Appendix
Mathematical Equations
Equation 1: Reserve Ratio Equation
Equation 2: Buy/Sell Function & Current Price(Bancor Formula for Automated Market Making)
Current Price function:
Buy function:
Sell function:
Equation 3: Expansion Rate Formula
Equation 4: Mint G$ from Declining Reserve Ratio - Once a day the reserve ratio is reduced while all other parameters are unchanged.
Equation 5: Mint G$ from Deposit Formula - The number of new tokens based on the daily interest deposited in the Reserve.
Z - Value deposited into the reserve
E - Newly minted tokens
Monetary Example
This is an illustrative example with no relation to real parameters.
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 via two methods: the decline in reserve ratio and from the deposit of interest to the GoodReserve.
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.
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