# Bonding Curve - Bera

### Introduction <a href="#introduction" id="introduction"></a>

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 <a href="#definitions" id="definitions"></a>

#### **Curve** <a href="#curve" id="curve"></a>

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** <a href="#setting-initial-values" id="setting-initial-values"></a>

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** <a href="#values" id="values"></a>

* 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) :** <a href="#calculation-on-tokens-to-migrate-m" id="calculation-on-tokens-to-migrate-m"></a>

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)** <a href="#calculating-tokens-to-burn-b" id="calculating-tokens-to-burn-b"></a>

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