On this context, capital effectivity is measured relative to the canonical fixed product AMM which enumerates costs from zero to infinity.
We’ll assume the canonical AMM is a two-token, equal-weights AMM with a liquidity pool with reserve balances of 1M tokens on all sides, e.g. 1,000,000 USDC and 1,000,000 USDT.
These two tokens are anticipated to commerce at near parity (1:1) with one another.
Assume that the market will settle for a worth vary for USDC:
Inside its desired peg right down to 0.999998 USDT per USDCWithin its desired peg as much as 1.000002 USDT per USDC.
What number of tokens will be traded on the canonical 1,000,000:1,000,000 USDT/USDC liquidity pool on this worth vary?
Solely a single token!
A swap of a single USDT for USDC will transfer the value of USDC to 1.000002 USDT per USDC.A swap of a single USDC for USDT will transfer the value of USDC to 0.999998 USDT per USDC.
Subsequently, the opposite 999,999 tokens on all sides of the pool are successfully ineffective (as long as the stipulated peg worth vary is revered).
