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Structure de marché

Constant-product pools: where price impact comes from

A pool equation makes the execution price depend on the size of the trade relative to available reserves.

Technical reference · automated market makers · 1 min read

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Dans cet article
  1. A numerical example
  2. Fees and real implementations
  3. Sources et originaux

A numerical example

Consider a simplified pool with 100 units of token X and 10,000 units of token Y. Ignoring fees, the constant product is 1,000,000. A buyer who adds 1,000 Y leaves 11,000 Y in the pool. The X reserve must become approximately 90.909, so the buyer receives about 9.091 X.

The average execution price is therefore about 110 Y per X, although the initial marginal price was 100. The trade itself changes the inventory ratio. A large market-cap figure elsewhere does not change this pool's available reserves.

In a fee-free constant-product example, adding 1,000 Y to a pool holding 100 X and 10,000 Y returns about 9.091 X. The finite trade moves along the pricing curve; it does not execute entirely at the starting marginal price.
In a fee-free constant-product example, adding 1,000 Y to a pool holding 100 X and 10,000 Y returns about 9.091 X. The finite trade moves along the pricing curve; it does not execute entirely at the starting marginal price.
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Fees and real implementations

Real pools incorporate fees and may use different invariants, concentrated ranges or hooks. The simple equation is a teaching model, not a quote for every decentralised exchange. A production quote must use the actual pool state and implementation.

Slippage tolerance limits what the transaction accepts relative to its quote; it does not make the price impact disappear. Active ranges explain why total deposited value can be misleading, and MASTR's ANSEM research applies that distinction to reported liquidity and volume.

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