Bonding Curve - Bera
Introduction
This is an implementation of a bonding curve mechanism for buying and selling Moonshot tokens based on virtual collateral and token reserves, also known as a Constant Product curve. The curve has an exponential shape so that the price rises slowly at the start and fast towards the end.
Once ~80% of the 1B token supply is sold on the curve, the fully diluted market cap reaches over 10,000 BERA and all remaining tokens & collateral migrate to Kodiak. Approximately ~1965 BERA of collateral is collected on the curve.
The price at migration is 16.56 times the initial price on curve
Definitions
Curve
vTOKEN * vBERA = k
Where,
vTOKEN = virtual reserve of the token
vBERA = virtual reserve of the collateral (BERA)
k = constant that determines the shape of the curve
Setting initial values
We set the value of the coefficient k based on the initial price of the token
k = vTOKEN * vBERA = iVTOKEN * iVBERA - (1)
Where, iVTOKEN and iVBERA are the initial amount of vTOKEN and vBERA respectively
We set these as follows :
iVTOKEN = 1.06 * 10^27 minimal unit token
iVBERA = 6.4 * 10^18 minimal unit token
Values
Total supply of tokens (T) = 1,000,000,000
Minimum price is set to 1gwei or 10^-9 BERA
MarketCapThreshold is set to a fully diluted market cap of 10,000 BERA at ~80% of tokens sold. It is simply the (1 billion ) * (Price of token at allocation A)
Allocation at Migration (A) = ~80% of total supply
The exact minimal token amount is 799,538,871. Tokens have 18 decimals. That will be the exact point passed when trading stops and the migration begins.
If a buyer places a larger trade right before the ~80% threshold, a max allocation of 80.94% can be sold on the curve
Fee to be deducted at the time of migration (F) = 45 BERA
Calculation on tokens to Migrate (M) :
For calculating M, we will calculate, at the time of migration (when supply reaches the allocation A),
BERA collected as collateral
Reduce the fee to be charged from the collateral BERA
Calculate the price at the time of migration (allocation reached)
Determine the no of tokens (to be migrated) based on the collateral collected and price at allocation
M = (collateral collected - migration fees) / price of token
Collateral Collected= current_virtual_collateral_reserves - initial_collateral_reserves
Migration fees = Fee charged for creating a pool on Uniswap + Moonshot migration Fee = 45 BERA
Price of token = current_virtual_collateral_reserve / current_virtual_token_reserve
Calculating tokens to Burn (B)
Tokens to Burn (B) = T - A - M
= Total Supply - allocation(tokens sold at migration) - tokens to migrate (M)
So the total tokens in circulation post migration would be = A + M
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