Understanding and Automating Token Price Adjustments on Uniswap

1. Understanding the AMM Formula for Price Adjustment

On Uniswap and other AMMs (Automated Market Makers), the price of a token is based on the formula: 𝑥 × 𝑦 = 𝑘

adjustPrice()

: This function calculates the new target price based on the number of tokens sold and adjusts the Uniswap pool by adding or removing tokens so that the price follows the curve.

getReserves()

: This function retrieves the current reserves of the Uniswap pool to calculate the current price and adjust accordingly.

addLiquidity() and removeLiquidity()

: These are placeholders that you must implement to interact with Uniswap to add or remove liquidity.

2. Price Curve Calculation

You already have an equation that describes the price progression curve for your ICO. For example, let’s say your price progression equation is: 𝑃(𝑡) = 𝑃₀ × (1 + 𝑟𝑡) Where:

P(t)

= price at time t.

P₀

= initial token price (e.g., 0.01 ETH).

r

= price growth rate (e.g., 0.1 for a 10% increase per tranche).

t

= time period or tranche (e.g., after the sale of N tokens). Your goal is to adjust the liquidity pool so that the price follows this equation.

3. Integrating the Price Progression Equation into the Smart Contract

Your smart contract will need to:

Calculate the target price

at each stage (according to the price progression equation).

Adjust the pool’s liquidity

so that the price reaches the target price by adding or removing tokens from the pool.

Example Logic

: Suppose you want the smart contract to automatically adjust liquidity when certain events occur, such as the sale of N tokens. Here’s how you might structure the logic.

Calculate the target price

: At each sales tranche or whenever the smart contract is called, calculate the target price based on the price curve you’ve defined: 𝑃cible = 𝑃₀ × (1 + 𝑟𝑡)

Calculate the new token proportions

: To adjust liquidity, you need to recalibrate the ratio of x (your token) and y (ETH) so that the token price follows the price progression curve. The price is given by the formula: 𝑃 = 𝑦 / 𝑥 You need to set x and y such that P = P_{\text{cible}}. If y is fixed (i.e., you’re not changing the amount of ETH), you can solve for x: 𝑥 = 𝑦 / 𝑃cible This means you must adjust the quantity of your token in the pool to x so that the price matches the target price.

Smart Contract Implementation Example

: Here’s a simplified example of the logic you might include in your smart contract, written in Solidity, the programming language used for smart contracts on Ethereum.

4. Deployment and Automation

Once this smart contract is deployed, you can automate the calls to the

adjustPrice()

function at each critical stage of the ICO (for example, after selling a tranche of tokens). You can use off-chain scripts or services like Chainlink Keepers to automate this task.

Conclusion

The implementation of automatic price adjustment via a smart contract is based on the AMM formula used by Uniswap, with the goal of maintaining the ratio between your token and the other cryptocurrency (ETH or others) according to your predefined price curve. By dynamically adjusting the liquidity in the Uniswap pool, you can ensure that the price of your token follows the defined curve for your ICO.

x

= quantity of your token in the pool (e.g., your token XYZ).

y

= quantity of the other token in the pool (e.g., ETH or USDT).

k

= constant (which doesn’t change during transactions). The price of the token at a given moment is given by the formula: 𝑃 = 𝑦 / 𝑥 Where:

P

= token price (in the other token, e.g., ETH).

y

= the quantity of the other token (e.g., ETH).

x

= the quantity of your token in the pool.