Note: This is strictly a post about Bitcoin as a payment system. If you have something to say about Bitcoin as a store of value, a bubble or a long-term investment, you are off topic.
That said, I want to think about the interaction between transaction fees, seignorage and the number of miners. I’m sure there are people who have thought far harder about this than I have, and I dare to expect that some of those people are reading this. I hope one or more of those people will let me know whether I’m thinking about it correctly.
It seems to me that at least in the short run, the following things are more or less fixed:
a) The cost of mining (call it C)
b) The maximum possible daily transaction volume (call it T)
c) The fee per transaction at which users demand exactly T daily transactions (call it F)
d) The daily seignorage earned by miners (that is the newly minted Bitcoins that a miner receives upon successfully completing a block). (Call it S.)
Now:
1) There is free entry into mining; therefore each miner has to earn C. If there are M miners, then the total revenue earned by miners is CM.
2) That total revenue breaks into two parts: Transaction fees, which total TF per day, and seignorage, which totals S per day.
3) So CM = TF + S, or M = (TF + S)/C , where everything on the right side of that equation is more or less fixed in the short run.
4) If the seignorage were to stop flowing (as it will on some fixed date in the near future), then the equation becomes M=TF/C.
5) Currently, the value of S is about 9 times the value of TF (these are my crude off-the-cuff estimates; see below). Therefore TF/C is about 10% of (TF + S)/C. In other words, when the seignorage disappears, the number of miners should fall to about 10% of the current number.
(Of course many of the things I am treating as more-or-less fixed can change, so this is a ceteris paribus calculation, not a forecast.) My questions (below the fold for those who are reading this on my website):
Question 1: It seems to me that because the transaction fee can adjust to equilibrate supply and demand for Bitcoin as a medium of exchange, the price of Bitcoins (in terms of, say, 2020 dollars) is free to equilibrate the supply and demand for Bitcoins as a store of value. This is fundamentally different than the supply and demand for dollars, where there is only one price that must equilibrate the combined demand. Am I right about this?
Question 2: Does the rest of the above make sense?
Question 3: The above would seem to be testable, since the rate of seignorage flow has changed abruptly (and predictably) several times in the history of Bitcoin. On those occasions, has the number of miners adjusted roughly as the theory would predict? If not, why not?
Question 4: How far can the number of miners fall before Bitcoin is either insecure or perceived to be?
Appendix: Some very rough numbers:
A) A block is a megabyte. A transaction is typically about a half a kilobyte. That makes about 2000 transactions per block. At 6 blocks per hour that’s a bit more than 250,000 transactions per day. I understand that Segwit can in principle get this up to about a million, but for reasons I don’t fully understand it seems hard to go past that. I also understand that there are things like the Lightning Network that allow a lot of transactions to take place off the chain, but (in my perhaps limited understanding) they seem to require levels of trust that might undercut the motivation for using Bitcoins in the first place. So let’s conservatively write T=250,000.
B) The current transaction fee (F) seems to be hovering around $20. From this and A), we have TF=$5 million.
C) The current mining reward is 6.25 Bitcoin per block. At (conservatively) $50,000 per Bitcoin, that’s about $300,000 per block, and at 144 blocks per day that’s about $45 million.
D) So (again very approximately) TF + S = $50 million. Divide by about a million current miners to get C (the reward per miner, which must be close to the cost per miner) equal to $50.
E) Take away the seignorage and you get to TF + S = TF = $5 million. At $50 per miner, that supports 100,000 miners, which is 10% of the current number.
Feel free to correct the numbers, but I’d prefer that you correct the theory.
I think the analysis in your appendix is pretty good, though tx fees are currently about $10 on average, not $20. That said, to get to the rest of your post:
1. I think your assumption that there’s a known or knowable amount of transaction demand per day at a given fee level is a bit simplistic. There is currently a huge transaction backlog in Bitcoin. As I type, it sits at 87MB. This pool represents many transactions that will eventually be processed, but also many transactions which will not be processed (nodes generally drop transactions from the mempool if they sit unconfirmed for two weeks).
2. The fixed date in the “near” future for seignorage revenue to stop is not that near. It does halve every few years, though, so generally this is an important issue as seignorage revenue will go down over time, at least as measured in Bitcoin.
3. Question 1 – I think you’re correct.
4. Question 2 – see my points 1 & 2. Otherwise, yes, I think your analysis to that point is correct.
5. Question 3 – No, the number of miners, or more precisely the amount of has generally gone up during “halvenings” because to this point technological progress with miners has outpaced the effect of the decreased revenue. Miners have also speculated on price increases in the past. I have no idea how large that effect is, though, and I would guess that it’s decreasing as mining itself has become more professional. I suspect that in the long run, your analysis is correct, but it won’t stand up well to history to this point.
6. This is a good question which I don’t think is easy to answer. Security in Bitcoin is not binary. It exists on a scale. The question boils down somewhat to what would motivate an attack and who would be impacted by such an attack. The primary economic motivation to 51% attack Bitcoin would be for the attacker to be able to reverse one or more of their own transactions. Why would an attacker care about reversing other transactions other than to create chaos (which would, in turn, drop the value of their own Bitcoin holdings as people panicked that their transactions weren’t working). Therefore, the required “security level” of a given Bitcoin transaction depends heavily on its value. The level of assurance that any transaction is permanent is increased by each block which is mined on top of it (ie, the accumulated work that has essentially buries the transaction deeper and deeper in the blockchain). So, an attacker who would be economically motivated to 51% attack the network would probably want to reverse a very large transaction. Otherwise, it wouldn’t be rational. On the flip side, the recipient of a very large transaction may insist on several block confirmations before considering it finalized, which would mean there would be ever more work required of the attacker to reverse it. We’d have to get into calculation of the cost of SHA256 mining power, the value of the transaction, and the network difficulty level to figure this out. Additionally, it’s possible for a network to achieve finality as far as transaction security is concerned by instituting things like “checkpoints.” In the Bitcoin Cash (BCH) network, it is impossible to roll back the network by more than 10 blocks, so any transaction that is 10 blocks deep (or has 10 confirmations) can be considered to be, essentially, 100% secure even though the BCH network itself has only a few percent of the hash rate of the BTC network. BTC has no such checkpoint system in place, but in theory it could be added (after all, BCH and BTC are two forks of Bitcoin from the genesis block).
Anyway, I think it was a mistake for the Bitcoin network to not raise the blocksize beyond the SegWit upgrade (which in theory made the maximum block size around 4MB, but in practice it’s much lower). Transaction fees are very difficult to calculate because the network is now constantly running up against a supply cap on block space. This has also driven transaction fees to amounts ($10 right now) which are impractical for most people when they consider currency usage.
My personal opinion is that Bitcoin Cash has a better economic model, and the only significant difference is the dramatically higher block size cap (currently 32MB, but probably to be raised significantly down the road). One should worry at that point about the ability to set non-zero transaction fees, but I believe miners will act in their rational self-interest to form a cartel organization where minimum transaction fees are enforced by all miner participants under threat of having the rest of the network orphan blocks containing transactions deemed too low-fee. The enforcement mechanism available here is incredibly strong, certainly much stronger than an organization such as OPEC, since the enforcers can burn all of the revenue of a defector as long as they represent a majority of the mining hash power.
David (#1): You have both confirmed my expectation that I have readers who have thought much harder about this than I have and fulfilled my hope that we’d hear from at least one of those readers. Thank you on both counts. This was very helpful.
But here is what I do not understand:
I take you at your word that past halvings have not resulted in mass exoduses of miners. But I don’t see how to reconcile that with simple theory. Namely:
1) I presume there is a large population of more-or-less interchangeable potential miners. Suppose that miners earn, say, $100 a day. Then everybody who is willing to mine for $100 a day or less is already in the mining pool, and everyone else is out.
2) Now a halving comes along, and rewards fall to, say, $60 per miner. Then every miner with a reservation wage between $60 and $100 should initially want to drop out. As they drop out, rewards come back up to, say, $75 a miner in equilibrium. That means every miner with a reservation wage between $75 and $100 is gone. That should be a lot of miners.
So the simple theory predicts that a halving should trigger a mass exodus. Yet you tell me (and I believe you) that this has not happened. Do you have some insight into why not?
In general, yes, there is a large pool of generally interchangeable miners. This used to be more true than it is now, however. When Bitcoin started out, any person could mine in a meaningful way using nothing more than their home computer. As the price of Bitcoin has increased, it became worthwhile to develop specialized hardware that is many orders of magnitude faster at mining Bitcoin than any general-purpose computing device. Bitcoin mining these days effectively takes place only at an industrial scale in data centers packed floor-to-ceiling with hardware that can essentially only be used for mining Bitcoin. But with all that said, of course the laws of economics still apply and when it becomes unprofitable to mine with certain hardware or in certain areas (due to electricity rates), mining there does shut down. This is why most Bitcoin mining takes place in areas with excess electrical production and low rates.
Anyway, I think the key point here is that so far the rate of advancement of hardware and the price of Bitcoin itself has been such that even with the halving of the block reward, Bitcoin miners are making more in dollar terms than before. Whatever the reasons, though, this is observable in data.
You can see Bitcoin halvenings at this site: https://bitcoinblockhalf.com/ The TL;DR info is that halvenings happened so far on 11/28/2012, 7/9/2016, and 5/11/2020.
You can compare that to the hash rate over time here: https://www.blockchain.com/charts/hash-rate (adjust the chart to “all time” and log scale). In late 2012, hash rate held constant during the first halvening. In mid-2016, it rose throughout the year. Recently in 2020, it’s also been fairly constant.
Anyway, here are my reasons for why this is and some thoughts on the future:
1. Hardware advancements have dramatically increased the amount of hashes that a given joule of electricity can buy. This advancement will slow over time, though, as we have now essentially reached the point where hardware advances in Bitcoin mining specifically will no longer outpace those of general computing. It won’t be exponential anymore.
2. Bitcoin mining has migrated over time from more expensive geographies to less expensive geographies (in electrical cost primarily, but also rent and labor). It used to be that the majority of mining power was in the US. Now it’s in China and very little is in the US.
3. The price of Bitcoin has risen dramatically over time, so while the rewards to mining may have halved, it has not been unreasonable for people to speculate that the price may double (or more), which would lead to “real” rewards staying steady or increasing.
4. I believe the volatility of Bitcoin’s price attracts risk seekers, including miners to a degree.
5. Mining is a great tool for money laundering. One can convert relatively tainted traditional currency into clean Bitcoin by paying electric bills. This could lead to mining being somewhat resistant to typical profit-seeking behavior.
6. Similar to point 5, Bitcoin is also useful for evading capital controls. A government can prevent its citizens from exchanging cash for Bitcoin, but it is more difficult to prevent them from mining Bitcoin. Bitcoin mining has been popular in China and Venezuela in part because of this.
With all that said, I do think that the “good times” for Bitcoin mining will come to an end at some point. I would have predicted that it would happen sooner, though. I think recently the rapid price appreciation of Bitcoin may be staving off a collapse in the hash rate. I think that the price of Bitcoin is highly manipulated by Tether (aka USDT, which is the most traded cryptocurrency asset, bar none and which is what Bitcoin is actually priced in IMO), which is likely to collapse at any moment, but that’s a story for another day.
Just a heads up, I submitted a long reply which is probably caught in a spam filter or moderation queue because I included URLs in the text.
David (#3): My assistant spotted this first and fished it out of spam. About to approve it for posting, then will read and reply.
It is my understanding that when payment providers such as Paypal and Visa and companies such as Starbucks allow payment in Bitcoin, they will not actually do blockchain-based transactions for the most part, but will hold the Bitcoin and do the transaction as an internal accounting operation, avoiding transaction costs.
@Advo (#6): you’re correct that PayPal and companies offering credit cards “backed” by Bitcoin don’t actually transact in Bitcoin. In PayPal’s case, they use Paxos as custodian and all conversion between BTC and fiat is done by Paxos. There’s no ability to transfer Bitcoin into or out of PayPal, so you really just have a derivative situation there. With the “Bitcoin credit cards,” it’s a similar situation where you give custody of your Bitcoin balance to some other financial institution and they debit your account with them each time you make a transaction with the credit card. I personally don’t see the attraction of this as I could just as easily use USD-denominated accounts for these purposes and not have to worry about a very complex tax situation later.