# Bonding curve - EVM
### 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 25 ETH and all remaining tokens & collateral migrate to [Uniswap V2](https://app.uniswap.org/swap)(for base) and [Abstract Swap](https://www.abs.xyz/trade)(for Abstract). Approximately \~4.9 ETH of collateral is collected on the curve.
The price at migration is 16.56 times the initial price on curve
### Definitions
#### **Curve**
vTOKEN \* vETH = k
Where,
* vTOKEN = virtual reserve of the token
* vETH = virtual reserve of the collateral (ETH)
* 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 \* vETH = iVTOKEN \* iVETH - (1)
Where, iVTOKEN and iVETH are the initial amount of vTOKEN and vETH respectively
We set these as follows :
* iVTOKEN = 1.06 \* 10^27 minimal unit token
* iVETH = 1.6 \* 10^18 minimal unit token
So initial price = iVETH/iVTOKEN = 1.509433962 gwei
#### **Values**
* Total supply of tokens (T) = 1,000,000,000
* Minimum price is set to 1gwei or 10^-9 ETH
* MarketCapThreshold is set to a fully diluted market cap of 25 ETH 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) = 0.15 ETH
#### **Calculation on tokens to Migrate (M) :**
For calculating M, we will calculate, at the time of migration (when supply reaches the allocation A),
* ETH collected as collateral
* Reduce the fee to be charged from the collateral ETH
* 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 = 0.15 ETH
* 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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