I stumbled across this short and well-written blog https://petertodd.org/2022/surprisingly-tail-emission-is-not-inflationary from this very unhinged reddit argument: https://old.reddit.com/r/Monero/comments/16wuha9/what_would_you_list_as_some_risk_factors_or/k2zwkar/

I took a physics course and I immediately recognized the differential equation listed in the blog post. The differential equation (and therefore its solution) looks exactly the same as the velocity of an object in freefall where there’s drag that’s proportional to the objects speed (I.E. basically it’s terminal velocity. You can’t accelerate forever under freefall in an atmosphere).

In physics, you can feel this yourself. When you’re a passenger in a slow moving car, putting your hand out of the window you’ll notice some slight force. But when you’re in the freeway, putting your hand out is like arm wrestling the air. The drag is proportional to the velocity

The blog post argues that the circulating supply of Monero is asymptotically constant (more specifically, the ratio of the rate of increase of the Monero supply divided by the rate of Monero being lost from the Monero supply)

Now there’s a LOT of assumptions hidden under the differential equation. A diff eq only really makes sense in predicting something when the assumptions are checked. There are two assumptions:

1. The rate at which Monero increases is constant

2. The rate at which Monero is lost (from lost wallets, boating accidents, savings accounts) is proportional to the amount of Monero in the system.

1 seems solid: it’s 0.6 per block. Assumption 2 however is a bit confusing? I expect the amount of Monero being lost from the money supply proportional to the adoption of Monero. Monero adoption can be loosely proportional to the amount of Monero in the supply, given that Monero adoption is linear over time, but that is a big assumption.

I have, however, found an explanation for the tail emission of Monero that I found to be more compelling. Overall, let’s say, worst case scenario, that nobody loses and nobody saves their Monero, and that monero whill increase a fixed amount per year with no decrease in the money supply. For the sake of simplicity, let’s say there’s 100 Monero in supply, and every year 10 Monero gets added into the supply. Then,

100 -> 110: 10% increase

In the second year, it goes from 110 to 120, which amounts to a:

110 -> 120: 9.1% increase

120 -> 130: 8% increase

Notice that every year, the rate at which your Monero inflates decreases asymptotically. After the 20th year, there’s 300 Monero in supply, and on the 21nd year that’s a 5% increase, so on and so forth.

So, the rate of inflation goes to zero. That doesn’t mean that Monero has an asymptotically fixed supply, it just means that eventually there’d be enough Monero floating around where adding 0.6 per block wouldn’t make a huge dent to the money supply and purely serves to incentivize mining without the exorbitant transaction fees seen in Bitcoin.

I’m no economist, I studied Math. But I studied enough Math to know when a diff eq doesn’t really hold up in an argument. In reality, coins DO get lost, and at what rate who knows? (especially in an obfuscated blockchain only God knows) Overall, my take is that people are really hyperfixating on the fact that Monero has a constant inflation of its money supply, but the real problem economically is unpredictable and large changes in money supply over short periods of time (IE gov’t bailing out banks, printing money during a famine, etc)

What you think??