The current economic proposal has an inherent problem, which is that many people will be discouraged from buying XRD during stage 1. The reason being that at stage 2, it is very likely that genesis holders may choose to sell at a market price of far less than the target $1, with very little downside protection due to lack of reserves. This inevitable drop in price, along with the large range between Pmin and Pmax, may result in the price simply fluctuating within Pmin and Pmax indefinitely, resulting in poor stability.
In addition to this, the model does not provide any price inflation, only supply inflation, which limits the ROI significantly and naturally deters buyers from buying close to Pmax.
I propose that rather than trying to keep XRD within a discrete price range ($0.9-$1.1), the system instead tries to limit the volatility within a certain time period (for example, 24 hours). This model would allow the price to rise and fall at the mercy of the market, but as the system matures, can be tightened to an increasingly smaller range of daily volatility.
Pmin = 0
Pmax = $1.1
Initial Price = $1
Genesis Supply = 79M XRD
From the start of stage 1, tokens can either be purchased from the genesis holders at market price, or at Pmax ($1.1) from the DEX (if the demand exceeds supply). At this stage, there is no downside protection but the price can rise by up to 10% (in each 24 hour period).
If demand drives the price above Pmax ($1.1), the DEX will mint XRD and the proceeds from these sales will go into the reserves and start to build Pmin. Note: there is no distribution at this stage.
Perhaps more realistically, with insufficient demand to hold the price at Pmax, the price will naturally fall (potentially close to 0).
At the end of 24 hours, the DEX will re-set Pmax to the current market price +10%. For example, assuming at the end of day 1, the price of XRD is now trading at $0.50, Pmax for day 2 will become $0.55. As before, the price is free to float within Pmin and Pmax, with any proceeds from XRD minted by the DEX, further increasing the reserves and the Pmin value. Note: still no distribution at this stage.
This model continues with Pmax being reset every 24 hours. As the Pmin floor increases, once it reaches a defined value, for example Pmin = P-10%, stage 2 can begin.
Pmin = P-10%
Pmax = P+10%
During stage 2, the market will have naturally discovered a price for XRD and has become more mature with daily volatility reduced to +/- 10%. There are now sufficient reserves to purchase all XRD in circulation at a price of Pmin. As demand increases, any XRD purchased at Pmax will provide a profit to the DEX (Pmax - Pmin), with 50% of these proceeds being distributed to holders, and 50% being used to further increase the reserves:
R = Rm(Pmax - Pmin)/2
where, Rm = number of new XRD minted
and, R = redistribution amount to holders and reserves.
If demand falls and the price drops to Pmin, the DEX will step-in to purchase XRD at Pmin and burn these tokens.
During stage 2, half of the redistribution goes to increasing reserves, and thus Pmin will continue to rise. During periods of high demand, holders will be rewarded with an increase in price, as well as increased supply from distribution.
During periods of low demand, XRD will benefit from limited daily volatility of 20%.
Stage 2 continues with Pmax being reset every 24 hours and until Pmin reaches a mature value of, for example P-1%. At this point, stage 3 begins.
Pmin = P-1%
Pmax = P+1%
At stage 3, the volatility has been significantly reduced to +/-1% per day and could be tightened further to provide increased stability. At stage 3, any XRD that is minted will result in a profit to the DEX (Pmax-Pmin) which will be redistributed 100% to holders.
Note: The values shown are for example only. The volatility range for each stage could vary, along with the time period for recalculating Pmax.
In theory, this system rewards early adopters with both price and supply inflation (at the risk of higher volatility) and as adoption increases and the system matures, ultimately results in stability (of volatility, rather than price).