What is the purpose of the tail emission? How does it relate to dynamic block sizes and miners penalties?
The first question one needs to ask before even considering adaptive blocksize limits is: Can a fee market actually work in the absence of a base emission?
- We first consider a blocksize large enough (or effectively infinite). In this scenario competition among miners will drive fees towards zero since there is no scarcity. This will in turn cause the difficulty and consequently the security of the crypto currency to collapse. We must keep in mind that orphan block based arguments will also fail since these are based on the presence of a base emission. This is in fact the very legitimate fear of the small block proponents.
- In the second case we consider a fixed blocksize, where the blocksize is small enough to impact fees. In this scenario we have a potentially infinite demand with a fixed supply. In theory fees therefore would go to infinity. We must keep in mind that as the legitimate demand rises towards the fixed limit, It becomes economically attractive for miners with a even small percentage of the hash rate to spam the network in order to profit by raising the overall fees. At this point only external competitive factors can stop the fees from rising to infinity. These take the form of fiat payment methods and other crypto currencies with the latter being not affected by a fixed blocksize limit. The impact of these external competitive factors is to reduce demand by devaluing the entire crypto currency. This will be delayed by miner spam, as miners will increase the spam in order to preserve the dwindling purchasing power of their fees until the system collapses to little or no transaction demand leading the first case above.
The problem as I see it is that the system is inherently unstable. Either the mining revenue collapses first or the purchasing power of the mining revenue collapses first. We now come to the next question. Can one create an adaptive blocksize limit formula that does not converge as time increases towards (1) or (2) above? My instinct tells me no, particularly since the network has no way to measure the key parameter namely the amount of fees collected per block due to out of bound payments to miners. Furthermore there have been many brilliant minds looking at this issue and they have not come up with a solution. Proving this negative, in a rigorous mathematical sense, is of course another matter entirely. What the tail emission in Monero does is provide a stable anchor outside of the control of the miners on top of which an adaptive blocksize limit and a fee market can actually develop, by avoiding the instability above.
Another purpose is the equilibrium of the supply (over a very long period of time):
Let me give a slightly different perspective though, which is that Monero has a de facto limited supply, and we can even estimate it.
If we assume there will always be a percentage of the private keys being lost due to technical failures, human error, people dying and not arranging for access, etc., then any fixed rate of supply will reach an equilibrium where the rate of production (0.3/minute in Monero) is equal to the rate of loss which is PM (P=percentage lost keys per unit time, M=money supply). If we solve this equation for M we get M=0.3/Pminute which comes out to around 30 million XMR with P=0.5% per year.
We don't know P exactly, and P may not quite be constant over time, but this is a very reasonable model and it shows that Monero's money supply is not actually infinite in practice.
What if there was no gold to mine? The fact that it might be more efficient or beneficial to mine rather than buy from a collector adds needed complexity to market decisions. Beanie Babies were limited, and nobody gives a shit about them and I doubt even if they were infinitely divisible it would make a difference. Why not limit bitcoin to 10? why not 10 trillion? It's arbitrary.. there is only 1 Bitcoin and people are buying a percentage of it. At least if someone wants to get some Monero or gold without buying from someone else they will always have that option. Although inflation was not the intended goal, this property of Monero is a huge advantage over limited crypto currencies, though not as interesting as gold due to Monero's predictability.