Please try to wrap up this discussion between you and I (which I'm feel was worthwhile for me). Because I don't have free time to expend on this.
Thank you for your time and your insightful comments which were worthwile for me as well. Please let me some final comments for further clarification.
You don't need to answer them if you don't have enough free time (or prefer to work on your own coin design).
You've clarified a key detail just now highlighted in bold above. So you are saying that users need one mining account to enable earning interest on their non-mining tokens (your prior descriptions led me to assume interest was per mining account and had nothing to do with tokens owned)? So you are saying that there is no reason to own more than one mining account, because mining does not return enough to recoup the cost of buying an account. So you are implying mining is not profitable in the sense of total ROI, but it does produce profitable operating income. You did not make that distinction clear in your description and terminology before.
That was not at all clear to me from your original summary of your system. I suggest you improve your abstract.
Yes, you're right. I really should improve the abstract...
So now that I properly understand your design, I can more easily identify the flaws.
I think were are on the same page now, maybe with the exception of one very important aspect: Interests on coins are credited to every account every time a block is built (by anybody).
So, interest alone cannot be an incentive factor to buy more than one account since you get the very same interests (at the same pace), no matter how you split up your coins
between your accounts.
If the supply of new mining accounts is insufficient to match the number of new users who are buying tokens (which you state decline exponentially in order to make the mining account a sunk cost relative to mining profits), then it means competition in pricing for mining accounts means that only some tokens owners earn interest.
The supply of new accounts is linear: One new block = one new account.
Coin supply will depend on the percentage of stake held by minter accounts (since free accounts don't receive interests) and the interest rate set by the protocol.
Neither token will decline exponentially. What will decline (in theory) is the chance of successfully minting a new block as the competition will grow.
If we assume that investors actually use their accounts to mine, then for someome who is only using 1 account to mine, the expected intervals between mining your first, second, third... child account should increase exponentially.
(Of course, it's not realistic to assume that every investor will mint all the time, so that the intervals will be sub-exponential)
So in order to earn interest, there will be competition to consolidate token ownership ever and ever more concentrated. So that the price of new accounts keep rising until the supply of tokens is owned by a very individuals. This will also drive the price of the token down and down, because eventually only a very few large token holders can justify buying new accounts.
It's clear that the price of new account will be determined by those who have most stake. But assuming 10 minute block time, there will be 144 new accounts every day.
Even they can justify buying more than one new account, because their interest earned per mining account purchased is higher than their competition.
Their interests will be the same regardless of the number of accounts they own. Buying two accounts instead of one means that you get half the yield (w.r.t. interest).