{"type":"rich","version":"1.0","provider_name":"Transistor","provider_url":"https://transistor.fm","author_name":"Web3 Tech Brief By HackerNoon","title":"A Mathematical Breakdown of How Automated Market Makers Price Assets","html":"<iframe width=\"100%\" height=\"180\" frameborder=\"no\" scrolling=\"no\" seamless src=\"https://share.transistor.fm/e/fc3b96c7\"></iframe>","width":"100%","height":180,"duration":635,"description":"\n        This story was originally published on HackerNoon at: https://hackernoon.com/a-mathematical-breakdown-of-how-automated-market-makers-price-assets.\n             Learn how AMMs price tokens using x·y=k, how fees accrue, and why impermanent loss hurts LPs. From Uniswap V2 to V3, the math explained clearly. \n            Check more stories related to web3 at: https://hackernoon.com/c/web3.\n            You can also check exclusive content about #defi, #automated-market-makers, #amm-math, #uniswap-v2, #concentrated-liquidity, #liquidity-pools, #curve-finance, #crypto-liquidity,  and more.\n            \n            \n            This story was written by: @durdana-yembergenova. Learn more about this writer by checking @durdana-yembergenova's about page,\n            and for more stories, please visit hackernoon.com.\n            \n                \n                \n                AMMs use the formula x·y=k to price tokens without an order book. Swaps move reserves along a hyperbola, causing price impact on large trades. A 0.30% fee grows k over time, rewarding liquidity providers. LPs face impermanent loss — always worse than holding when price moves, calculated as IL(r) = 2√r/(1+r) − 1. Uniswap V3 improves capital efficiency via concentrated liquidity ranges, while Curve and Balancer extend the model to stablecoins and multi-asset pools.\n        \n        ","thumbnail_url":"https://img.transistorcdn.com/eO2Jn0gxT_H9qDuuD0uleszE2n40sbZ-1T2r0zOcj9c/rs:fill:0:0:1/w:400/h:400/q:60/mb:500000/aHR0cHM6Ly9pbWct/dXBsb2FkLXByb2R1/Y3Rpb24udHJhbnNp/c3Rvci5mbS9zaG93/LzQxMTY4LzE2ODMz/MTU4ODQtYXJ0d29y/ay5qcGc.webp","thumbnail_width":300,"thumbnail_height":300}