How Does the Constant Product Formula (X Y=k) Ensure Liquidity Is Always Available, Regardless of Trade Size?

The constant product formula (x y=k) ensures liquidity is always available by creating an asymptotic price curve. As a trader buys more of one asset, its price approaches infinity, while the price of the other asset approaches zero.

This means that no matter how large a trade is, the pool can technically never run out of the other asset. However, for very large trades, the price becomes prohibitively expensive, a phenomenon known as slippage, which disincentivizes draining the pool entirely.