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I'm confused, though I think I'm putting it together. I see you're threading the needle of making the fee adaptive while giving the fee the ability to serve its intended purpose of preventing blocksize expansion. I think you were on to something before with using the difficulty as an on-chain surrogate of external value. I think the need for that factor will exist at any stage of the chain's life - during initial distribution curve and during the tail emission. Your second scenario above seems focused on the tail emission portion of the coins existence, which doesn't happen for another ... however many years.
No the second scenario is determined by the median blocksize becoming larger than 60,000 bytes, not Monero reaching the tail emission. One can consider Bitcoin here as a special case where the penalty is infinite and with a fixed blocksize of 300,000 bytes. This was to a large degree the situation with Bitcoin until the spring of 2013.
In either case the top three fee tiers would be determined by the blocksize penalty formula. There is really not much choice here if these fee tiers are going to challenge the blocksize penalty formula. There is no reason, however, why the bottom two fee tiers could be not based on a difficulty ratio as was my original idea even after tail emission. The one proviso here would be to cap the lower two tiers at some percentages of the third tier. If the difficulty were to increase with time due to much more efficient hardware this could cause a spread in the fees over time that would make the Monero transactions when there was no pressure on the blocksize very affordable. Spammers would still be blocked by the third and higher tiers.
Here is some research on Metcalfe's Law which to a large degree does support the case for not relying solely on the blocksize scaling / penalty formula for the lower two fee tiers, since the research indicates n log (n) rather than n as the rate of growth of the value of a network with n nodes. The extrapolation here is to replace the size of the network by the number of transactions in a given period of time.
http://spectrum.ieee.org/computing/networks/metcalfes-law-is-wrongEdit 1: There was an effective maximum blocksize in Bitcoin of around 256 KB until the spring of 2013.
Edit 2: A better distinction here is between those fee tiers at the lower end that are not challenging the penalty and those above that are challenging the penalty rather than between the two scenarios I indicated before.
I'm going to copy the formula you posted earlier to make sure I get it -
For simplicity I will define:
BlkSize = (1+B) M
NBaseReward = R
basePenalty (for a given B) = P
BNewReward (for a given B) = R
BI'm assuming that B is the current block? Is it the size of the block in bytes? kb? I think its the 1 + B that is throwing me off. Does that just mean "the next block"?
The penalty for a given B becomes:
P
B = R
baseB
2While the new reward for a given B becomes:
R
B = R
base(1 - B
2)
The first derivative of P
B with respect to B is
dP
B /
dB = 2R
baseB
I apologize that I can't parse the equations. Its even worse as I type now with the bbcode or whatever formatting it is.
So if I'm reading this right, you're using hashrate as an indicator of the size of the network? Or just use something other than blocksize scaling / penalty formula for the first two tiers?
I apologize for being obtuse in my understanding.
The way that I understand things is that we need a way to match the internal cost (xmr) with the external value of xmr for adding data to the blockchain. With the multi-tiered system you propose, something is used to adjust the xmr cost for the first two tiers, and then for tiers 3,4,5 , it uses a component of the block size penalty. I think what I'm not getting is that as the network becomes more valuable, the internal xmr cost has to go down to maintain the usability of the network. Now, if the change in the transaction fee is coupled to a transaction priority system and is dependent on the block penalty... wouldn't all those things imply that the transaction fee is increasing?