RE: Where does the money come from? A look into the economics of Steem.

[arhag]

There is 100% APR inflation of STEEM. 10% goes towards expenses and the other 90% goes to the vest pool (that is what causes an increase in your Steem Power amount over time). So to understand what the effective tax rate is for both liquid STEEM and Steem Power we need to do a little bit of math. For liquid STEEM, the tax rate is easy to calculate: if the STEEM supply doubles in a year and you just hold onto a fixed amount of liquid STEEM over this time, then clearly (on a relative basis) you were effectively taxed at 50% per year.

For calculating the tax rate on Steem Power, it gets much trickier. To simplify we assume that the percentage of STEEM held as Steem Power remains constant over the year. We also assume that all Steem Dollars received are converted back into STEEM as soon as possible, and the conversion price happens at the same price at which they were issued to simplify the analysis.

Now if that percentage was exactly 90%, then no net powering up/down would need to be done to maintain the percentage of STEEM held as Steem Power over the year. In that case, the fractional ownership of Steem Power for someone who earns no rewards and doesn't power up/down would remain the same, or a 0% change over the year.

Then we can look at the other extreme case. What if virtually all of the STEEM was held in Steem Power throughout the year? Well, if the total supply of STEEM was initially T, the supply of STEEM after the year would be approximately 2 T STEEM. 0.9 T STEEM would have been issued and added to the vest pool directly, while 0.1 T STEEM would have been issued and distributed to users as the various rewards but eventually all powered up (in order to maintain the 100% STEEM held in Steem Power condition). A user that just held onto their Steem Power (which originally was a fraction f of the original Steem Power), would have had a claim to an additional 0.9 T f STEEM from the amount of STEEM added to the vest pool directly. So, at the end of the year, that user would had a claim to1.9 T f STEEM from the total 2 T STEEM existing in the system at that time (which would all be in the vest pool). So their new fractional ownership would be f' = (1.9 T f) / (2 T) = 0.95 f. The percentage decrease in their fractional ownership of Steem Power would be 100% * (f - 0.95 f) / f = 5%. So, the fractional ownership of Steem Power for someone who earns no rewards and doesn't power up/down would decrease by 5% over the year in this scenario where virtually all STEEM is held as Steem Power.

The reality is somewhere in between those two extremes (actually, in reality, you would need to bring in the effect of Steem Dollar conversions which complicates things considerably and requires you to use models that make some prediction about the future price of STEEM and the how many Steem Dollars are converted to STEEM and when). One expects a large percentage of STEEM to be held in Steem Power, but it obviously won't be 100%. So that is why I say that the effective tax rate on Steem Power (on a relative basis) is some variable amount that is less than 5% per year.

Comments

[anonymint]

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

[arhag]

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%.

[anonymint]

At every block, SP holders receive 9 SP for every 1 STEEM created. So their debasement is already 1 ÷ 9 = 11.1% on that aspect alone. But slowing down to look at it again, I realize that is only looking at the delta of the debasement not the dilution of the existing. To correct your original computation to my assumption of a steady 9-to-1 ratio between SP and STEEM, then SP holders would have 1.80 out of 2.0 yearly, so that is a 0% debasement as they start and end with 90% of the supply.

But that computation above does not factor the debasement of SP holders by the fact that 50% of the 7.75% annual rewards are distributed as SP. Thus that is a debasement of existing SP holders because the 9 tokens that are distributed proportionally so these new SP holders take some of the 1.80 in the calculation above. The precise calculation requires a compounded function. It is going to be some where in the realm of your 1.7% factor in your most recent calculation. It is 3.875% yearly, but it accrues throughout the year. So I'll just round off (because I am lacking time to write down the precise math for that small difference) and say debasement is 0.85% (instead of my 15%) in this case of 9-to-1 ratio. But I'd need to check your compounding calculations to be sure it is that low. Obviously that considerably alters my analysis of the value of powering up to SP.

In my second calculation (21%) which had the same assumptions as you did that all STEEM is powered up immediately, then I had the same error of considering only the delta, wherein the correct is 1.90 of 2.0 so 5%. And I did add the a factor for 7.75% being powered up, and again this needs a compounding calculation to be accurate. You seem to have computed 1.7% which seems low to me, so a total of 6.7%, but I guess that is the power of compounding and I'll assume your math is correct.

With a ratio lower than 9-to-1, the compounding debasement is changed to a compounding gain.

I will correct my post which linked to this one. Thanks.

[anonymint]

I don't exactly see how your formula relates to the formula I arrived at, although our numbers end up very close. Perhaps you can explain and relate your computation to mine?