It is important the Steem(it) users and investors have an accurate understanding of how much debasement is accrued yearly to fund the various rewards paid by Steem, 77.5% of which is for blogging and curation rewards.
Although it is (multiples) higher now and falling fast, in the future the rate of Steem’s money supply growth will stabilize at approximately 100% (a doubling) yearly. Of that 100% yearly increase¹, 5% is created as STEEM DOLLARS (SD) and the rest as STEEM POWER (SP). And 90% is distributed to existing SP holders.
Approximate STEEM POWER (SP) Debasement Rate
The yearly SP debasement rate depends on the ratio of SP to non-SP (i.e. STEEM and SD).
An approximate mathematical model of the effect on SP holders, is to assume the ratio is 95:5, i.e. that there is no net powering up or down so the relative rate of creation of money supply dominates the ratio. In a recent video interview with @dollarvigilante, @dan and @ned confirmed that 95% SP is the approximate ratio currently.
So on a yearly basis, in a normalized to 100 money supply example, the holders of SP at the start of the year possess 95 of the money supply and end the year with 95 + 90 = 185 of the 200 money supply. Thus those SP holders’ percentage of the money supply drops from 95% to 185 ÷ 200 = 92.5%. Thus the SP holders from the start of the year are debased by (95% - 92.5%) ÷ 95% = -2.6%.
Note a percentage of the money supply is equivalent to percentage of the market capitalization. Thus any change in price due to the 100% increase (i.e. 50% dilution) of the money supply (such as in the often maligned Quantity Theory of Money) is irrelevant given the above computation is a percentage of the market capitalization.
Interestingly if the ratio of SP to non-SP is 90:10 then in our approximate model model above, the SP holders from the start of the year are not debased, because 90 + 90 = 180 and 180 ÷ 200 = 90% and this is functionally just a forward stock split for the SP holders in this approximate model.
The generalized equation for the debasement in this approximate model is ((100 × (x + 90) ÷ 200) - x) ÷ x where x is the numerator of the ratio normalized to 100. So if all the money supply is SP then the approximate yearly debasement is ((100 × (100 + 90) ÷ 200) - 100) ÷ 100 = -5%. And if 50% of the money supply is SP then the approximate yearly debasement is (100 × (50 + 90) ÷ 200) - 50) ÷ 50 = +40%, i.e. the SP holders gain 40% value as a proportion of the money supply!
Precise SP Debasement Rate
The approximate model ignored the fact that disbursements happen every day (or even intra-day frequency) throughout the year and that 5% of the newly created money supply is SP. Thus these new holders of SP take some of the normalized 90 units of the money supply that the approximate model above assumed would all go to the holders of SP at the start of the year.
The mathematical series for this daily compounded model is:
(90÷365) + ((90-5÷r÷36)÷365) + ((90-2×(5÷r÷365))÷365) + ... + ((90-365×(5÷r÷365))÷365)
where r is the SP to non-SP ratio.
Which can be simplified with the nth triangular number:
(90 - (5÷r÷365)×(1+2+...+365))÷365 = (90 - 5÷r÷365×365(365+1)÷2)÷365 = 90 - 5÷r×183÷365
So for ratio 95:5, the holders of SP at the start of the year will receive 90 - 5÷0.95×183÷365 = 87.4 normalized units of money supply. So we can precisely calculate the debasement (100 × (95 + 87.4) ÷ 200) - 95) ÷ 95 = -4%
| SP:non-SP | Yearly Debasement Rate |
|---|---|
| 100:0 | -6.3% loss |
| 95:5 | -4.0% loss |
| 90:10 | -1.5% loss |
| 80:20 | +4.3% gain |
| 70:30 | +11.7% gain |
| 60:40 | +21.5% gain |
| 50:50 | +35.0% gain |
| 40:60 | +54.7% gain |
| 30:70 | +86.1% gain |
| 20:80 | +147% gain |
| 10:90 | +275% gain |
| 5:95 | +349% gain |
Obviously if the market capitalization of the money supply of Steem (and thus including SP) increases (via less price declines than the creation of money supply would proportionally dictate) more than the negative debasement rate, then there is not a loss in exchange value. So the price can actually decline while the SP holders will see their net worth increase in exchange value.
In Part 2, I will do the calculations for the debasement of STEEM.
P.S. note there was a prior blog post about this, in which we had discussed the correct math in the comments. I believe my explanation above is more succinct and clear for the average person.
¹ Note this doesn’t include the currently 10% APR interest paid to SD holders, but we will ignore that relatively insignificant factor for our first estimates, given that currently only 2% of the money supply is SD. And also relatively insignificant given that the 10% APR can decline in the future.