These assumptions aren’t right (ergo the downstream conclusions aren’t built on a good foundation).
Given that we’re maintaining a 1 Grain = 1 Dai peg, we have the following quantities:
- Outstanding Grain (G)
- Dollar/Dai reserve (D)
With the following flows:
- Grain Issuance to contributors (+G)
- Grain burn rate due to boosting (-G)
- Grain Redemption for dollars (-G, -D)
- Grain Minting from Dollars (+G, +D)
The project “goes bust” if D==0, since at that point we can no longer redeem Grain at peg.
The “reserve ratio” is what proportion of outstanding Grain is backed by dollars, i.e. D/G. When the reserve ratio is over 1, it’s impossible for the project to go bust, even if everyone decides to redeem. When the reserve ratio is below one, a “Grain run” is possible. When the reserve ratio is 0, we are busted.
Note the big difference from your construction, is that at the first-order level we aren’t worried about having long-run net Grain issuance, i.e. the total outstanding Grain can grow indefinitely without the org ever going bust. What we do care about is the redemption flows, and the reserve ratio.
I do agree that we want to reduce the volatility of contributors’ grain flows. Here’s a simple proposal for doing so: Grain Vesting