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References: <Ysl4t9K8lfxRSsNM@petertodd.org>
In-Reply-To: <Ysl4t9K8lfxRSsNM@petertodd.org>
From: Jacob Eliosoff <jacob.eliosoff@gmail.com>
Date: Sun, 10 Jul 2022 05:18:17 -0500
Message-ID: <CAAUaCygd1dBXTNG_Hh9K-JBAMkAWqbRVRrY=N8obLtRLGEtgtg@mail.gmail.com>
To: Peter Todd <pete@petertodd.org>, 
 Bitcoin Protocol Discussion <bitcoin-dev@lists.linuxfoundation.org>
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Subject: Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary
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> 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.
>
>
> <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
> 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
>

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<div dir=3D"auto"><div dir=3D"auto">&gt; Credit where credit is due: after =
writing the bulk of this article I found out</div><div dir=3D"auto">&gt; th=
at Monero developer [smooth_xmr](<a href=3D"https://www.reddit.com/user/smo=
oth_xmr/">https://www.reddit.com/user/smooth_xmr/</a>)</div><div dir=3D"aut=
o">&gt; also observed that tail emission results in a stable coin supply</d=
iv><div dir=3D"auto">&gt; [a few years ago](<a href=3D"https://www.reddit.c=
om/r/Monero/comments/4z0azk/maam_28_monero_ask_anything_monday/d6sixyi/">ht=
tps://www.reddit.com/r/Monero/comments/4z0azk/maam_28_monero_ask_anything_m=
onday/d6sixyi/</a>).</div><div dir=3D"auto">&gt; There&#39;s probably other=
s too: it&#39;s a pretty obvious result.</div><div dir=3D"auto"><br></div><=
div dir=3D"auto">Fwiw, Joe Lubin, April 2014:=C2=A0 &quot;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.&quot;=C2=A0 <a href=3D"https://blog.ethereum.=
org/2014/04/10/the-issuance-model-in-ethereum/">https://blog.ethereum.org/2=
014/04/10/the-issuance-model-in-ethereum/</a></div><div dir=3D"auto"><br></=
div><div dir=3D"auto">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&#39;ve had a fixed rather than halving block subsidy since =
launch so the question of whether it implied infinite supply often came up.=
)</div><div dir=3D"auto"><br></div></div><br><div class=3D"gmail_quote"><di=
v dir=3D"ltr" class=3D"gmail_attr">On Sat, Jul 9, 2022, 7:47 AM Peter Todd =
via bitcoin-dev &lt;<a href=3D"mailto:bitcoin-dev@lists.linuxfoundation.org=
">bitcoin-dev@lists.linuxfoundation.org</a>&gt; wrote:<br></div><blockquote=
 class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc soli=
d;padding-left:1ex">New blog post:<br>
<br>
<a href=3D"https://petertodd.org/2022/surprisingly-tail-emission-is-not-inf=
lationary" rel=3D"noreferrer noreferrer" target=3D"_blank">https://petertod=
d.org/2022/surprisingly-tail-emission-is-not-inflationary</a><br>
<br>
tl;dr: Due to lost coins, a tail emission/fixed reward actually results in =
a<br>
stable money supply. Not an (monetarily) inflationary supply.<br>
<br>
...and for the purposes of reply/discussion, attached is the article itself=
 in<br>
markdown format:<br>
<br>
---<br>
layout: post<br>
title:=C2=A0 &quot;Surprisingly, Tail Emission Is Not Inflationary&quot;<br=
>
date:=C2=A0 =C2=A02022-07-09<br>
tags:<br>
- bitcoin<br>
- monero<br>
---<br>
<br>
At present, all notable proof-of-work currencies reward miners with both a =
block<br>
reward, and transaction fees. With most currencies (including Bitcoin) phas=
ing<br>
out block rewards over time. However in no currency have transaction fees<b=
r>
consistently been more than 5% to 10% of the total mining<br>
reward[^fee-in-reward], with the exception of Ethereum, from June 2020 to A=
ug 2021.<br>
To date no proof-of-work currency has ever operated solely on transaction<b=
r>
fees[^pow-tweet], and academic analysis has found that in this condition bl=
ock<br>
generation is unstable.[^instability-without-block-reward] To paraphrase An=
drew<br>
Poelstra, it&#39;s a scary phase change that no other coin has gone through=
.[^apoelstra-quote]<br>
<br>
[^pow-tweet]: [I asked on Twitter](<a href=3D"https://twitter.com/peterktod=
d/status/1543231264597090304" rel=3D"noreferrer noreferrer" target=3D"_blan=
k">https://twitter.com/peterktodd/status/1543231264597090304</a>) and no-on=
e replied with counter-examples.<br>
<br>
[^fee-in-reward]: [Average Fee Percentage in Total Block Reward](<a href=3D=
"https://bitinfocharts.com/comparison/fee_to_reward-btc-eth-bch-ltc-doge-xm=
r-bsv-dash-zec.html#alltime" rel=3D"noreferrer noreferrer" target=3D"_blank=
">https://bitinfocharts.com/comparison/fee_to_reward-btc-eth-bch-ltc-doge-x=
mr-bsv-dash-zec.html#alltime</a>)<br>
<br>
[^instability-without-block-reward]: [On the Instability of Bitcoin Without=
 the Block Reward](<a href=3D"https://www.cs.princeton.edu/~arvindn/publica=
tions/mining_CCS.pdf" rel=3D"noreferrer noreferrer" target=3D"_blank">https=
://www.cs.princeton.edu/~arvindn/publications/mining_CCS.pdf</a>)<br>
<br>
[^apoelstra-quote]: [From a panel at TABConf 2021](<a href=3D"https://twitt=
er.com/peterktodd/status/1457066946898317316" rel=3D"noreferrer noreferrer"=
 target=3D"_blank">https://twitter.com/peterktodd/status/145706694689831731=
6</a>)<br>
<br>
Monero has chosen to implement what they call [tail<br>
emission](<a href=3D"https://www.getmonero.org/resources/moneropedia/tail-e=
mission.html" rel=3D"noreferrer noreferrer" target=3D"_blank">https://www.g=
etmonero.org/resources/moneropedia/tail-emission.html</a>):<br>
a fixed reward per block that continues indefinitely. Dogecoin also has a f=
ixed<br>
reward, which they widely - and incorrectly - refer to as an &quot;abundant=
&quot; supply[^dogecoin-abundant].<br>
<br>
[^dogecoin-abundant]: Googling &quot;dogecoin abundant&quot; returns dozens=
 of hits.<br>
<br>
This article will show that a fixed block reward does **not** lead to an<br=
>
abundant supply. In fact, due to the inevitability of lost coins, a fixed<b=
r>
reward converges to a **stable** monetary supply that is neither inflationa=
ry<br>
nor deflationary, with the total supply proportional to rate of tail emissi=
on<br>
and probability of coin loss.<br>
<br>
Credit where credit is due: after writing the bulk of this article I found =
out<br>
that Monero developer [smooth_xmr](<a href=3D"https://www.reddit.com/user/s=
mooth_xmr/" rel=3D"noreferrer noreferrer" target=3D"_blank">https://www.red=
dit.com/user/smooth_xmr/</a>)<br>
also observed that tail emission results in a stable coin supply<br>
[a few years ago](<a href=3D"https://www.reddit.com/r/Monero/comments/4z0az=
k/maam_28_monero_ask_anything_monday/d6sixyi/" rel=3D"noreferrer noreferrer=
" target=3D"_blank">https://www.reddit.com/r/Monero/comments/4z0azk/maam_28=
_monero_ask_anything_monday/d6sixyi/</a>).<br>
There&#39;s probably others too: it&#39;s a pretty obvious result.<br>
<br>
<br>
&lt;div markdown=3D&quot;1&quot; class=3D&quot;post-toc&quot;&gt;<br>
# Contents<br>
{:.no_toc}<br>
0. TOC<br>
{:toc}<br>
&lt;/div&gt;<br>
<br>
## Modeling the Fixed-Reward Monetary Supply<br>
<br>
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=
<br>
block reward is fixed we can model the reward as a slope $$k$$ added to an<=
br>
initial supply $$N_0$$:<br>
<br>
$$<br>
N(t) =3D N_0 + kt<br>
$$<br>
<br>
Of course, this isn&#39;t realistic as coins are constantly being lost due =
to<br>
deaths, forgotten passphrases, boating accidents, etc. These losses are<br>
independent: I&#39;m not any more or less likely to forget my passphrase be=
cause<br>
you recently lost your coins in a boating accident =E2=80=94 an accident I =
probably<br>
don&#39;t even know happened. Since the number of individual coins (and the=
ir<br>
owners) is large =E2=80=94 as with the number of blocks =E2=80=94 we can mo=
del this loss as<br>
though it happens continuously.<br>
<br>
Since coins can only be lost once, the *rate* of coin loss at time $$t$$ is=
<br>
proportional to the total supply *at that moment* in time. So let&#39;s loo=
k at the<br>
*first derivative* of our fixed-reward coin supply:<br>
<br>
$$<br>
\frac{dN(t)}{dt} =3D k<br>
$$<br>
<br>
...and subtract from it the lost coins, using $$\lambda$$ as our [coin loss=
<br>
constant](<a href=3D"https://en.wikipedia.org/wiki/Exponential_decay" rel=
=3D"noreferrer noreferrer" target=3D"_blank">https://en.wikipedia.org/wiki/=
Exponential_decay</a>):<br>
<br>
$$<br>
\frac{dN(t)}{dt} =3D k - \lambda N(t)<br>
$$<br>
<br>
That&#39;s a first-order differential equation, which can be easily solved =
with<br>
separation of variables to get:<br>
<br>
$$<br>
N(t) =3D \frac{k}{\lambda} - Ce^{-\lambda t}<br>
$$<br>
<br>
To remove the integration constant $$C$$, let&#39;s look at $$t =3D 0$$, wh=
ere the<br>
coin supply is $$N_0$$:<br>
<br>
$$<br>
\begin{align}<br>
=C2=A0 =C2=A0 N_0 &amp;=3D \frac{k}{\lambda} - Ce^{-\lambda 0} =3D \frac{k}=
{\lambda} - C \\<br>
=C2=A0 =C2=A0 =C2=A0 C &amp;=3D \frac{k}{\lambda} - N_0<br>
\end{align}<br>
$$<br>
<br>
Thus:<br>
<br>
$$<br>
\begin{align}<br>
=C2=A0 =C2=A0 N(t) &amp;=3D \frac{k}{\lambda} - \left(\frac{k}{\lambda} - N=
_0 \right)e^{-\lambda t} \\<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0&amp;=3D \frac{k}{\lambda} + \left(N_0 - =
\frac{k}{\lambda} \right)e^{-\lambda t}<br>
\end{align}<br>
$$<br>
<br>
<br>
## Long Term Coin Supply<br>
<br>
It&#39;s easy to see that in the long run, the second half of the coin supp=
ly<br>
equation goes to zero because $$\lim_{t \to \infty} e^{-\lambda t} =3D 0$$:=
<br>
<br>
$$<br>
\begin{align}<br>
=C2=A0 =C2=A0 \lim_{t \to \infty} N(t) &amp;=3D \lim_{t \to \infty} \left[ =
\frac{k}{\lambda} + \left(N_0 - \frac{k}{\lambda} \right)e^{-\lambda t} \ri=
ght ] =3D \frac{k}{\lambda} \\<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0N(\inf=
ty) &amp;=3D \frac{k}{\lambda}<br>
\end{align}<br>
$$<br>
<br>
An intuitive explanation for this result is that in the long run, the initi=
al<br>
supply $$N_0$$ doesn&#39;t matter, because approximately all of those coins=
 will<br>
eventually be lost. Thus in the long run, the coin supply will converge tow=
ards<br>
$$\frac{k}{\lambda}$$, the point where coins are created just as fast as th=
ey<br>
are lost.<br>
<br>
<br>
## Short Term Dynamics and Economic Considerations<br>
<br>
Of course, the intuitive explanation for why supply converges to<br>
$$\frac{k}{\lambda}$$, also tells us that supply must converge fairly slowl=
y:<br>
if 1% of something is lost per year, after 100 years 37% of the initial sup=
ply<br>
remains. It&#39;s not clear what the rate of lost coins actually is in a ma=
ture,<br>
valuable, coin. But 1%/year is likely to be a good guess =E2=80=94 quite po=
ssibly less.<br>
<br>
In the case of Monero, they&#39;ve introduced tail emission at a point wher=
e it<br>
represents a 0.9% apparent monetary inflation rate[^p2pool-tail]. Since the=
 number of<br>
previously lost coins, and the current rate of coin loss, is<br>
unknown[^unknowable] it&#39;s not possible to know exactly what the true mo=
netary<br>
inflation rate is right now. But regardless, the rate will only converge<br=
>
towards zero going forward.<br>
<br>
[^unknowable]: Being a privacy coin with [shielded amounts](<a href=3D"http=
s://localmonero.co/blocks/richlist" rel=3D"noreferrer noreferrer" target=3D=
"_blank">https://localmonero.co/blocks/richlist</a>), it&#39;s not even pos=
sible to get an estimate of the total amount of XMR in active circulation.<=
br>
<br>
[^p2pool-tail]: P2Pool operates [a page with real-time date figures](<a hre=
f=3D"https://p2pool.io/tail.html" rel=3D"noreferrer noreferrer" target=3D"_=
blank">https://p2pool.io/tail.html</a>).<br>
<br>
If an existing coin decides to implement tail emission as a means to fund<b=
r>
security, choosing an appropriate emission rate is simple: decide on the<br=
>
maximum amount of inflation you are willing to have in the worst case, and =
set<br>
the tail emission accordingly. In reality monetary inflation will be even l=
ower<br>
on day zero due to lost coins, and in the long run, it will converge toward=
s<br>
zero.<br>
<br>
The fact is, economic volatility dwarfs the effect of small amounts of<br>
inflation. Even a 0.5% inflation rate over 50 years only leads to a 22% dro=
p.<br>
Meanwhile at the time of writing, Bitcoin has dropped 36% in the past year,=
 and<br>
gained 993% over the past 5 years. While this discussion is a nice excuse t=
o<br>
use some mildly interesting math, in the end it&#39;s totally pedantic.<br>
<br>
## Could Bitcoin Add Tail Emission?<br>
<br>
...and why could Monero?<br>
<br>
Adding tail emission to Bitcoin would be a hard fork: a incompatible rule<b=
r>
change that existing Bitcoin nodes would reject as invalid. While Monero wa=
s<br>
able to get sufficiently broad consensus in the community to implement tail=
<br>
emission, it&#39;s unclear at best if it would ever be possible to achieve =
that for<br>
the much larger[^btc-vs-xmr-market-cap] Bitcoin. Additionally, Monero has a=
<br>
culture of frequent hard forks that simply does not exist in Bitcoin.<br>
<br>
[^btc-vs-xmr-market-cap]: [As of writing](<a href=3D"https://web.archive.or=
g/web/20220708143920/https://www.coingecko.com/" rel=3D"noreferrer noreferr=
er" target=3D"_blank">https://web.archive.org/web/20220708143920/https://ww=
w.coingecko.com/</a>), the apparent market cap of Bitcoin is $409 billion, =
almost 200x larger than Monero&#39;s $2.3 billion.<br>
<br>
Ultimately, as long as a substantial fraction of the Bitcoin community cont=
inue<br>
to run full nodes, the only way tail emission could ever be added to Bitcoi=
n is<br>
by convincing that same community that it is a good idea.<br>
<br>
<br>
## Footnotes<br>
_______________________________________________<br>
bitcoin-dev mailing list<br>
<a href=3D"mailto:bitcoin-dev@lists.linuxfoundation.org" target=3D"_blank" =
rel=3D"noreferrer">bitcoin-dev@lists.linuxfoundation.org</a><br>
<a href=3D"https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev" =
rel=3D"noreferrer noreferrer" target=3D"_blank">https://lists.linuxfoundati=
on.org/mailman/listinfo/bitcoin-dev</a><br>
</blockquote></div>

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