Bonding Curve: y = k/x

How does this bonding curve work?

The formula y = k / x defines a constant product bonding curve where the token price decreases as more tokens are bought. Here, x represents the current token supply, and k is a constant that determines the overall price level.

When x is small, the denominator is small, so the price is very high. As more tokens are minted and x increases, the denominator grows, causing the price to decrease smoothly over time.

This creates an inverse relationship between supply and price, meaning early buyers pay significantly higher prices, while later participants can buy tokens more cheaply.

Advantages and limitations

One of the main advantages of this model is its simplicity and mathematical consistency. The price is fully determined by a single formula, making it easy to implement and reason about.

However, the model has clear limitations. The price always decreases as supply increases, which reduces incentives for early buyers. Additionally, the price approaches infinity as x approaches zero, which can make the initial state unstable or impractical. Like other bonding curves, it also does not reflect real market demand, meaning prices are purely mechanical rather than market-driven.