Non-Linear Price Curves

Non-linear price curves are the mathematical functions used by AMMs to determine the exchange rate between two assets based on the pool's current reserves. Unlike a traditional order book that has a linear or flat price structure, AMM curves become increasingly expensive as a trader attempts to purchase a larger percentage of the pool's reserves.

This curve is defined by the underlying algorithm, such as the constant product or stable-swap models. These curves are designed to ensure that the pool never runs out of assets, as the price asymptotically approaches infinity as reserves approach zero.

Understanding these curves is essential for traders to predict the cost of their transactions. They provide a deterministic and transparent method for pricing assets in a decentralized, automated fashion.