How Do Concentrated Liquidity AMMs Change the Price Calculation Mechanism?

Concentrated liquidity AMMs (like Uniswap V3) allow LPs to allocate their capital within specific, narrow price ranges instead of across the entire $0$ to $infty$ range. This creates "virtual liquidity" that is much deeper around the current market price.

The price calculation still follows the $x cdot y = k$ logic within each range, but the effective price is determined by the specific range where the trade is executed, making capital more efficient.