ElasticGovernanceToken (EGT) is a positively rebasing asset-backed governance token.
TLDR: The overall supply of EGT and the amount of assets backing each EGT increase every time a rebase happens.
lambda The base value of EGT; increases every time someone joins the DAO. Decreases every time someone exits the DAO.
m: Lambda modifier - the rebasing modifier ; increases every time someone joins the DAO and is the technical driver behind the rebasing mechanism
elasticity: The percentage increase in backing assets every time a rebase is triggered.
k: Token multiplier; increases the number of EGT that each base unit (lambda) represents.
The redemption value of each EGT is given by Capital Delta(δ), which is calculated by:
Capital Delta (δ):
e - The total amount of backing assets in the DAO's vault (ETH)
t - The total supply of EGT
The total supply of EGT (t) is given by:
λ - Lambda
m - Lambda modifier
k - Token multiplier
Capital Delta ( δ ) and Tokens (t) are functions on ElasticMath.sol.
The rebase is triggered when someone calls the join function in ElasticDAO.sol
function join(uint256 _deltaLambda)
The amount of ETH required to mint deltaLambda accounts for the increase in the value of each EGT. The increase in m value provides the increase in number of EGT for all existing token holders. (math explained below).
The amount of ETH required to purchase deltaLambda ( ΔE ) is given by:
δ - Capital Delta
k - Token multiplier
λ' - The amount of lambda after the rebase.
λ - The amount of Lambda before the rebase.
m' - The value of the Lambda modifier after the rebase.
m - The value of the Lambda modifier before the rebase.
elasticity - Increase in the number of assets backing each EGT.
Every time the rebase is triggered, the lambda modifier m gets modified:
λ' - Number of Lambda after the join
λ - Number of Lambda before the join
Δλ - DeltaLambda - The Amount of Lambda minted
resulting in the new supply of tokens being,
deltaLambda > 0 (uint can never be negative), this results in
λ' > λ, and
m' > m.
t' > t, i.e, the supply of tokens has increased.
Note that, upon every rebase
δ' > δ i.e the number of assets backing each EGT has gone up.
The numerical value of
elasticity and ETH provided at summoning determines the price trend and supply of the token.
There exists a logical range between the assets required to mint each EGT (via the join function - triggering a rebase) and the assets received for each EGT during redemption (a call to the exit function).
For a given set of values of
k the trend is given by: