Bitcoin Box

A magazine dedicated to all things Bitcoin


The Wasted Electricity Objection to Bitcoin, Part II

author: Vitalik Buterin
published: 2011-05-29 10:47:20 UTC

In the last part of this series, I talked about why the electricity used by the Bitcoin network is not, as some believe, as unnecessary waste. Now, let us see just how much electricity is being used up. According to the mining hardware comparison table, the best mining computers can perform 2.5 megahashes per joule. The entire network does 3.5 terahashes per second, so assuming that in reality mining is, on average, a fifth as efficient as the maximum (0.5 Mhash/J) with casual CPU miners and people using suboptimal GPUs, we get a figure of 7 million joules per second, or 7000 kW. With an electricity cost of 11 cents per kWh, we find that maintaining the network costs about $18480 per day. This is expensive: at the current 8.3 USD/BTC exchange rate, 250000 BTC sent in the past 24 hours, or $2.08 million USD, we get an average transaction cost of 1%.

Even this is a misleading figure: as I have previously mentioned, the majority of bitcoin transactions do not, in fact, entirely represent one person sending bitcoin to another. Doing further research since writing that article, I have found the cause behind the excess in transactions: every transaction must be linked to a previous transaction, so when you receive 200000 BTC all at once and spend 1000, the system creates a transaction with 1 input, the 200000 BTC you received, and two outputs, 1000 to your recipient and 199000 back to another one of your own addresses. Thus, if those 200000 BTC get slowly spent, one thousand at a time, a transaction volume of 201 million BTC will be seen. This is an extreme case, and it is difficult to tell what the average case is since it depends on the precise distribution of the transaction sizes and how people spend their money, but the general principle applies. The true transaction cost may be as high as 10%.

This is extreme, but I believe the problem will decrease considerably in the short term, and even more in the long term. In the short term, Bitcoin is set to become a much more specialized enterprise: version 0.3.22 of Bitcoin will remove the "generate coins" GUI option from the client (although the ability to generate coins is still there in the command line), removing the casual CPU miners from the equation. Economically, CPU mining already does not make sense, and most CPU miners do so because they do not realize how unprofitable mining is, so removing CPU miners allows the market to enforce a standard of energy efficiency since without them everyone involved will be a professional miner, calculating whether or not mining for them will be profitable. The market will continue to be more and more optimized: as GPU mining becomes more and more of a for-profit enterprise, with mining companies listed on the GLBSE, the higher end mining computers will become more and more necessary, and the lower end miners will be forced to shut down as mining revenue approaches cost. FPGA mining promises a value of 20 megahashes per joule, but I will ignore these in my analysis so far; their prevalence will increase difficulty, counteracting the energy efficiency gains, and the effects of this will take weeks to sort themselves out. If the average mining efficiency increases to 2 megahashes per joule, the transaction cost will reduce to 0.25%, or, with our conservative estimate, 2.5%.

From there, however, there are two further improvements that can be made: first, the electricity used to mine is ultimately released as heat. Therefore, it may become standard practice, with downloadable packages preconfigured for that very purpose, for homes in cold climates to turn on GPU mining (on a low priority, so web browsing and other computations would take precedence and not be impeded by it) as part of their heating system, making the electricity essentially free since it would otherwise be used by the main heating system. Secondly, there exist supercomputers that run at over 500 megaflops per watt - with the rate of 12.7 flops per hash used here, 40 megahashes per joule. This seems like it will make Bitcoin mining take up far less electricity, but, just like FPGA miners, this is not the case: if the cost of mining bitcoin decreases, mining will be more profitable, so there will be more miners until profitability returns to what it was before (I will explain this in more detail below). It is important to remind ourselves once again that the loss of CPU miners does not follow this principle because CPU miners are casual users and do not make economic calculations of profitability.

But, once the market stabilizes, what can increase or reduce the electricity expenditure of the grid? Let us consider the economic calculations that miners make, from first principles:

1) Revenue > Cost
2) Block creation reward * block creation chance > power expenditure in watts * 600 (1 block per 10 min) * dollars per joule
3) BTC price * (money creation + transaction fees) * miner Mhash/s / network Mhash/s > watts * 6 * cents per joule
4) BTC price * (money creation + transaction fees) * miner Mhash/J > average Mhash/s * number of miners * cents per kWh / 600000

Let us make the simplifying assumption that all miners have equal Mhash/s and Mhash/J. The latter should occur naturally as miners shift to the best gear possible, and the former can be justified by saying that a powerful miner is equivalent to a hundred normal miners.

5) BTC price * (money creation + transaction fees) * miner Mhash/s / watts > miner Mhash/s * number of miners * cents per kWh / 600000
6) BTC price * (money creation + transaction fees) > watts * number of miners * cents per kWh / 600000
7) network power consumption < BTC price * (money creation + transaction fees) / cents per kWh * 600000

As the market approaches full efficiency, the limit of network power consumption will be equal to the expression on the right. What does this tell us? Essentially, the cost network power consumption is not influenced at all by the level of technology, and it is only influenced by the revenue of generating new blocks.

Right now, demand for mining is artificially high because of the 50 BTC reward for creating a new block. However, this value is set to decrease to 25 BTC in 2013, and continue decreasing exponentially. What happens when money creation reaches zero? In the long term, once this reward disappears, what level would the market make the transaction cost settle down to? The equation of the market that we have deduced does not provide for a natural level of transaction fees. Logically, the answer is the electricity cost of including a transaction in a block as opposed to not including it divided by the probability that that miner will be the one that solves the block, or, simplifying, the electricity cost hashing a transaction multiplied by the number of miners. This value will never be reached, since it would result in a loss for all miners, but transaction costs would approach it, perhaps going within one order of magnitude. Transactions do not need to be hashed every time an attempt at solving the block is made, fortunately - if that were the case, then there would be a strong incentive for a miner not to include any transactions. Taking a random sample from here, the average transaction is 7500 bytes long equivalent to 60 hashes (80 bytes, rounded up to 128 by the SHA256 algorithm) or 30 block-solving attempts. Right now, the number of block solving hashes done by the network is 3.2 trillion per second, while the number of transaction including hashes is:

0.06 transactions per second * 60 equivalent hashes per transaction * number of miners

We will estimate the latter figure, discounting casual CPU miners, as being:

3,000,000 Mhash/s * 0.4 (not in pools) / 100 Mhash/s per computer (estimate) = 12000

This brings us to 43200 transaction hashes per second, an insignificant amount compared to the 3.2 trillion done to solve the block. Thus, the theoretical average transaction fee is extremely low compared to the mining revenue we see right now. Thus, there are three scenarios that could arise in the very long term:

  1. Transaction fees are somewhere close to this minimum, and the network power consumption is very low - even smaller than what we have now.
  2. The bitcoin client enforces a minimum transaction fee at an arbitrarily high value (eg. the 0.0005 BTC it is now; probably lower then), and transactions hoping for near-instant acceptance compete with each other, making many transaction fees multiples of the minimum.
  3. People offer transaction fees benevolently, understanding that having a substantial number of miners is necessary for network security (I will get to this later) and transaction revenue is substantial, perhaps as high as 50 BTC total.

The average total transaction revenue right now, from a random block explorer sample, is 0.038 BTC per block. Thus, without the money creation revenue, the network power right now would fall by a factor of 1315, to 2.73 Ghash/s, or $14 per day. Thus, we seem to be at the second scenario at the moment, so the first seems unlikely to take hold.

It is important to keep in mind just how much power we should have working on the blockchain: more than any single attacker could muster. It is important to note that nowhere in the economics of mining is this value calculated, so we will have to rely on competition and benevolence to provide security. However, the security of the network will increase not only with the amount of mining done, but also with the type of mining done - a more specialized mining economy, with GPUs and supercomputers, is more robust. The role of specialized supercomputer miners and GUI miners is in fact very similar to that of a fiat currency mint - just as a fiat currency mint produces bills with holographic and other techniques that conventional printers do not have, specialized miners will secure the network with computing efficiency that attackers do not have.

There are two possible threats to the Bitcoin block chain: botnets and governments. Botnets run on average computers, and they need to run far below 100% CPU to remain undetected, so as the network becomes more specialized they will become weaker and weaker. Governments, on the other hand, are a potential problem - if mining falls into the control of large institutions, governments have the power to compel large institutions to secretly manipulate the network to serve them, a power which they do not, in practice, hold over individuals. But if Bitcoin becomes that important, then it is likely that some governments will provide computing power to the network benevolently, in order to prevent other governments from attacking it. Right now, this is all speculation; we will have to revisit this question in several years when we see what the demographics of Bitcoin miners actually end up being.

Arguably, it is necessary for Bitcoin to have a strong mining community at the start to protect the block chain while it is still nascent, but ultimately the long-term trend is that the Bitcoin mining network, relative to the Bitcoin system as a whole, will decrease in size and importance. It is true that interest in mining is growing very rapidly at the moment, but this is a short-term trend due to the sudden increase in Bitcoin prices, which, as we have deduced, the number of miners grows to become proportional to. In the long term, Bitcoin price growth will stabilize, the Bitcoin economy will grow and the 1-10% transaction cost that I talked about at the start of this article will not last.

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