Let: - the price of one 1G$ in Supported Currency; - the amount of Supported Currency in the reserve; - total G$ coins in circulation.
Then - the reserve ratio - is defined as:
At launch, and overtime, will computationally decline at a daily rate in accordance with the Expansion Rate. In Equation 1, given and the system has two degrees of freedom, and that will be calculated as described below.
Current Price function:
Buy function:
Sell function:
The GoodReserve contract mints an amount of G$ to satisfy Equation 1 . If P and R do not change and the daily change in r=𝚫r and the corresponding change in S is 𝚫S, then and from here we can see that:
From Equation 2 we get and thus:
Z - Value deposited into the reserve
E - Newly minted tokens
The formula does not change the price or reserve ratio:
This is an illustrative example, with simple rounded numbers, aimed at trackability:
10 Supporters have staked a total value of US$10 million in supported crypto to a third-party protocol
Protocol annual interest rate of 10%
Daily interest of US$2,736
G$ Price = US $1
GoodReserve = US $1,000,000
Supply of G$ = 1,250,000
G$ Market Capitalization = US$ 1,250,000
G$ Reserve Ratio = 80%
Daily Expansion Rate = 1%
Every day G$ minting occurs from two methods: From the deposit of interest to the GoodReserve and from the decline in reserve ratio.
Minting derived from deposite of daily interest to the GoodReserve
Deposit of US$2,736 to GoodReserve
Calculated as follows:
(1,250,000 +X)*1=(1,000,000 + 2736)/0.8
1,250,000 + X = 1,002,736/0.8
1,250,000 + X = 1,253,420
X = 3,420
3,420 G$ are minted
2,736 G$ are allocated back to the 10 supporters
684 G$ are distributed as basic income
Mint from Reserve Ratio Decline
Lower the Reserve Ratio from 80% to 79%
Calculated as follows:
(1,253,420+X)*1= 1,002,736/0.79
1,253,420 + X = 1,269,286
X = 15,866
15,866 G$ are distributed as UBI
In total, on that day 16,550 G$ were distributed as basic income to Claimers.