PraSaga SagaCoin Management Model
By: David Beberman and Lawrence H. White, PhD.
Abstract
Bitcoin uses an arbitrary pre-determined release schedule to govern the number of coins in circulation. Most other cryptocurrencies have followed suit. Because the quantity of coins is completely unresponsive to changes in demand for the coin, price bears the entire burden of adjustment, which renders the market value of the coin highly volatile and unpredictable. The potential for appreciation of such a coin may attract speculation in it, but a highly volatile and unpredictable purchasing power does not support a coin’s use as a transactions medium. Its unresponsive quantity renders Bitcoin (and others of similar design) unable to deliver on the promise that it would become the world’s money.
To provide a useful on-chain exchange medium, so-called stablecoins have emerged. But coins pegged to the US dollar can provide purchasing-power stability no greater than that of the US dollar. We propose a different approach, a coin that will, after an initial launch period, transition to a money whose supply expansion is programmed to respond appropriately to variations in the growth of the demand for it. Appropriately demand-responsive supply will make its purchasing power stable and predictable over the medium to long term. This model –sometimes called a “flatcoin” — stands the best chance of enabling a decentralized Layer 1 coin to be widely adopted as a medium of exchange.
The coin’s “purchasing power” means its average exchange rate against goods and services. Put another way, purchasing power (bundles of goods / coin) is the inverse of a price index measured in the coin (coins / bundle of goods). A stable purchasing power means that an index of prices measured in SagaCoin will exhibit a flat trend.
We propose four successive stages in programmed coin supply management. The first two are “launch” stages. The third and fourth are mature stages, in which supply will respond to price with the aim of making the coin’s purchasing power stable and predictable. Expected stability of purchasing power makes SagaCoin attractive to hold as a medium of exchange, promotes its widespread adoption as a payment medium, and thereby enhances demand for the coin from the start.
The classical gold standard may be considered a prototype flatcoin. Long-term inflation was near-zero because more gold would be produced per year when the purchasing power per unit of gold was above normal (the level determined by the long-run marginal cost of mining). Faster growth in the stock of monetary gold brought the purchasing power back down. On the other hand, when the purchasing power was below long-run cost, less gold was produced per year, bringing its purchasing power back up. In a similar way SagaCoin will have a mean-reverting purchasing-power, although our supply will adjust more rapidly.
The program can maintain a given total money supply over any period by having the minting rate and the burning rate equal each other. Increasing money supply means minting beyond burning. We expect minimal need to ever shrink the total money supply, with demand continuing to grow, even as the growth rate of demand varies.
Stage One:
In the initial phase, SagaCoin may appreciate in periods with growing demand to acquire and use it (or not appreciate in periods without growing demand). The purchasing power per coin is not capped during any quarter, nor over the entire first stage. Once it has a market price on exchanges, SagaCoin will acquire a reference path for its purchasing power per coin.
Stage Two:
Starting with the purchasing power per coin achieved at the end of Stage One, the program introduces a target appreciation path and quarterly resets of the coin expansion rate. If the target is exceeded during a quarter, the net expansion rate increases in the next four quarters to return purchasing power to the reference path. The targeted appreciation rate per quarter may be gradually diminishing. Such a moderation of the appreciation path allows a more gradual approach to stage three, where purchasing power is stabilized.
In this stage, the supply formula is
gMt = gCt3–0.25 (ppt — ppt*)
where
gMt = percentage expansion of SagaCoin quantity to be created in quarter t by net minting
gCt3 = quarterly trend growth in purchasing power (3-quarter moving average over t-3 to t-1)
ppt = natural log of purchasing power at start of quarter t
ppt* = natural log of target purchasing power at start of quarter t, where ppt* = ppt-1 times the target appreciation rate.
(ppt — ppt*) is thus the percentage difference of purchasing power from its target path.
An example illustrates how an undershoot of the purchasing power target triggers error-correction in supply. Suppose that demand growth temporarily slows such that the coin is trading for R$9 when R$10 was the end-of-quarter target (R$ are “real dollars,” i.e. R$10 = US$10 + adjustment for $ inflation). In this example, the real price is 10% below target. The program responds to the discrepancy by reducing quarterly coin supply growth by one-fourth of the discrepancy, here 2.5 percentage points, to 7.5% per quarter. Other things equal, assuming that real demand for the coin resumes growing along a lower path, the supply growth reduction to 7.5% will allow faster appreciation per coin. With appreciation 2.5 percentage points higher, the 10 percent shortfall in purchasing power (R$9 versus R$10), will be eliminated in approximately 4 quarters, bringing the coin’s purchasing power back to target.
A market value above target will correspondingly prompt faster quantity expansion to eliminate the gap.
Stage Three:
Once appreciation to the desired level has been achieved [or after a set number of quarters] a flat purchasing power path is targeted. Zero expected appreciation or depreciation, and low volatility through monthly adjustment of the minting rate, makes SagaCoin attractive to users as a medium of exchange. The net expansion rate (minting minus burning) will increase as necessary to return purchasing power to its reference path if purchasing power begins to rise, and decrease as necessary to return purchasing power to path should it begin to fall.
In this stage, the appreciation target being zero, the supply formula becomes
gMt = gCt3–0.25 (ppt — pp*), with pp* constant.
We assume that transaction volume on the SagaChain is still small at this stage, and that the prices of goods and services are predominantly quoted in US dollars. Purchasing power stability will maintained by targeting a flat path for the constant dollar price of SagaCoin, that is, by targeting its nominal dollar price adjusted for dollar inflation as measured by a combination of dollar price indexes (the monthly urban consumer price index, the quarterly GDP deflator, and the quarterly personal consumption expenditure deflator). Con price and USD inflation data will be fed to the program by oracles. To the degree that the US dollar loses purchasing power due to price inflation (the dollar price level rises), while the coin’s purchasing power succeeds in its objective of remaining constant (see below), SagaCoin will appreciate against the dollar.
For example: During the 2nd quarter of 2022, the US CPI-U index rose 2.33% (which compounds to an annualized rate of 9.66%). In response to such a data point the program will raise the next quarter’s nominal dollar price target for SagaCoin by 2.33 percentage points.
Stage Four:
Once SagaCoin becomes widely used as a payment medium, we envision a transition to an internal pricing model. The supply expansion formula remains the same as in Stage Three, but in place of oracle-reported fiat price indexes we deflate using an index of SagaCoin-denominated prices taken directly from the SagaChain.
The internal reporting will be based on encrypted reporting of results by businesses using the blockchain. It will make use of zkSNARKs and equivalent to provide provable rough estimates, instead of actual values. The approach is to have something analogous to 10K type reporting. In this way the price-sampling process will maintain transactional privacy.
The expected model will combine these two factors, and additional factors as we gain experience with the chain’s use. The weight on internal prices can adjust as the internal market grows. Thus the transition from Stage Three to Stage Four can be gradual.
