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Metcalfe’s Law, Network Effects and Numbers - the Economic Network Called Bitcoin

Bitcoin is an economic network – it started from nothing seven years ago and continues to grow fast. Its economics are much more interesting than its technology. The technology isn’t new or revolutionary, but the application of the technology has created a new economic phenomenon, making Bitcoin fascinating to observe.

The Bitcoin network is multi-sided, with two categories of participants, the users and the enablers. The users are merchants, consumers, investors and speculators, and the enablers are miners, exchanges and developers.

As an economic network, Bitcoin exhibits network effects, both positive and negative. Network effects are observable in many other networks, such as telephones, fax machines, social media, PC operating systems and airlines. In this blog I explore these network effects in Bitcoin from an economic perspective. Many are positive, and extremely powerful, but there is also one negative network effect that is a big challenge.

A Qualitative View

The numbers of merchants and consumers using Bitcoin may be small at the moment, but the more merchants there are accepting Bitcoin, the more consumers are likely to pay with Bitcoin; and the more consumers use Bitcoin, the more likely merchants are to accept it. This is called a cross-side network effect and it is a positive one.

There are also same-sided network effects, for example the more investors there are, the more likely the price of bitcoins to go up, and the more it goes up, the more investors are drawn in. The effect can be both positive and negative, as price drops can cause investors to leave. There is a similar same-sided network effect for speculators.

The enabler participants are dependent on the user participants for positive cross-side network effects. The more the Bitcoin network is used, the more incentives there are for exchanges to set up (to enable buying and selling bitcoins), for developers to build apps and platforms such as wallets or micropayment mechanisms, and for miners to compete for block rewards and transaction fees.

The miners are worthy of closer examination, as they underpin the whole Bitcoin network and make it work. Specifically, they compete with each other to create the blocks where bitcoin transactions are stored and they validate transactions through a proof-of-work consensus mechanism. Validated transactions are immutable, they can’t be changed (unless the network is compromised, but this would require an unfeasibly large amount of computing power and electricity). This immutability makes Bitcoin what it is: transactions cannot be duplicated, there can be no double-spend of bitcoins, the network can be trusted, and because it can be trusted, it is used more and more.

Miners make this happen because they get rewarded in bitcoins for their efforts, and bitcoins have value, so miners generate revenue. The more the network is used, the more valuable bitcoins become, so the more money miners make, the more they compete, and the more they compete, the stronger the immutability and trust of the network becomes.

As you can see, there are various sets of self-reinforcing dynamics in the Bitcoin network that interact and make it stronger and more valuable the more it used.

In the following section, I look at the mathematics of these dynamics and specifically at the economics of:

  • User numbers
  • Miners
  • Transaction scaling


A Quantative View


User Numbers


Metcalfe’s law for networks states that the value of a network is proportional to the number of connected users in the network. In the Bitcoin network there are millions of wallets that people have downloaded to transact in bitcoin, but in this analysis, I have chosen to use the daily number of unique Bitcoin addresses. Currently there are about 400,000 unique addresses used each day, a figure that has approximately doubled over the past year.


Taking the daily figures for the past year (June 2015 – May 2016), a scatter diagram of the Bitcoin market capitalisation (number of bitcoins x market price) versus the square of the unique addresses, does show a rough correlation between the two – applying a rather heroic least-squares fit to these points gives a formula:

Bitcoin network value ($bn) = 2.5 + 2.4 x 10-11 u squared where u= no. of daily unique addresses in use

This formula gives a network value of $6.3bn for 400,000 daily unique addresses on 30 May 2016, compared to the actual value of $8.1bn. The points on the scatter diagram lie from 41% below to 53% above the line produced by this formula, so it is only very approximate.

Please do not use this formula or rely on it to make any buying, selling or other decisions, it is empirical, based on only 12 months of daily data, unproven and will be different, perhaps very different, for the next 12 months of data to come. I only highlight it here to make three observations:

1.    Metcalfe’s law appears to be taking hold on the Bitcoin network - there is currently a positive correlation between the number of unique addresses used each day and the network value

2.   the value of the Bitcoin network may continue to rise significantly if the number of unique addresses increases – if the number of daily unique addresses doubles again to 800,000, this formula shows the network value may more than double to $18bn, but could be anywhere between $11bn - $28bn

3.    each additional unique address per day adds about $20,000 of value to the Bitcoin network – if the number of daily unique addresses does double, the value of each new address increases further to nearer $40,000. This illustrates the power of positive network effects when more people join and use the network.

The correlation between value and unique addresses will not hold during periods of excess speculation – as an example, the Bitcoin network value peaked at $13.9bn on 4 December 2013 when bitcoin speculation was at its highest. However, the number of unique addresses then was only 151,000. Even so, Metcalfe’s law is still becoming a useful way to understand network effects in Bitcoin and perhaps also to help identify when speculative excess is taking hold.


Miners get paid block rewards and transaction fees. A new block is created roughly every 10 minutes, and the miner winning the race to create a block gets 25 bitcoins at the moment. The reward halves every four years, with the next halving date being in July this year. After this date, miners will receive only 12.5 bitcoins per block.


Additionally, miners receive transaction fees – these are set by the sender of a transaction, and can range from 0, in which case miners may ignore the transaction (and never confirm it in a block) to 291 bitcoins in a recent case in April 2016 where it is assumed the sender made a spectacular error, perhaps transposing the fee with the principal. However, the transaction fee over the past 12 months has averaged 0.0002 bitcoins per transaction, or roughly 7 US cents.


Over the past 12 months (June 15 – May 16), miners have generated an income of $486m, split 99% in block rewards and 1% in transaction fees. Obviously, as the block rewards halve every four years, miners over time need to become less reliant on block rewards and more reliant on transaction fees. This means it is in their interest for the network to grow in use – the more transactions, the more fees and the more valuable the network (which helps compensate for the fewer block rewards). This again shows the positive network effects and incentives in the Bitcoin network.


Over time (perhaps 10+ years), the 99:1 split of block rewards to fees will reverse. Assuming that the $486m earned in revenue over the past 12 months broadly reflects the economic return required by miners to operate, at an average of 7 US cents per transaction miners should theoretically need to build capacity to support at least 7 bn transactions per year to be viable long term (at current growth rates, it will take 6 – 7 years to reach this level of transactions).


The proof-of-work consensus mechanism in Bitcoin gets criticised for consuming vast quantities of electricity to solve “pointless” algorithms, but instead you can view it as miners creating capacity for huge future growth. Even so, $486m per year to process 7bn transactions is still roughly 10 x the cost of running a comparable, conventional high volume domestic payments clearing system. I expect that the economics of mining will change significantly as the source of revenue shifts from block rewards to transaction fees, and will be very different in the future – in particular, if Bitcoin transactions do rise to the billions per year, I would expect transaction fees to be a lot lower than 7 US cents per transaction.


There is however a big “BUT” – miners may be building capacity in terms of hardware and data centres, but as I am sure you are aware, the Bitcoin protocol itself limits capacity. A block is created every ~10 minutes, each block is only 1mb in size limiting it to hold a finite number of transactions, therefore the number of transactions per second (TPS) on the Bitcoin network is finite, in fact only around 7 TPS.


This limit is already close to being reached – the miners may need the capacity to process 7bn transactions per year, or 220 TPS, but even if they have it, they are constrained by the 7 TPS of the current Bitcoin network. There is a massive gap between required and actual network capacity, and congestion is already occurring.


Congestion is an example of a negative network effect and can significantly impact the economics and use of a network (anyone taking a taxi in central London nowadays during the day can get first-hand experience of this network effect – slow, frustrating, expensive, regrettable).


So what does this mean for Bitcoins’s network economics?


Transaction Scaling


Increasing the fee for a bitcoin transaction is not really an answer. No matter how much you pay, transactions won’t get prioritised for confirmation if there are too many to handle. In fact, miners don’t necessarily prioritise transactions with high fees over those with lower fees. They want to maximise their fees per block, so their key metric is “fees per byte of transaction size” because, for various reasons, bitcoin transactions vary in size. Wallets are starting to calculate fees dynamically based on transaction size – this is probably improving confirmation and block efficiency, but it does not solve the congestion problem.


Congestion is not the only negative network effect. There are others such as price volatility, hostility in some sections of the press and academia, rejection by the banking industry, legal and regulatory uncertainty, perceptions/misconceptions of criminality and so on, but congestion is the most critical at the moment. It is clear that unless the Bitcoin network is configured to scale, then the positive network effects will reverse and the network will unravel – if users cannot get transactions confirmed they will stop initiating them, the number of unique addresses used then diminishes, the network value decreases making it unprofitable for miners, who then stop mining. The network collapses.


Solutions to the capacity issue already exist – block-size increases, segregated witness, Lightning networks to name a few. The challenge is for the enabler participants of the Bitcoin network to adopt these. For the Bitcoin network to continue growing, these solutions need to show network capacity can be scaled continuously, and can match the economic capacity miners need long term, say at least 20m transactions per day, or 7bn+ transactions per year.


In this blog, I have shown the power of Bitcoin’s positive network effects – but are they powerful enough to drive adoption of solutions to increase capacity and overcome the congestion challenge?


My guess is that we will find out over the next few months.


All data for the analysis in this blog is sourced from



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