Building Liquidity Pools with the x Times y Equals k Formula

Automated Market Makers (AMMs) have become the backbone of modern DeFi, as explored in depth in the core mechanics of automated market makers.
They provide continuous, on‑chain price discovery without relying on traditional order books, and they enable liquidity providers to earn trading fees and governance rewards.
The constant product rule that governs every AMM is the key to this innovation, and its formal definition and practical implications are explained in our guide on Understanding AMMs and the Constant Product Formula.

Constant Product Formula

The constant product formula, often written as
(x \cdot y = k),
requires that the product of the two reserve balances in a pool never changes.
For a deeper look at how this rule replaces order books, see Understanding AMMs and the Constant Product Formula.

What is a Constant Product AMM?

The constant product model is the backbone of many popular AMMs, such as Uniswap V2, SushiSwap, and PancakeSwap, all of which are examined in A Deep Dive Into DeFi Primitives and Constant Product Pools.
These platforms demonstrate how the x · y = k invariant creates a continuous market that is resilient to order‑book fragmentation.

Fees and Their Impact

Your fee revenue over time equals
revenue = (your share) · (total fees added to reserves).
Because fees are reinvested into the pool, they help protect against impermanent loss and increase the overall value of LP tokens.
For a comprehensive discussion of how AMM fee structures are designed and adjusted, refer to the core mechanics of automated market makers.

Impermanent Loss

Impermanent loss occurs when the relative price of the two tokens in a pool diverges from the price at which you deposited them.
The loss is called “impermanent” because if the token prices return to their original ratio, the loss disappears.
To understand the trade‑offs between fees and impermanent loss, you can revisit the concepts presented in A Deep Dive Into DeFi Primitives and Constant Product Pools.

Strategies for Liquidity Providers

Pairing liquidity provision with staking rewards from additional protocols can enhance overall returns.
For example, deposit LP tokens into a farming contract that pays governance tokens on top of the trading fees, a strategy outlined in A Deep Dive Into DeFi Primitives and Constant Product Pools.