miner reward mostly dependent on the block reward into one completely dependent on regular transaction fees in the far future may look like.
Sceptics of the Bitcoin network often argue that the average cost per transaction is ridiculously high. They do not refer to the on-chain transaction fee per transaction but they describe the ratio of the total Bitcoin mining effort to the total amount of transactions. Since the status quo of the Bitcoin network is miners mostly mining for the block rewards instead of the transaction fees, this is not a suitable metric right now. The chart below shows how the total mining effort per transaction naturally will go down in the future when miners are more and more relying on the income of transaction fees instead of block rewards. The assumption of a constant profitability of 50% results in a mining effort per transaction converging to $1.33 at an average transaction fee of $2.
Finally, an interesting key parameter also is the ratio of market capitalization to yearly mining effort. Since the market capitalization is a metric to at least somehow value the Bitcoin network and the mining effort put towards Bitcoin’s PoW mining algorithm is relevant for the security of transactions taking place, those two values are somehow linked. The graph shoes that one parameter goes down in favor of the Bitcoin network (mining effort per transaction decreases) and the other one goes up against it (ratio of market capitalization to mining effort increases).
Estimation of electricity costs
Based on data for global electricity consumption for mining Bitcoin and technical specification data for the Bitmain Antminer S19 pro, the ratio of global electricity in the charts is valid for an estimated average price of $0.05 per kWh and an estimated average Antminer S19 efficiency ratio of 55% (on average, all hardware used for mining Bitcoin is assumed to have this efficiency ratio of this one specific hardware product).
Conclusion
The aim was to show how basic assumptions and rules (constant miner profitability, limited amount of global electricity, long term conversion to a transaction fee based total miner reward) put a natural limit on the Bitcoin price in a specific year. The further into the future we go, the less electricity is needed to sustain a relatively high Bitcoin price because of the ever decreasing block reward. The generated outcomes based on the combination of set rules and the used model to estimate a future price could show, that the price model is reasonable. It is demonstrating how a transition from profitable mining via block rewards to profitable mining via regular transaction fees only can look like - starting at the lower limit of 0% after the genesis block and ending at the higher limit of 100% after the last block reward will have been emitted. There is no point in the model where an unreasonable high ratio of global electricity consumption is needed to sustain the model price at a realistic mining profitability.
The final conclusion of this combined model is that today’s mining effort can only be long term sustainable if there is some sort of scaling or higher transaction fees in the future in order to generate more transaction fee revenue on the network. The market price of Bitcoin may be completely detached from the global mining effort from a mathematical point of view but it will still be dependent on it - the amount of energy put towards securing the network is still a fundamental key parameter of Bitcoin.
There is another possibility left to take into consideration. The mining infrastructure may shift from a smaller number of high-scale farms built for making profits from block rewards to a higher number of low-scale setups run by the people on their own expenses for the worthy cause. This way, the preservation of the network’s security will be again in the hands of the people like it was in the very early days of Bitcoin - but then on a much bigger scale.
Adjusted model: growth of tx fee revenue and global electricity
Since it is unlikely that the average number of daily transactions on the network as well as the average transaction fee will remain constant within the future, the model can be adjusted in order to simulate some sort of scaling (more transactions per second) and a higher average transaction fee that users are willing to pay. Data from Dan Held’s article “Bitcoin’s Security is Fine” is used for this approach.
The referenced article gives two example scenarios for the year 2140. The output of the LGS-S2F model results in a Bitcoin market capitalization of roughly $80t which is in between those two scenarios. Now, an annual miner revenue can be modelled based on the given annual mining revenue as market cap percentage and the obtained market capitalization.
In this simple model of future scaling a linear growth of transactions per second until 138 tps in 2140 is assumed. The average transaction fee is assumed to increase linear as well in order to reach the desired value of roughly $295b/y transaction fee revenue.
It can be seen how the S-shaped curve of the Tx Fee Ratio goes up sooner because of the introduced scaling and increase of average transaction fee.
Now, due to the increasing transaction fee revenue the tipping point from a block reward focused to a transaction fee revenue focused mining business takes place earlier.
Finally, the graph for the ratio of global electricity consumption can be derived like it was done in the initial approach. Here, it is additionally assumed that the global amount of electricity is increasing with a ratio of roughly 3% per year. In this simplified model the electricity cost remains constant. The model is still flawed since it is not possible to estimate the growth of global electricity production/consumption and the price development of electricity cost within such a big time frame - yet it shows how a long term model of equilibrium between market price and miner adoption can be set up using different assumptions and parameters. The global electricity consumption can either be described as output of TWh/y or electricity cost in USD. A combined model using a lower growing global output (less than 3% TWh/y increase) and a decrease of miner electricity costs (electricity cost lower than 0.05 $/kWh) could be further developed to take these two crucial factors into consideration.
Final note: The LGS-S2F model price function was used to produce a future price in any given year because it is taking the relevant economic limitations into consideration - using a different model price function can give an insight how the linked parameters are affected as a result. However, the combined model taking all linked parameters into consideration can also be set up the other way round by specifying the global electricity consumption ratio as well as the transaction fee ratio as estimated parameter for every year and consequently deriving the model price in every year as a result. This way, the combined model can be set up for very different scenarios (values of specified parameters) and approaches (type of specified parameters).
