From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: from smtp3.osuosl.org (smtp3.osuosl.org [140.211.166.136]) by lists.linuxfoundation.org (Postfix) with ESMTP id 6F7ECC002D for ; Sun, 10 Jul 2022 10:18:33 +0000 (UTC) Received: from localhost (localhost [127.0.0.1]) by smtp3.osuosl.org (Postfix) with ESMTP id 43F0960A74 for ; Sun, 10 Jul 2022 10:18:33 +0000 (UTC) DKIM-Filter: OpenDKIM Filter v2.11.0 smtp3.osuosl.org 43F0960A74 Authentication-Results: smtp3.osuosl.org; dkim=pass (2048-bit key) header.d=gmail.com header.i=@gmail.com header.a=rsa-sha256 header.s=20210112 header.b=jYjL1SXQ X-Virus-Scanned: amavisd-new at osuosl.org X-Spam-Flag: NO X-Spam-Score: -2.097 X-Spam-Level: X-Spam-Status: No, score=-2.097 tagged_above=-999 required=5 tests=[BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, DKIM_VALID_EF=-0.1, FREEMAIL_FROM=0.001, HTML_MESSAGE=0.001, RCVD_IN_DNSWL_NONE=-0.0001, SPF_HELO_NONE=0.001, SPF_PASS=-0.001, URI_DOTEDU=0.001] autolearn=ham autolearn_force=no Received: from smtp3.osuosl.org ([127.0.0.1]) by localhost (smtp3.osuosl.org [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id Wpd9vHJw4xeU for ; Sun, 10 Jul 2022 10:18:30 +0000 (UTC) X-Greylist: whitelisted by SQLgrey-1.8.0 DKIM-Filter: OpenDKIM Filter v2.11.0 smtp3.osuosl.org 2A2AE60A72 Received: from mail-vk1-xa31.google.com (mail-vk1-xa31.google.com [IPv6:2607:f8b0:4864:20::a31]) by smtp3.osuosl.org (Postfix) with ESMTPS id 2A2AE60A72 for ; Sun, 10 Jul 2022 10:18:30 +0000 (UTC) Received: by mail-vk1-xa31.google.com with SMTP id b81so1280516vkf.1 for ; Sun, 10 Jul 2022 03:18:29 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20210112; h=mime-version:references:in-reply-to:from:date:message-id:subject:to; bh=0Cn9eSrKTO6TY4YXtexGah25t5/tmfiRtpyQOGSu6FE=; b=jYjL1SXQiYNP7uOz5GNCde5Rv0Ul23D47HPoYUQe7pQjfIfjp2AXHpe6cDlKEN9a1S AQ9Jo91d0P6g2Bx26A35Z5Zk38f55h4yNMUIRKZvjEAPMiy9dn3bzGkmVNfl48djG8vG ePP0053DH/d4n612mhTU5LrRb9OTSTIQAIZ4tCPcpWmaMl14sgIABOVEn5HEmTU3Taf1 RsUUv7xHUp0i5ZAesyolk/cGy01G5xaKMSNcr5kNJKNkhnsIOlLnMrQsPWQJn+uevJZN vVLK0C1KKuGf14tCxtMd7+VG/UWcP9q52aj6OPCcteyaP0TDyklB3T7PDPt29/1pXRAq 2YkA== X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20210112; h=x-gm-message-state:mime-version:references:in-reply-to:from:date :message-id:subject:to; bh=0Cn9eSrKTO6TY4YXtexGah25t5/tmfiRtpyQOGSu6FE=; b=3RxNEgbbQItzrq30nNpjY0Yr/81XAqy8UuiIDvLcj3a08wOa/TVrjqmqioCvpQOQXZ 5weWVDSm4lZv0zBWJeZ45PinwYKVUe99IwdR0TCcIUL8khczV6YZVepGSD2TLomuScfy aiFMNVM0IdpyvecmwCHnoDetSBO1ti3IEBseRr3A9WzW9jucbPRfHoP37a7rfQJlv23u wTHyddPY9IHnctk3E6BgFAWcI3thiH9Sg2sDkfv4FNvCeciZKGB9XrLxMKdPZz2zwmNd mVdm2Rwm/zvZqYfJ8CzZKUG5FFUiBcMvuQ5MyHB4TrISWpiNYRVKn7hpB7yIYVD447Fg GXIg== X-Gm-Message-State: AJIora/U8O6Lj3C2i/QQMvQfLTGa1xIklRB3DiO/tLKz4Y5xxJGxSwZE hiab9x6ZZ6KclbpVdI4jkC0TsDR2mslbE2ANK5bm5AWL X-Google-Smtp-Source: AGRyM1sDBrcR8CxP6bTR12hxLJf4FunL3Q2+r3cX39tyMKsxZ1HYacnSy1fSUscOZtLdWmi2tqQ1Y9XBwcyDx/i//1o= X-Received: by 2002:a1f:17d2:0:b0:374:3ca2:def3 with SMTP id 201-20020a1f17d2000000b003743ca2def3mr4628449vkx.18.1657448308792; Sun, 10 Jul 2022 03:18:28 -0700 (PDT) MIME-Version: 1.0 References: In-Reply-To: From: Jacob Eliosoff Date: Sun, 10 Jul 2022 05:18:17 -0500 Message-ID: To: Peter Todd , Bitcoin Protocol Discussion Content-Type: multipart/alternative; boundary="000000000000ade02205e370c1b4" X-Mailman-Approved-At: Sun, 10 Jul 2022 10:24:44 +0000 Subject: Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary X-BeenThere: bitcoin-dev@lists.linuxfoundation.org X-Mailman-Version: 2.1.15 Precedence: list List-Id: Bitcoin Protocol Discussion List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-List-Received-Date: Sun, 10 Jul 2022 10:18:33 -0000 --000000000000ade02205e370c1b4 Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable > Credit where credit is due: after writing the bulk of this article I found out > that Monero developer [smooth_xmr](https://www.reddit.com/user/smooth_xmr= / ) > also observed that tail emission results in a stable coin supply > [a few years ago]( https://www.reddit.com/r/Monero/comments/4z0azk/maam_28_monero_ask_anything= _monday/d6sixyi/ ). > There's probably others too: it's a pretty obvious result. Fwiw, Joe Lubin, April 2014: "The expected rate of annual loss and destruction of ETH will balance the rate of issuance. Under this dynamic, a quasi-steady state is reached and the amount of extant ETH no longer grows." https://blog.ethereum.org/2014/04/10/the-issuance-model-in-ethereum/ As you say, probably an observation various people have made. (Ethereum has had some updates to its issuance model since 2014, in particular EIP-1559 and the block reward reduction coming with PoS. But they've had a fixed rather than halving block subsidy since launch so the question of whether it implied infinite supply often came up.) On Sat, Jul 9, 2022, 7:47 AM Peter Todd via bitcoin-dev < bitcoin-dev@lists.linuxfoundation.org> wrote: > New blog post: > > https://petertodd.org/2022/surprisingly-tail-emission-is-not-inflationary > > tl;dr: Due to lost coins, a tail emission/fixed reward actually results i= n > a > stable money supply. Not an (monetarily) inflationary supply. > > ...and for the purposes of reply/discussion, attached is the article > itself in > markdown format: > > --- > layout: post > title: "Surprisingly, Tail Emission Is Not Inflationary" > date: 2022-07-09 > tags: > - bitcoin > - monero > --- > > At present, all notable proof-of-work currencies reward miners with both = a > block > reward, and transaction fees. With most currencies (including Bitcoin) > phasing > out block rewards over time. However in no currency have transaction fees > consistently been more than 5% to 10% of the total mining > reward[^fee-in-reward], with the exception of Ethereum, from June 2020 to > Aug 2021. > To date no proof-of-work currency has ever operated solely on transaction > fees[^pow-tweet], and academic analysis has found that in this condition > block > generation is unstable.[^instability-without-block-reward] To paraphrase > Andrew > Poelstra, it's a scary phase change that no other coin has gone > through.[^apoelstra-quote] > > [^pow-tweet]: [I asked on Twitter]( > https://twitter.com/peterktodd/status/1543231264597090304) and no-one > replied with counter-examples. > > [^fee-in-reward]: [Average Fee Percentage in Total Block Reward]( > https://bitinfocharts.com/comparison/fee_to_reward-btc-eth-bch-ltc-doge-x= mr-bsv-dash-zec.html#alltime > ) > > [^instability-without-block-reward]: [On the Instability of Bitcoin > Without the Block Reward]( > https://www.cs.princeton.edu/~arvindn/publications/mining_CCS.pdf) > > [^apoelstra-quote]: [From a panel at TABConf 2021]( > https://twitter.com/peterktodd/status/1457066946898317316) > > Monero has chosen to implement what they call [tail > emission]( > https://www.getmonero.org/resources/moneropedia/tail-emission.html): > a fixed reward per block that continues indefinitely. Dogecoin also has a > fixed > reward, which they widely - and incorrectly - refer to as an "abundant" > supply[^dogecoin-abundant]. > > [^dogecoin-abundant]: Googling "dogecoin abundant" returns dozens of hits= . > > This article will show that a fixed block reward does **not** lead to an > abundant supply. In fact, due to the inevitability of lost coins, a fixed > reward converges to a **stable** monetary supply that is neither > inflationary > nor deflationary, with the total supply proportional to rate of tail > emission > and probability of coin loss. > > Credit where credit is due: after writing the bulk of this article I foun= d > out > that Monero developer [smooth_xmr](https://www.reddit.com/user/smooth_xmr= / > ) > also observed that tail emission results in a stable coin supply > [a few years ago]( > https://www.reddit.com/r/Monero/comments/4z0azk/maam_28_monero_ask_anythi= ng_monday/d6sixyi/ > ). > There's probably others too: it's a pretty obvious result. > > >
> # Contents > {:.no_toc} > 0. TOC > {:toc} >
> > ## Modeling the Fixed-Reward Monetary Supply > > Since the number of blocks is large, we can model the monetary supply as = a > continuous function $$N(t)$$, where $$t$$ is a given moment in time. If t= he > block reward is fixed we can model the reward as a slope $$k$$ added to a= n > initial supply $$N_0$$: > > $$ > N(t) =3D N_0 + kt > $$ > > Of course, this isn't realistic as coins are constantly being lost due to > deaths, forgotten passphrases, boating accidents, etc. These losses are > independent: I'm not any more or less likely to forget my passphrase > because > you recently lost your coins in a boating accident =E2=80=94 an accident = I probably > don't even know happened. Since the number of individual coins (and their > owners) is large =E2=80=94 as with the number of blocks =E2=80=94 we can = model this loss as > though it happens continuously. > > Since coins can only be lost once, the *rate* of coin loss at time $$t$$ = is > proportional to the total supply *at that moment* in time. So let's look > at the > *first derivative* of our fixed-reward coin supply: > > $$ > \frac{dN(t)}{dt} =3D k > $$ > > ...and subtract from it the lost coins, using $$\lambda$$ as our [coin lo= ss > constant](https://en.wikipedia.org/wiki/Exponential_decay): > > $$ > \frac{dN(t)}{dt} =3D k - \lambda N(t) > $$ > > That's a first-order differential equation, which can be easily solved wi= th > separation of variables to get: > > $$ > N(t) =3D \frac{k}{\lambda} - Ce^{-\lambda t} > $$ > > To remove the integration constant $$C$$, let's look at $$t =3D 0$$, wher= e > the > coin supply is $$N_0$$: > > $$ > \begin{align} > N_0 &=3D \frac{k}{\lambda} - Ce^{-\lambda 0} =3D \frac{k}{\lambda} - = C \\ > C &=3D \frac{k}{\lambda} - N_0 > \end{align} > $$ > > Thus: > > $$ > \begin{align} > N(t) &=3D \frac{k}{\lambda} - \left(\frac{k}{\lambda} - N_0 > \right)e^{-\lambda t} \\ > &=3D \frac{k}{\lambda} + \left(N_0 - \frac{k}{\lambda} > \right)e^{-\lambda t} > \end{align} > $$ > > > ## Long Term Coin Supply > > It's easy to see that in the long run, the second half of the coin supply > equation goes to zero because $$\lim_{t \to \infty} e^{-\lambda t} =3D 0$= $: > > $$ > \begin{align} > \lim_{t \to \infty} N(t) &=3D \lim_{t \to \infty} \left[ > \frac{k}{\lambda} + \left(N_0 - \frac{k}{\lambda} \right)e^{-\lambda t} > \right ] =3D \frac{k}{\lambda} \\ > N(\infty) &=3D \frac{k}{\lambda} > \end{align} > $$ > > An intuitive explanation for this result is that in the long run, the > initial > supply $$N_0$$ doesn't matter, because approximately all of those coins > will > eventually be lost. Thus in the long run, the coin supply will converge > towards > $$\frac{k}{\lambda}$$, the point where coins are created just as fast as > they > are lost. > > > ## Short Term Dynamics and Economic Considerations > > Of course, the intuitive explanation for why supply converges to > $$\frac{k}{\lambda}$$, also tells us that supply must converge fairly > slowly: > if 1% of something is lost per year, after 100 years 37% of the initial > supply > remains. It's not clear what the rate of lost coins actually is in a > mature, > valuable, coin. But 1%/year is likely to be a good guess =E2=80=94 quite = possibly > less. > > In the case of Monero, they've introduced tail emission at a point where = it > represents a 0.9% apparent monetary inflation rate[^p2pool-tail]. Since > the number of > previously lost coins, and the current rate of coin loss, is > unknown[^unknowable] it's not possible to know exactly what the true > monetary > inflation rate is right now. But regardless, the rate will only converge > towards zero going forward. > > [^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. > > [^p2pool-tail]: P2Pool operates [a page with real-time date figures]( > https://p2pool.io/tail.html). > > If an existing coin decides to implement tail emission as a means to fund > security, choosing an appropriate emission rate is simple: decide on the > maximum amount of inflation you are willing to have in the worst case, an= d > set > the tail emission accordingly. In reality monetary inflation will be even > lower > on day zero due to lost coins, and in the long run, it will converge > towards > zero. > > The fact is, economic volatility dwarfs the effect of small amounts of > inflation. Even a 0.5% inflation rate over 50 years only leads to a 22% > drop. > Meanwhile at the time of writing, Bitcoin has dropped 36% in the past > year, and > gained 993% over the past 5 years. While this discussion is a nice excuse > to > use some mildly interesting math, in the end it's totally pedantic. > > ## Could Bitcoin Add Tail Emission? > > ...and why could Monero? > > Adding tail emission to Bitcoin would be a hard fork: a incompatible rule > change that existing Bitcoin nodes would reject as invalid. While Monero > was > able to get sufficiently broad consensus in the community to implement ta= il > emission, it's unclear at best if it would ever be possible to achieve > that for > the much larger[^btc-vs-xmr-market-cap] Bitcoin. Additionally, Monero has= a > culture of frequent hard forks that simply does not exist in Bitcoin. > > [^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 th= an > Monero's $2.3 billion. > > Ultimately, as long as a substantial fraction of the Bitcoin community > continue > to run full nodes, the only way tail emission could ever be added to > Bitcoin is > by convincing that same community that it is a good idea. > > > ## Footnotes > _______________________________________________ > bitcoin-dev mailing list > bitcoin-dev@lists.linuxfoundation.org > https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev > --000000000000ade02205e370c1b4 Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable
> Credit where credit is due: after = writing the bulk of this article I found out
> th= at Monero developer [smooth_xmr](https://www.reddit.com/user/smooth_xmr/)
> also observed that tail emission results in a stable coin supply
> There's probably other= s too: it's a pretty obvious result.

<= div dir=3D"auto">Fwiw, Joe Lubin, April 2014:=C2=A0 "The expected rate= of annual loss and destruction of ETH will balance the rate of issuance.= =C2=A0 Under this dynamic, a quasi-steady state is reached and the amount o= f extant ETH no longer grows."=C2=A0 https://blog.ethereum.org/2= 014/04/10/the-issuance-model-in-ethereum/

As you say, probably an observation various people ha= ve made.=C2=A0 (Ethereum has had some updates to its issuance model since 2= 014, in particular EIP-1559 and the block reward reduction coming with PoS.= =C2=A0 But they've had a fixed rather than halving block subsidy since = launch so the question of whether it implied infinite supply often came up.= )


On Sat, Jul 9, 2022, 7:47 AM Peter Todd = via bitcoin-dev <bitcoin-dev@lists.linuxfoundation.org> wrote:
New blog post:

https://petertod= d.org/2022/surprisingly-tail-emission-is-not-inflationary

tl;dr: Due to lost coins, a tail emission/fixed reward actually results in = a
stable money supply. Not an (monetarily) inflationary supply.

...and for the purposes of reply/discussion, attached is the article itself= in
markdown format:

---
layout: post
title:=C2=A0 "Surprisingly, Tail Emission Is Not Inflationary" date:=C2=A0 =C2=A02022-07-09
tags:
- bitcoin
- monero
---

At present, all notable proof-of-work currencies reward miners with both a = block
reward, and transaction fees. With most currencies (including Bitcoin) phas= ing
out block rewards over time. However in no currency have transaction fees consistently been more than 5% to 10% of the total mining
reward[^fee-in-reward], with the exception of Ethereum, from June 2020 to A= ug 2021.
To date no proof-of-work currency has ever operated solely on transaction fees[^pow-tweet], and academic analysis has found that in this condition bl= ock
generation is unstable.[^instability-without-block-reward] To paraphrase An= drew
Poelstra, it's a scary phase change that no other coin has gone through= .[^apoelstra-quote]

[^pow-tweet]: [I asked on Twitter](https://twitter.com/peterktodd/status/1543231264597090304) and no-on= e replied with counter-examples.

[^fee-in-reward]: [Average Fee Percentage in Total Block Reward](https://bitinfocharts.com/comparison/fee_to_reward-btc-eth-bch-ltc-doge-x= mr-bsv-dash-zec.html#alltime)

[^instability-without-block-reward]: [On the Instability of Bitcoin Without= the Block Reward](https= ://www.cs.princeton.edu/~arvindn/publications/mining_CCS.pdf)

[^apoelstra-quote]: [From a panel at TABConf 2021](https://twitter.com/peterktodd/status/145706694689831731= 6)

Monero has chosen to implement what they call [tail
emission](https://www.g= etmonero.org/resources/moneropedia/tail-emission.html):
a fixed reward per block that continues indefinitely. Dogecoin also has a f= ixed
reward, which they widely - and incorrectly - refer to as an "abundant= " supply[^dogecoin-abundant].

[^dogecoin-abundant]: Googling "dogecoin abundant" returns dozens= of hits.

This article will show that a fixed block reward does **not** lead to an abundant supply. In fact, due to the inevitability of lost coins, a fixed reward converges to a **stable** monetary supply that is neither inflationa= ry
nor deflationary, with the total supply proportional to rate of tail emissi= on
and probability of coin loss.

Credit where credit is due: after writing the bulk of this article I found = out
that Monero developer [smooth_xmr](https://www.red= dit.com/user/smooth_xmr/)
also observed that tail emission results in a stable coin supply
[a few years ago](https://www.reddit.com/r/Monero/comments/4z0azk/maam_28= _monero_ask_anything_monday/d6sixyi/).
There's probably others too: it's a pretty obvious result.


<div markdown=3D"1" class=3D"post-toc">
# Contents
{:.no_toc}
0. TOC
{:toc}
</div>

## Modeling the Fixed-Reward Monetary Supply

Since the number of blocks is large, we can model the monetary supply as a<= br> continuous function $$N(t)$$, where $$t$$ is a given moment in time. If the=
block reward is fixed we can model the reward as a slope $$k$$ added to an<= br> initial supply $$N_0$$:

$$
N(t) =3D N_0 + kt
$$

Of course, this isn't realistic as coins are constantly being lost due = to
deaths, forgotten passphrases, boating accidents, etc. These losses are
independent: I'm not any more or less likely to forget my passphrase be= cause
you recently lost your coins in a boating accident =E2=80=94 an accident I = probably
don't even know happened. Since the number of individual coins (and the= ir
owners) is large =E2=80=94 as with the number of blocks =E2=80=94 we can mo= del this loss as
though it happens continuously.

Since coins can only be lost once, the *rate* of coin loss at time $$t$$ is=
proportional to the total supply *at that moment* in time. So let's loo= k at the
*first derivative* of our fixed-reward coin supply:

$$
\frac{dN(t)}{dt} =3D k
$$

...and subtract from it the lost coins, using $$\lambda$$ as our [coin loss=
constant](https://en.wikipedia.org/wiki/= Exponential_decay):

$$
\frac{dN(t)}{dt} =3D k - \lambda N(t)
$$

That's a first-order differential equation, which can be easily solved = with
separation of variables to get:

$$
N(t) =3D \frac{k}{\lambda} - Ce^{-\lambda t}
$$

To remove the integration constant $$C$$, let's look at $$t =3D 0$$, wh= ere the
coin supply is $$N_0$$:

$$
\begin{align}
=C2=A0 =C2=A0 N_0 &=3D \frac{k}{\lambda} - Ce^{-\lambda 0} =3D \frac{k}= {\lambda} - C \\
=C2=A0 =C2=A0 =C2=A0 C &=3D \frac{k}{\lambda} - N_0
\end{align}
$$

Thus:

$$
\begin{align}
=C2=A0 =C2=A0 N(t) &=3D \frac{k}{\lambda} - \left(\frac{k}{\lambda} - N= _0 \right)e^{-\lambda t} \\
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0&=3D \frac{k}{\lambda} + \left(N_0 - = \frac{k}{\lambda} \right)e^{-\lambda t}
\end{align}
$$


## Long Term Coin Supply

It's easy to see that in the long run, the second half of the coin supp= ly
equation goes to zero because $$\lim_{t \to \infty} e^{-\lambda t} =3D 0$$:=

$$
\begin{align}
=C2=A0 =C2=A0 \lim_{t \to \infty} N(t) &=3D \lim_{t \to \infty} \left[ = \frac{k}{\lambda} + \left(N_0 - \frac{k}{\lambda} \right)e^{-\lambda t} \ri= ght ] =3D \frac{k}{\lambda} \\
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0N(\inf= ty) &=3D \frac{k}{\lambda}
\end{align}
$$

An intuitive explanation for this result is that in the long run, the initi= al
supply $$N_0$$ doesn't matter, because approximately all of those coins= will
eventually be lost. Thus in the long run, the coin supply will converge tow= ards
$$\frac{k}{\lambda}$$, the point where coins are created just as fast as th= ey
are lost.


## Short Term Dynamics and Economic Considerations

Of course, the intuitive explanation for why supply converges to
$$\frac{k}{\lambda}$$, also tells us that supply must converge fairly slowl= y:
if 1% of something is lost per year, after 100 years 37% of the initial sup= ply
remains. It's not clear what the rate of lost coins actually is in a ma= ture,
valuable, coin. But 1%/year is likely to be a good guess =E2=80=94 quite po= ssibly less.

In the case of Monero, they've introduced tail emission at a point wher= e it
represents a 0.9% apparent monetary inflation rate[^p2pool-tail]. Since the= number of
previously lost coins, and the current rate of coin loss, is
unknown[^unknowable] it's not possible to know exactly what the true mo= netary
inflation rate is right now. But regardless, the rate will only converge towards zero going forward.

[^unknowable]: Being a privacy coin with [shielded amounts](https://localmonero.co/blocks/richlist), it's not even pos= sible to get an estimate of the total amount of XMR in active circulation.<= br>
[^p2pool-tail]: P2Pool operates [a page with real-time date figures](https://p2pool.io/tail.html).

If an existing coin decides to implement tail emission as a means to fund security, choosing an appropriate emission rate is simple: decide on the maximum amount of inflation you are willing to have in the worst case, and = set
the tail emission accordingly. In reality monetary inflation will be even l= ower
on day zero due to lost coins, and in the long run, it will converge toward= s
zero.

The fact is, economic volatility dwarfs the effect of small amounts of
inflation. Even a 0.5% inflation rate over 50 years only leads to a 22% dro= p.
Meanwhile at the time of writing, Bitcoin has dropped 36% in the past year,= and
gained 993% over the past 5 years. While this discussion is a nice excuse t= o
use some mildly interesting math, in the end it's totally pedantic.

## Could Bitcoin Add Tail Emission?

...and why could Monero?

Adding tail emission to Bitcoin would be a hard fork: a incompatible rule change that existing Bitcoin nodes would reject as invalid. While Monero wa= s
able to get sufficiently broad consensus in the community to implement tail=
emission, it's unclear at best if it would ever be possible to achieve = that for
the much larger[^btc-vs-xmr-market-cap] Bitcoin. Additionally, Monero has a=
culture of frequent hard forks that simply does not exist in Bitcoin.

[^btc-vs-xmr-market-cap]: [As of writing](https://web.archive.org/web/20220708143920/https://ww= w.coingecko.com/), the apparent market cap of Bitcoin is $409 billion, = almost 200x larger than Monero's $2.3 billion.

Ultimately, as long as a substantial fraction of the Bitcoin community cont= inue
to run full nodes, the only way tail emission could ever be added to Bitcoi= n is
by convincing that same community that it is a good idea.


## Footnotes
_______________________________________________
bitcoin-dev mailing list
bitcoin-dev@lists.linuxfoundation.org
https://lists.linuxfoundati= on.org/mailman/listinfo/bitcoin-dev
--000000000000ade02205e370c1b4--