Quote from: iamnotback on July 25, 2016, 09:00:26 PM

Quote from: chryspano on July 25, 2016, 08:21:03 PM

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anonymint · 3 hours ago
The 5% calculation appears to me incorrect. I calculate 15 - 21%. You are not factoring for example the 50% payout in STEEM POWER.

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arhag · 35 minutes ago
No, I am factoring in the payouts in Steem Power. A far more sophisticated analysis of the math is necessary to get more accurate numbers in more realistic scenarios, but I am pretty sure the numbers you have calculated are incorrect. However, by being slightly more careful in my analysis (rather than the first approximation I did for the OP), I find that my original number of 5% was also too low of an estimate in the worst case scenario. It is really more like 6.7%.

First, as I mention before, I am not factoring in the effect of price changes and Steem Dollar conversions on STEEM supply (or the virtual supply used in the code). Trying to factor that in makes things too complicated and requires assuming models for how the price of STEEM will change and how people will convert Steem Dollars. To greatly simplify the analysis I assume that people convert Steem Dollars into STEEM as soon as possible and at the same price at which it was issued (actually I really go further and assume the blockchain skips a step and just gives the bloggers the reward as STEEM rather than Steem Dollars so that they can then convert to Steem Power as soon as possible).

Second, I am looking at the worst case (in terms of maximum inflation of Steem Power) by assuming nearly all of the STEEM is kept in Steem Power at all times. Meaning if people receive rewards in any other form, they convert it into Steem Power as soon as possible.

Converting STEEM into Steem Power (i.e. VESTs) does not change the ratio of STEEM in the vest pool to the total amount of VESTs, whether done by the user or done by the blockchain directly. The only thing that changes (specifically increases) that ratio is when the blockchain directly adds STEEM it issued into the vest pool without creating a corresponding amount of VESTs.

If we define S to be the current virtual supply of STEEM (which with the assumptions above is also exactly the amount of STEEM in the vest pool), then we can approximately say that the blockchain creates 7.894E-5 * S STEEM each hour (90% of which is added directly into the vest pool and the other 10% is given out as rewards which are ultimately all, since this is the worst case scenario we are looking at, converted into Steem Power).

Let S_0 be the virtual supply of STEEM at the start of the year period that we will be analyzing. Let S_n be the virtual supply of STEEM n hours after that start time. Then we can write that S_n = S_0 * (1 + 7.894E-5)^n.

The recurrence relation for updating the total outstanding amount of VEST tokens V_{n+1}(at the time n+1 hours after the start time) is given by

V_{n+1} = V_n (1 + \frac{\Delta s_n}{S_n})
where \Delta s_n is total net amount of STEEM converted into Steem Power (VESTs) within the corresponding hour (because I am lumping these conversions into hour intervals it is actually just an approximation of the real update rule, but good enough for our purposes). The quantity \Delta s_n is given by 7.894E-6 * S_n, since in this worst case scenario I assume all STEEM created for distribution as rewards (the 10% of the total amount created) will all be converted back into Steem Power. I can use the recurrence relation above to write an expression for V_n:

V_n = V_0 ( 1 + 7.894E-6)^n
If a user initially holds v VESTs, which is a fraction f of the total VESTs at that time (so v = f * V_0), then after a year (n = 8766) the total virtual supply of STEEM will be S_{8766} = 2 * S_0 and the total outstanding amount of VEST tokens will be V_{8766} = (1.07165 )* V_0. And so the new fraction of total VESTs the user will hold (assuming they received no more VESTs through rewards or powering up) is f' = v / V_{8766} = 0.93314 * f, which corresponds to a 6.7% decrease over the year in the user's fractional ownership of VEST (and therefore their fractional ownership of the marketcap of STEEM in this worst case scenario). So, if the market cap of STEEM were to stay constant (in USD), the user would need to buy up approximately 6.7% of their holding value each year to maintain the same USD value they started with, thus we can say it amounts to a 6.7% wealth tax (via a hidden inflation tax) on their Steem Power holdings. But this is the worst case scenario where all STEEM is held in Steem Power. In reality, not all of it will be held as Steem Power, and so the actual wealth tax rate for Steem Power holders should be less than 6.7% (again assuming we ignore other complicated effects left out of the above analysis like the Steem Dollar conversion effect).

Unfortunately, since the OP has already paid out, I cannot edit it to correct the 5% number to 6.7%.

https://steemit.com/steem/@arhag/where-does-the-money-come-from-a-look-into-the-economics-of-steem#@anonymint/re-arhag-re-innuendo-re-arhag-where-does-the-money-come-from-a-look-into-the-economics-of-steem-20160725t173848519z

Agreed he has corrected his calculation incorporating the term that I showed he had forgotten and also I have realized that I was stating the delta for my first term. So we both had a mistake.

The correct value is 6.7% where everyone is powering up, and lower than that if many are not powering up.

Note this doesn't change the point that not powering up is a 50% debasement/100% dilution (assuming liquidity rewards are restored, else 46.125% debasement/92.5% dilution). Thus I am still questioning the incentive for long-term investors to power up given the 1 year weighted price risk to cash out and the requirement that they must ramp up transaction (transfers) demand to the level that the STEEM not powering up is at least 10% of the money supply so that SP holders aren't debased.

Also it doesn't change my criticism that they've killled medium-term investment.

Quote from: Pheonike on July 25, 2016, 08:43:20 PM

Where does the 10% interest paid to holders of Steem Dollars factor in your equations? I don't see.

Please re-read that post as I have corrected it.

In both @arhag and my computations, we are assuming they are converted to STEEM.

Either arhag's computation is wrong or I don't completely understand his formula. In any case, the numbers end up being very close to what he had. I think I have explained it more clearly:

https://steemit.com/steem/@anonymint/who-pays-for-the-blogging-and-curation-rewards-part-1-steem-power