{"type":"rich","version":"1.0","title":"Eric Voskuil [ARCHIVE] wrote","author_name":"Eric Voskuil [ARCHIVE] (npub1sg…ppx3c)","author_url":"https://yabu.me/npub1sgs97fe0n9wehe6zw7drcxdz4cy9yt9pfqjv8gasz5jlk4zezc0quppx3c","provider_name":"njump","provider_url":"https://yabu.me","html":"📅 Original date posted:2022-07-09\n📝 Original message:\u003e Due to lost coins, a tail emission/fixed reward actually results in a stable money supply. Not an (monetarily) inflationary supply.\n\nThis observation is not a proof of lost coins, that is an assumption. It is the provable consequence of market, as opposed to monopoly, production.\n\nhttps://github.com/libbitcoin/libbitcoin-system/wiki/Inflation-Principle\n\nMises’ unfortunate error in the application of the Cantillon Effect to gold perpetuates this misperception. One could imagine applying this theory to all goods, not just money, and conclude perpetual loss of value in everything produced, as a consequence of production. One might then be tempted to attribute the fact that this is not observable to loss/depreciation/consumption. While it is certainly possible that the amount of gold produced every year is offset by the amount lost, this of course implies that all of it is lost.\n\n“Circulation” does not determine demand, all money is always held by someone. Changing hands only changes who owns the money, not its purchasing power. See Rothbard’s critique of monetary “velocity”.\n\ne\n\n\u003e On Jul 9, 2022, at 05:47, Peter Todd via bitcoin-dev \u003cbitcoin-dev at lists.linuxfoundation.org\u003e wrote:\n\u003e \n\u003e New blog post:\n\u003e \n\u003e https://petertodd.org/2022/surprisingly-tail-emission-is-not-inflationary\n\u003e \n\u003e tl;dr: Due to lost coins, a tail emission/fixed reward actually results in a\n\u003e stable money supply. Not an (monetarily) inflationary supply.\n\u003e \n\u003e ...and for the purposes of reply/discussion, attached is the article itself in\n\u003e markdown format:\n\u003e \n\u003e ---\n\u003e layout: post\n\u003e title:  \"Surprisingly, Tail Emission Is Not Inflationary\"\n\u003e date:   2022-07-09\n\u003e tags:\n\u003e - bitcoin\n\u003e - monero\n\u003e ---\n\u003e \n\u003e At present, all notable proof-of-work currencies reward miners with both a block\n\u003e reward, and transaction fees. With most currencies (including Bitcoin) phasing\n\u003e out block rewards over time. However in no currency have transaction fees\n\u003e consistently been more than 5% to 10% of the total mining\n\u003e reward[^fee-in-reward], with the exception of Ethereum, from June 2020 to Aug 2021.\n\u003e To date no proof-of-work currency has ever operated solely on transaction\n\u003e fees[^pow-tweet], and academic analysis has found that in this condition block\n\u003e generation is unstable.[^instability-without-block-reward] To paraphrase Andrew\n\u003e Poelstra, it's a scary phase change that no other coin has gone through.[^apoelstra-quote]\n\u003e \n\u003e [^pow-tweet]: [I asked on Twitter](https://twitter.com/peterktodd/status/1543231264597090304) and no-one replied with counter-examples.\n\u003e \n\u003e [^fee-in-reward]: [Average Fee Percentage in Total Block Reward](https://bitinfocharts.com/comparison/fee_to_reward-btc-eth-bch-ltc-doge-xmr-bsv-dash-zec.html#alltime)\n\u003e \n\u003e [^instability-without-block-reward]: [On the Instability of Bitcoin Without the Block Reward](https://www.cs.princeton.edu/~arvindn/publications/mining_CCS.pdf)\n\u003e \n\u003e [^apoelstra-quote]: [From a panel at TABConf 2021](https://twitter.com/peterktodd/status/1457066946898317316)\n\u003e \n\u003e Monero has chosen to implement what they call [tail\n\u003e emission](https://www.getmonero.org/resources/moneropedia/tail-emission.html):\n\u003e a fixed reward per block that continues indefinitely. Dogecoin also has a fixed\n\u003e reward, which they widely - and incorrectly - refer to as an \"abundant\" supply[^dogecoin-abundant].\n\u003e \n\u003e [^dogecoin-abundant]: Googling \"dogecoin abundant\" returns dozens of hits.\n\u003e \n\u003e This article will show that a fixed block reward does **not** lead to an\n\u003e abundant supply. In fact, due to the inevitability of lost coins, a fixed\n\u003e reward converges to a **stable** monetary supply that is neither inflationary\n\u003e nor deflationary, with the total supply proportional to rate of tail emission\n\u003e and probability of coin loss.\n\u003e \n\u003e Credit where credit is due: after writing the bulk of this article I found out\n\u003e that Monero developer [smooth_xmr](https://www.reddit.com/user/smooth_xmr/)\n\u003e also observed that tail emission results in a stable coin supply\n\u003e [a few years ago](https://www.reddit.com/r/Monero/comments/4z0azk/maam_28_monero_ask_anything_monday/d6sixyi/).\n\u003e There's probably others too: it's a pretty obvious result.\n\u003e \n\u003e \n\u003e \u003cdiv markdown=\"1\" class=\"post-toc\"\u003e\n\u003e # Contents\n\u003e {:.no_toc}\n\u003e 0. TOC\n\u003e {:toc}\n\u003e \u003c/div\u003e\n\u003e \n\u003e ## Modeling the Fixed-Reward Monetary Supply\n\u003e \n\u003e Since the number of blocks is large, we can model the monetary supply as a\n\u003e continuous function $$N(t)$$, where $$t$$ is a given moment in time. If the\n\u003e block reward is fixed we can model the reward as a slope $$k$$ added to an\n\u003e initial supply $$N_0$$:\n\u003e \n\u003e $$\n\u003e N(t) = N_0 + kt\n\u003e $$\n\u003e \n\u003e Of course, this isn't realistic as coins are constantly being lost due to\n\u003e deaths, forgotten passphrases, boating accidents, etc. These losses are\n\u003e independent: I'm not any more or less likely to forget my passphrase because\n\u003e you recently lost your coins in a boating accident — an accident I probably\n\u003e don't even know happened. Since the number of individual coins (and their\n\u003e owners) is large — as with the number of blocks — we can model this loss as\n\u003e though it happens continuously.\n\u003e \n\u003e Since coins can only be lost once, the *rate* of coin loss at time $$t$$ is\n\u003e proportional to the total supply *at that moment* in time. So let's look at the\n\u003e *first derivative* of our fixed-reward coin supply:\n\u003e \n\u003e $$\n\u003e \\frac{dN(t)}{dt} = k\n\u003e $$\n\u003e \n\u003e ...and subtract from it the lost coins, using $$\\lambda$$ as our [coin loss\n\u003e constant](https://en.wikipedia.org/wiki/Exponential_decay):\n\u003e \n\u003e $$\n\u003e \\frac{dN(t)}{dt} = k - \\lambda N(t)\n\u003e $$\n\u003e \n\u003e That's a first-order differential equation, which can be easily solved with\n\u003e separation of variables to get:\n\u003e \n\u003e $$\n\u003e N(t) = \\frac{k}{\\lambda} - Ce^{-\\lambda t}\n\u003e $$\n\u003e \n\u003e To remove the integration constant $$C$$, let's look at $$t = 0$$, where the\n\u003e coin supply is $$N_0$$:\n\u003e \n\u003e $$\n\u003e \\begin{align}\n\u003e    N_0 \u0026= \\frac{k}{\\lambda} - Ce^{-\\lambda 0} = \\frac{k}{\\lambda} - C \\\\\n\u003e      C \u0026= \\frac{k}{\\lambda} - N_0\n\u003e \\end{align}\n\u003e $$\n\u003e \n\u003e Thus:\n\u003e \n\u003e $$\n\u003e \\begin{align}\n\u003e    N(t) \u0026= \\frac{k}{\\lambda} - \\left(\\frac{k}{\\lambda} - N_0 \\right)e^{-\\lambda t} \\\\\n\u003e         \u0026= \\frac{k}{\\lambda} + \\left(N_0 - \\frac{k}{\\lambda} \\right)e^{-\\lambda t}\n\u003e \\end{align}\n\u003e $$\n\u003e \n\u003e \n\u003e ## Long Term Coin Supply\n\u003e \n\u003e It's easy to see that in the long run, the second half of the coin supply\n\u003e equation goes to zero because $$\\lim_{t \\to \\infty} e^{-\\lambda t} = 0$$:\n\u003e \n\u003e $$\n\u003e \\begin{align}\n\u003e    \\lim_{t \\to \\infty} N(t) \u0026= \\lim_{t \\to \\infty} \\left[ \\frac{k}{\\lambda} + \\left(N_0 - \\frac{k}{\\lambda} \\right)e^{-\\lambda t} \\right ] = \\frac{k}{\\lambda} \\\\\n\u003e                   N(\\infty) \u0026= \\frac{k}{\\lambda}\n\u003e \\end{align}\n\u003e $$\n\u003e \n\u003e An intuitive explanation for this result is that in the long run, the initial\n\u003e supply $$N_0$$ doesn't matter, because approximately all of those coins will\n\u003e eventually be lost. Thus in the long run, the coin supply will converge towards\n\u003e $$\\frac{k}{\\lambda}$$, the point where coins are created just as fast as they\n\u003e are lost.\n\u003e \n\u003e \n\u003e ## Short Term Dynamics and Economic Considerations\n\u003e \n\u003e Of course, the intuitive explanation for why supply converges to\n\u003e $$\\frac{k}{\\lambda}$$, also tells us that supply must converge fairly slowly:\n\u003e if 1% of something is lost per year, after 100 years 37% of the initial supply\n\u003e remains. It's not clear what the rate of lost coins actually is in a mature,\n\u003e valuable, coin. But 1%/year is likely to be a good guess — quite possibly less.\n\u003e \n\u003e In the case of Monero, they've introduced tail emission at a point where it\n\u003e represents a 0.9% apparent monetary inflation rate[^p2pool-tail]. Since the number of\n\u003e previously lost coins, and the current rate of coin loss, is\n\u003e unknown[^unknowable] it's not possible to know exactly what the true monetary\n\u003e inflation rate is right now. But regardless, the rate will only converge\n\u003e towards zero going forward.\n\u003e \n\u003e [^unknowable]: Being a privacy coin with [shielded amounts](https://localmonero.co/blocks/richlist), it's not even possible to get an estimate of the total amount of XMR in active circulation.\n\u003e \n\u003e [^p2pool-tail]: P2Pool operates [a page with real-time date figures](https://p2pool.io/tail.html).\n\u003e \n\u003e If an existing coin decides to implement tail emission as a means to fund\n\u003e security, choosing an appropriate emission rate is simple: decide on the\n\u003e maximum amount of inflation you are willing to have in the worst case, and set\n\u003e the tail emission accordingly. In reality monetary inflation will be even lower\n\u003e on day zero due to lost coins, and in the long run, it will converge towards\n\u003e zero.\n\u003e \n\u003e The fact is, economic volatility dwarfs the effect of small amounts of\n\u003e inflation. Even a 0.5% inflation rate over 50 years only leads to a 22% drop.\n\u003e Meanwhile at the time of writing, Bitcoin has dropped 36% in the past year, and\n\u003e gained 993% over the past 5 years. While this discussion is a nice excuse to\n\u003e use some mildly interesting math, in the end it's totally pedantic.\n\u003e \n\u003e ## Could Bitcoin Add Tail Emission?\n\u003e \n\u003e ...and why could Monero?\n\u003e \n\u003e Adding tail emission to Bitcoin would be a hard fork: a incompatible rule\n\u003e change that existing Bitcoin nodes would reject as invalid. While Monero was\n\u003e able to get sufficiently broad consensus in the community to implement tail\n\u003e emission, it's unclear at best if it would ever be possible to achieve that for\n\u003e the much larger[^btc-vs-xmr-market-cap] Bitcoin. Additionally, Monero has a\n\u003e culture of frequent hard forks that simply does not exist in Bitcoin.\n\u003e \n\u003e [^btc-vs-xmr-market-cap]: [As of writing](https://web.archive.org/web/20220708143920/https://www.coingecko.com/), the apparent market cap of Bitcoin is $409 billion, almost 200x larger than Monero's $2.3 billion.\n\u003e \n\u003e Ultimately, as long as a substantial fraction of the Bitcoin community continue\n\u003e to run full nodes, the only way tail emission could ever be added to Bitcoin is\n\u003e by convincing that same community that it is a good idea.\n\u003e \n\u003e \n\u003e ## Footnotes\n\u003e _______________________________________________\n\u003e bitcoin-dev mailing list\n\u003e bitcoin-dev at lists.linuxfoundation.org\n\u003e https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev\n-------------- next part --------------\nAn HTML attachment was scrubbed...\nURL: \u003chttp://lists.linuxfoundation.org/pipermail/bitcoin-dev/attachments/20220709/3e785ca0/attachment-0001.html\u003e"}