Subject: Re: [bitcoin-dev] Surprisingly, Tail Emission Is Not Inflationary

From: Zac Greenwood <[email-masked]>
Date: Wed, 13 Jul 2022 20:29:53 +0200

> your proof is incorrect (or, rather, relies on a highly unrealistic
assumption)

The assumption that coin are lost ar a constant rate is not required. Tail
emission will asymptotically decrease the rate of inflation to zero, at
which point the increase in coin exactly matches the amount of coin lost.
The rate at which coin are lost is irrelevant.

This is easy to see. Consider no coin are ever lost. The rate of inflation
will slowly decline to zero as the amount of coin grows to infinity.
However, lost coin ensures that the point at which the rate of inflation
becomes zero will be reached sooner.

If a black swan event destroys 90% of all coin, the constant tail emission
will instantly begin to inflate the supply at a 10x higher percentage. The
inflation expressed as a percentage will also immediately start to decline
because each new coin will inflate the total supply with a slightly smaller
percentage than the previous new coin. The rate of inflation will continue
to decline until zero, at which point it again matches the coin-loss
induced deflation rate.

Another scenario. Suppose that the number of coin lost becomes
significantly less for instance because better wallets and a more mature
ecosystem prevent many common coin loss events. A constant issuance of new
coin would increase the total supply, but each new coin would add less to
the total supply when expressed as a percentage. The rate of inflation
would decline to zero, at which point it again has matched the rate of
deflation due to coin loss.

Even when the rate at which coin are lost will not be constant, a tail
emission will tend to an equilibrium.

It must be observed that tail emission causes the total *potential* supply
to vary greatly depending on the deflation rate. In a low-deflation
scenario, the supply will have to grow much larger before an equilibrium
can be reached than in a scenario with moderate deflation rate. Not being
able to predict the ultimate total supply of coin is however seems
undesirable. But is it really?

The rate of inflation required for keeping Bitcoin useful highly depends on
the value of the token. At US$100k, a tail emission of 1 BTC per block
ensures safety within a few blocks for even large amounts. Continuing this
example, 1 BTC per block would mean 5.25m extra coin per 100 years. At 21m
coins and 1 BTC perpetual reward per block, the rate of inflation would be
0.25% per year.

This should put things a bit into perspective.

On Tue, 12 Jul 2022 at 01:58, Anthony Towns via bitcoin-dev <
[email-masked]> wrote:

> On Mon, Jul 11, 2022 at 08:56:04AM -0400, Erik Aronesty via bitcoin-dev
> wrote:
> > > Alternatively, losses could be at a predictable rate that's entirely
> > > different to the one Peter assumes.
> > No, peter only assumes that there *is* a rate.
>
> No, he assumes it's a constant rate. His integration step gives a
> different result if lambda changes with t:
> https://www.wolframalpha.com/input?i=dN%2Fdt+%3D+k+-+lambda%28t%29*N
>
> On Mon, Jul 11, 2022 at 12:59:53PM -0400, Peter Todd via bitcoin-dev wrote:
> > Give me an example of an *actual* inflation rate you expect to see,
> given a
> > disaster of a given magnitude.
>
> All I was doing was saying your proof is incorrect (or, rather, relies
> on a highly unrealistic assumption), since I hadn't seen anybody else
> point that out already.
>
> But even if the proof were correct, I don't think it provides a useful
> mechanism (since there's no reason to think miners gaining all the coins
> lost in a year will be sufficient for anything), and I don't really
> think the "security budget" framework (ie, that the percentage of total
> supply given to miners each year is what's important for security)
> you're implicitly relying on is particularly meaningful.
>
> So no, not particularly interested in diving into it any deeper.
>
> Cheers,
> aj
>
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