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From: Eric Voskuil <eric@voskuil.org>
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Date: Sat, 9 Jul 2022 07:26:22 -0700
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References: <Ysl4t9K8lfxRSsNM@petertodd.org>
In-Reply-To: <Ysl4t9K8lfxRSsNM@petertodd.org>
To: Peter Todd <pete@petertodd.org>,
 Bitcoin Protocol Discussion <bitcoin-dev@lists.linuxfoundation.org>
Subject: Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary
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> Due to lost coins, a tail emission/fixed reward actually results in a stab=
le money supply. Not an (monetarily) inflationary supply.

This observation is not a proof of lost coins, that is an assumption. It is t=
he provable consequence of market, as opposed to monopoly, production.

https://github.com/libbitcoin/libbitcoin-system/wiki/Inflation-Principle

Mises=E2=80=99 unfortunate error in the application of the Cantillon Effect t=
o gold perpetuates this misperception. One could imagine applying this theor=
y to all goods, not just money, and conclude perpetual loss of value in ever=
ything produced, as a consequence of production. One might then be tempted t=
o attribute the fact that this is not observable to loss/depreciation/consum=
ption. 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.

=E2=80=9CCirculation=E2=80=9D does not determine demand, all money is always=
 held by someone. Changing hands only changes who owns the money, not its pu=
rchasing power. See Rothbard=E2=80=99s critique of monetary =E2=80=9Cvelocit=
y=E2=80=9D.

e

> On Jul 9, 2022, at 05:47, Peter Todd via bitcoin-dev <bitcoin-dev@lists.li=
nuxfoundation.org> wrote:
>=20
> =EF=BB=BFNew blog post:
>=20
> https://petertodd.org/2022/surprisingly-tail-emission-is-not-inflationary
>=20
> tl;dr: Due to lost coins, a tail emission/fixed reward actually results in=
 a
> stable money supply. Not an (monetarily) inflationary supply.
>=20
> ...and for the purposes of reply/discussion, attached is the article itsel=
f in
> markdown format:
>=20
> ---
> layout: post
> title:  "Surprisingly, Tail Emission Is Not Inflationary"
> date:   2022-07-09
> tags:
> - bitcoin
> - monero
> ---
>=20
> At present, all notable proof-of-work currencies reward miners with both a=
 block
> reward, and transaction fees. With most currencies (including Bitcoin) pha=
sing
> 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 b=
lock
> generation is unstable.[^instability-without-block-reward] To paraphrase A=
ndrew
> Poelstra, it's a scary phase change that no other coin has gone through.[^=
apoelstra-quote]
>=20
> [^pow-tweet]: [I asked on Twitter](https://twitter.com/peterktodd/status/1=
543231264597090304) and no-one replied with counter-examples.
>=20
> [^fee-in-reward]: [Average Fee Percentage in Total Block Reward](https://b=
itinfocharts.com/comparison/fee_to_reward-btc-eth-bch-ltc-doge-xmr-bsv-dash-=
zec.html#alltime)
>=20
> [^instability-without-block-reward]: [On the Instability of Bitcoin Withou=
t the Block Reward](https://www.cs.princeton.edu/~arvindn/publications/minin=
g_CCS.pdf)
>=20
> [^apoelstra-quote]: [=46rom a panel at TABConf 2021](https://twitter.com/p=
eterktodd/status/1457066946898317316)
>=20
> Monero has chosen to implement what they call [tail
> emission](https://www.getmonero.org/resources/moneropedia/tail-emission.ht=
ml):
> 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" su=
pply[^dogecoin-abundant].
>=20
> [^dogecoin-abundant]: Googling "dogecoin abundant" returns dozens of hits.=

>=20
> 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 inflation=
ary
> nor deflationary, with the total supply proportional to rate of tail emiss=
ion
> and probability of coin loss.
>=20
> 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.
>=20
>=20
> <div markdown=3D"1" class=3D"post-toc">
> # Contents
> {:.no_toc}
> 0. TOC
> {:toc}
> </div>
>=20
> ## Modeling the Fixed-Reward Monetary Supply
>=20
> 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 th=
e
> block reward is fixed we can model the reward as a slope $$k$$ added to an=

> initial supply $$N_0$$:
>=20
> $$
> N(t) =3D N_0 + kt
> $$
>=20
> 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 becau=
se
> 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 m=
odel this loss as
> though it happens continuously.
>=20
> Since coins can only be lost once, the *rate* of coin loss at time $$t$$ i=
s
> proportional to the total supply *at that moment* in time. So let's look a=
t the
> *first derivative* of our fixed-reward coin supply:
>=20
> $$
> \frac{dN(t)}{dt} =3D k
> $$
>=20
> ...and subtract from it the lost coins, using $$\lambda$$ as our [coin los=
s
> constant](https://en.wikipedia.org/wiki/Exponential_decay):
>=20
> $$
> \frac{dN(t)}{dt} =3D k - \lambda N(t)
> $$
>=20
> That's a first-order differential equation, which can be easily solved wit=
h
> separation of variables to get:
>=20
> $$
> N(t) =3D \frac{k}{\lambda} - Ce^{-\lambda t}
> $$
>=20
> To remove the integration constant $$C$$, let's look at $$t =3D 0$$, where=
 the
> coin supply is $$N_0$$:
>=20
> $$
> \begin{align}
>    N_0 &=3D \frac{k}{\lambda} - Ce^{-\lambda 0} =3D \frac{k}{\lambda} - C \=
\
>      C &=3D \frac{k}{\lambda} - N_0
> \end{align}
> $$
>=20
> Thus:
>=20
> $$
> \begin{align}
>    N(t) &=3D \frac{k}{\lambda} - \left(\frac{k}{\lambda} - N_0 \right)e^{-=
\lambda t} \\
>         &=3D \frac{k}{\lambda} + \left(N_0 - \frac{k}{\lambda} \right)e^{-=
\lambda t}
> \end{align}
> $$
>=20
>=20
> ## Long Term Coin Supply
>=20
> It's easy to see that in the long run, the second half of the coin supply
> equation goes to zero because $$\lim_{t \to \infty} e^{-\lambda t} =3D 0$$=
:
>=20
> $$
> \begin{align}
>    \lim_{t \to \infty} N(t) &=3D \lim_{t \to \infty} \left[ \frac{k}{\lamb=
da} + \left(N_0 - \frac{k}{\lambda} \right)e^{-\lambda t} \right ] =3D \frac=
{k}{\lambda} \\
>                   N(\infty) &=3D \frac{k}{\lambda}
> \end{align}
> $$
>=20
> An intuitive explanation for this result is that in the long run, the init=
ial
> supply $$N_0$$ doesn't matter, because approximately all of those coins wi=
ll
> eventually be lost. Thus in the long run, the coin supply will converge to=
wards
> $$\frac{k}{\lambda}$$, the point where coins are created just as fast as t=
hey
> are lost.
>=20
>=20
> ## Short Term Dynamics and Economic Considerations
>=20
> Of course, the intuitive explanation for why supply converges to
> $$\frac{k}{\lambda}$$, also tells us that supply must converge fairly slow=
ly:
> if 1% of something is lost per year, after 100 years 37% of the initial su=
pply
> remains. It's not clear what the rate of lost coins actually is in a matur=
e,
> valuable, coin. But 1%/year is likely to be a good guess =E2=80=94 quite p=
ossibly less.
>=20
> In the case of Monero, they've introduced tail emission at a point where i=
t
> represents a 0.9% apparent monetary inflation rate[^p2pool-tail]. Since th=
e 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 monet=
ary
> inflation rate is right now. But regardless, the rate will only converge
> towards zero going forward.
>=20
> [^unknowable]: Being a privacy coin with [shielded amounts](https://localm=
onero.co/blocks/richlist), it's not even possible to get an estimate of the t=
otal amount of XMR in active circulation.
>=20
> [^p2pool-tail]: P2Pool operates [a page with real-time date figures](https=
://p2pool.io/tail.html).
>=20
> 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 towar=
ds
> zero.
>=20
> 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% dr=
op.
> 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.
>=20
> ## Could Bitcoin Add Tail Emission?
>=20
> ...and why could Monero?
>=20
> Adding tail emission to Bitcoin would be a hard fork: a incompatible rule
> change that existing Bitcoin nodes would reject as invalid. While Monero w=
as
> able to get sufficiently broad consensus in the community to implement tai=
l
> emission, it's unclear at best if it would ever be possible to achieve tha=
t 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.
>=20
> [^btc-vs-xmr-market-cap]: [As of writing](https://web.archive.org/web/2022=
0708143920/https://www.coingecko.com/), the apparent market cap of Bitcoin i=
s $409 billion, almost 200x larger than Monero's $2.3 billion.
>=20
> Ultimately, as long as a substantial fraction of the Bitcoin community con=
tinue
> to run full nodes, the only way tail emission could ever be added to Bitco=
in is
> by convincing that same community that it is a good idea.
>=20
>=20
> ## Footnotes
> _______________________________________________
> bitcoin-dev mailing list
> bitcoin-dev@lists.linuxfoundation.org
> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev

--Apple-Mail-0A63F663-FFB5-4325-A4DD-CA9261D0E08C
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<html><head><meta http-equiv=3D"content-type" content=3D"text/html; charset=3D=
utf-8"></head><body dir=3D"auto"><div dir=3D"ltr"></div><div dir=3D"ltr"><fo=
nt color=3D"#000000"><span style=3D"caret-color: rgb(255, 255, 255); -webkit=
-text-size-adjust: auto;">&gt;&nbsp;</span></font>Due to lost coins, a tail e=
mission/fixed reward actually results in a stable money supply. Not an (mone=
tarily) inflationary supply.</div><div dir=3D"ltr"><font color=3D"#000000"><=
span style=3D"caret-color: rgb(255, 255, 255); -webkit-text-size-adjust: aut=
o;"><br></span></font></div><div dir=3D"ltr"><font color=3D"#000000"><span s=
tyle=3D"caret-color: rgb(255, 255, 255); -webkit-text-size-adjust: auto;">Th=
is observation is not a proof of lost coins, that is an assumption. It is th=
e provable consequence of market, as opposed to monopoly, production.<br></s=
pan></font><div style=3D"caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0);"><f=
ont color=3D"#000000"><span style=3D"caret-color: rgb(255, 255, 255); -webki=
t-text-size-adjust: auto;"><br></span></font></div><div style=3D"caret-color=
: rgb(0, 0, 0); color: rgb(0, 0, 0);"><a href=3D"https://github.com/libbitco=
in/libbitcoin-system/wiki/Inflation-Principle">https://github.com/libbitcoin=
/libbitcoin-system/wiki/Inflation-Principle</a><div dir=3D"ltr"><br></div><d=
iv dir=3D"ltr">Mises=E2=80=99 unfortunate error in the application of the Ca=
ntillon Effect to gold perpetuates this misperception. One could imagine app=
lying this theory to all goods, not just money, and conclude perpetual loss o=
f value in everything produced, as a consequence of production. One might th=
en be tempted to attribute the fact that this is not observable to loss/depr=
eciation/consumption. While it is certainly possible that the amount of gold=
 produced every year is offset by the amount lost, this of course implies th=
at all of it is lost.</div><div dir=3D"ltr"><br></div><div dir=3D"ltr">=E2=80=
=9CCirculation=E2=80=9D does not determine demand, all money is always held b=
y someone. Changing hands only changes who owns the money, not its purchasin=
g power. See Rothbard=E2=80=99s critique of monetary =E2=80=9Cvelocity=E2=80=
=9D.</div><div dir=3D"ltr"><br></div><div dir=3D"ltr">e</div></div></div><di=
v dir=3D"ltr"><br><blockquote type=3D"cite">On Jul 9, 2022, at 05:47, Peter T=
odd via bitcoin-dev &lt;bitcoin-dev@lists.linuxfoundation.org&gt; wrote:<br>=
<br></blockquote></div><blockquote type=3D"cite"><div dir=3D"ltr">=EF=BB=BF<=
span>New blog post:</span><br><span></span><br><span>https://petertodd.org/2=
022/surprisingly-tail-emission-is-not-inflationary</span><br><span></span><b=
r><span>tl;dr: Due to lost coins, a tail emission/fixed reward actually resu=
lts in a</span><br><span>stable money supply. Not an (monetarily) inflationa=
ry supply.</span><br><span></span><br><span>...and for the purposes of reply=
/discussion, attached is the article itself in</span><br><span>markdown form=
at:</span><br><span></span><br><span>---</span><br><span>layout: post</span>=
<br><span>title: &nbsp;"Surprisingly, Tail Emission Is Not Inflationary"</sp=
an><br><span>date: &nbsp;&nbsp;2022-07-09</span><br><span>tags:</span><br><s=
pan>- bitcoin</span><br><span>- monero</span><br><span>---</span><br><span><=
/span><br><span>At present, all notable proof-of-work currencies reward mine=
rs with both a block</span><br><span>reward, and transaction fees. With most=
 currencies (including Bitcoin) phasing</span><br><span>out block rewards ov=
er time. However in no currency have transaction fees</span><br><span>consis=
tently been more than 5% to 10% of the total mining</span><br><span>reward[^=
fee-in-reward], with the exception of Ethereum, from June 2020 to Aug 2021.<=
/span><br><span>To date no proof-of-work currency has ever operated solely o=
n transaction</span><br><span>fees[^pow-tweet], and academic analysis has fo=
und that in this condition block</span><br><span>generation is unstable.[^in=
stability-without-block-reward] To paraphrase Andrew</span><br><span>Poelstr=
a, it's a scary phase change that no other coin has gone through.[^apoelstra=
-quote]</span><br><span></span><br><span>[^pow-tweet]: [I asked on Twitter](=
https://twitter.com/peterktodd/status/1543231264597090304) and no-one replie=
d with counter-examples.</span><br><span></span><br><span>[^fee-in-reward]: [=
Average Fee Percentage in Total Block Reward](https://bitinfocharts.com/comp=
arison/fee_to_reward-btc-eth-bch-ltc-doge-xmr-bsv-dash-zec.html#alltime)</sp=
an><br><span></span><br><span>[^instability-without-block-reward]: [On the I=
nstability of Bitcoin Without the Block Reward](https://www.cs.princeton.edu=
/~arvindn/publications/mining_CCS.pdf)</span><br><span></span><br><span>[^ap=
oelstra-quote]: [=46rom a panel at TABConf 2021](https://twitter.com/peterkt=
odd/status/1457066946898317316)</span><br><span></span><br><span>Monero has c=
hosen to implement what they call [tail</span><br><span>emission](https://ww=
w.getmonero.org/resources/moneropedia/tail-emission.html):</span><br><span>a=
 fixed reward per block that continues indefinitely. Dogecoin also has a fix=
ed</span><br><span>reward, which they widely - and incorrectly - refer to as=
 an "abundant" supply[^dogecoin-abundant].</span><br><span></span><br><span>=
[^dogecoin-abundant]: Googling "dogecoin abundant" returns dozens of hits.</=
span><br><span></span><br><span>This article will show that a fixed block re=
ward does **not** lead to an</span><br><span>abundant supply. In fact, due t=
o the inevitability of lost coins, a fixed</span><br><span>reward converges t=
o a **stable** monetary supply that is neither inflationary</span><br><span>=
nor deflationary, with the total supply proportional to rate of tail emissio=
n</span><br><span>and probability of coin loss.</span><br><span></span><br><=
span>Credit where credit is due: after writing the bulk of this article I fo=
und out</span><br><span>that Monero developer [smooth_xmr](https://www.reddi=
t.com/user/smooth_xmr/)</span><br><span>also observed that tail emission res=
ults in a stable coin supply</span><br><span>[a few years ago](https://www.r=
eddit.com/r/Monero/comments/4z0azk/maam_28_monero_ask_anything_monday/d6sixy=
i/).</span><br><span>There's probably others too: it's a pretty obvious resu=
lt.</span><br><span></span><br><span></span><br><span>&lt;div markdown=3D"1"=
 class=3D"post-toc"&gt;</span><br><span># Contents</span><br><span>{:.no_toc=
}</span><br><span>0. TOC</span><br><span>{:toc}</span><br><span>&lt;/div&gt;=
</span><br><span></span><br><span>## Modeling the Fixed-Reward Monetary Supp=
ly</span><br><span></span><br><span>Since the number of blocks is large, we c=
an model the monetary supply as a</span><br><span>continuous function $$N(t)=
$$, where $$t$$ is a given moment in time. If the</span><br><span>block rewa=
rd is fixed we can model the reward as a slope $$k$$ added to an</span><br><=
span>initial supply $$N_0$$:</span><br><span></span><br><span>$$</span><br><=
span>N(t) =3D N_0 + kt</span><br><span>$$</span><br><span></span><br><span>O=
f course, this isn't realistic as coins are constantly being lost due to</sp=
an><br><span>deaths, forgotten passphrases, boating accidents, etc. These lo=
sses are</span><br><span>independent: I'm not any more or less likely to for=
get my passphrase because</span><br><span>you recently lost your coins in a b=
oating accident =E2=80=94 an accident I probably</span><br><span>don't even k=
now happened. Since the number of individual coins (and their</span><br><spa=
n>owners) is large =E2=80=94 as with the number of blocks =E2=80=94 we can m=
odel this loss as</span><br><span>though it happens continuously.</span><br>=
<span></span><br><span>Since coins can only be lost once, the *rate* of coin=
 loss at time $$t$$ is</span><br><span>proportional to the total supply *at t=
hat moment* in time. So let's look at the</span><br><span>*first derivative*=
 of our fixed-reward coin supply:</span><br><span></span><br><span>$$</span>=
<br><span>\frac{dN(t)}{dt} =3D k</span><br><span>$$</span><br><span></span><=
br><span>...and subtract from it the lost coins, using $$\lambda$$ as our [c=
oin loss</span><br><span>constant](https://en.wikipedia.org/wiki/Exponential=
_decay):</span><br><span></span><br><span>$$</span><br><span>\frac{dN(t)}{dt=
} =3D k - \lambda N(t)</span><br><span>$$</span><br><span></span><br><span>T=
hat's a first-order differential equation, which can be easily solved with</=
span><br><span>separation of variables to get:</span><br><span></span><br><s=
pan>$$</span><br><span>N(t) =3D \frac{k}{\lambda} - Ce^{-\lambda t}</span><b=
r><span>$$</span><br><span></span><br><span>To remove the integration consta=
nt $$C$$, let's look at $$t =3D 0$$, where the</span><br><span>coin supply i=
s $$N_0$$:</span><br><span></span><br><span>$$</span><br><span>\begin{align}=
</span><br><span> &nbsp;&nbsp;&nbsp;N_0 &amp;=3D \frac{k}{\lambda} - Ce^{-\l=
ambda 0} =3D \frac{k}{\lambda} - C \\</span><br><span> &nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;C &amp;=3D \frac{k}{\lambda} - N_0</span><br><span>\end{align}</spa=
n><br><span>$$</span><br><span></span><br><span>Thus:</span><br><span></span=
><br><span>$$</span><br><span>\begin{align}</span><br><span> &nbsp;&nbsp;&nb=
sp;N(t) &amp;=3D \frac{k}{\lambda} - \left(\frac{k}{\lambda} - N_0 \right)e^=
{-\lambda t} \\</span><br><span> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;&amp;=3D \frac{k}{\lambda} + \left(N_0 - \frac{k}{\lambda} \right)e^{-\=
lambda t}</span><br><span>\end{align}</span><br><span>$$</span><br><span></s=
pan><br><span></span><br><span>## Long Term Coin Supply</span><br><span></sp=
an><br><span>It's easy to see that in the long run, the second half of the c=
oin supply</span><br><span>equation goes to zero because $$\lim_{t \to \inft=
y} e^{-\lambda t} =3D 0$$:</span><br><span></span><br><span>$$</span><br><sp=
an>\begin{align}</span><br><span> &nbsp;&nbsp;&nbsp;\lim_{t \to \infty} N(t)=
 &amp;=3D \lim_{t \to \infty} \left[ \frac{k}{\lambda} + \left(N_0 - \frac{k=
}{\lambda} \right)e^{-\lambda t} \right ] =3D \frac{k}{\lambda} \\</span><br=
><span> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&n=
bsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;N(\infty) &amp;=3D \frac{k}{\lambda}=
</span><br><span>\end{align}</span><br><span>$$</span><br><span></span><br><=
span>An intuitive explanation for this result is that in the long run, the i=
nitial</span><br><span>supply $$N_0$$ doesn't matter, because approximately a=
ll of those coins will</span><br><span>eventually be lost. Thus in the long r=
un, the coin supply will converge towards</span><br><span>$$\frac{k}{\lambda=
}$$, the point where coins are created just as fast as they</span><br><span>=
are lost.</span><br><span></span><br><span></span><br><span>## Short Term Dy=
namics and Economic Considerations</span><br><span></span><br><span>Of cours=
e, the intuitive explanation for why supply converges to</span><br><span>$$\=
frac{k}{\lambda}$$, also tells us that supply must converge fairly slowly:</=
span><br><span>if 1% of something is lost per year, after 100 years 37% of t=
he initial supply</span><br><span>remains. It's not clear what the rate of l=
ost coins actually is in a mature,</span><br><span>valuable, coin. But 1%/ye=
ar is likely to be a good guess =E2=80=94 quite possibly less.</span><br><sp=
an></span><br><span>In the case of Monero, they've introduced tail emission a=
t a point where it</span><br><span>represents a 0.9% apparent monetary infla=
tion rate[^p2pool-tail]. Since the number of</span><br><span>previously lost=
 coins, and the current rate of coin loss, is</span><br><span>unknown[^unkno=
wable] it's not possible to know exactly what the true monetary</span><br><s=
pan>inflation rate is right now. But regardless, the rate will only converge=
</span><br><span>towards zero going forward.</span><br><span></span><br><spa=
n>[^unknowable]: Being a privacy coin with [shielded amounts](https://localm=
onero.co/blocks/richlist), it's not even possible to get an estimate of the t=
otal amount of XMR in active circulation.</span><br><span></span><br><span>[=
^p2pool-tail]: P2Pool operates [a page with real-time date figures](https://=
p2pool.io/tail.html).</span><br><span></span><br><span>If an existing coin d=
ecides to implement tail emission as a means to fund</span><br><span>securit=
y, choosing an appropriate emission rate is simple: decide on the</span><br>=
<span>maximum amount of inflation you are willing to have in the worst case,=
 and set</span><br><span>the tail emission accordingly. In reality monetary i=
nflation will be even lower</span><br><span>on day zero due to lost coins, a=
nd in the long run, it will converge towards</span><br><span>zero.</span><br=
><span></span><br><span>The fact is, economic volatility dwarfs the effect o=
f small amounts of</span><br><span>inflation. Even a 0.5% inflation rate ove=
r 50 years only leads to a 22% drop.</span><br><span>Meanwhile at the time o=
f writing, Bitcoin has dropped 36% in the past year, and</span><br><span>gai=
ned 993% over the past 5 years. While this discussion is a nice excuse to</s=
pan><br><span>use some mildly interesting math, in the end it's totally peda=
ntic.</span><br><span></span><br><span>## Could Bitcoin Add Tail Emission?</=
span><br><span></span><br><span>...and why could Monero?</span><br><span></s=
pan><br><span>Adding tail emission to Bitcoin would be a hard fork: a incomp=
atible rule</span><br><span>change that existing Bitcoin nodes would reject a=
s invalid. While Monero was</span><br><span>able to get sufficiently broad c=
onsensus in the community to implement tail</span><br><span>emission, it's u=
nclear at best if it would ever be possible to achieve that for</span><br><s=
pan>the much larger[^btc-vs-xmr-market-cap] Bitcoin. Additionally, Monero ha=
s a</span><br><span>culture of frequent hard forks that simply does not exis=
t in Bitcoin.</span><br><span></span><br><span>[^btc-vs-xmr-market-cap]: [As=
 of writing](https://web.archive.org/web/20220708143920/https://www.coingeck=
o.com/), the apparent market cap of Bitcoin is $409 billion, almost 200x lar=
ger than Monero's $2.3 billion.</span><br><span></span><br><span>Ultimately,=
 as long as a substantial fraction of the Bitcoin community continue</span><=
br><span>to run full nodes, the only way tail emission could ever be added t=
o Bitcoin is</span><br><span>by convincing that same community that it is a g=
ood idea.</span><br><span></span><br><span></span><br><span>## Footnotes</sp=
an><br><span>_______________________________________________</span><br><span=
>bitcoin-dev mailing list</span><br><span>bitcoin-dev@lists.linuxfoundation.=
org</span><br><span>https://lists.linuxfoundation.org/mailman/listinfo/bitco=
in-dev</span><br><div>&lt;signature.asc&gt;</div></div></blockquote></body><=
/html>=

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