Constant-product price impact

EN source master · P11-L02 · 30 minutes estimated · needs_review

Offline formative study. No wallet connection, real funds, private keys, signatures, live trade or personal portfolio inputs. Visuals are specifications; this is neither runtime content nor certification.

An output estimate is ambiguous unless it states whether fees, curve movement and subsequent state changes are included.

Put the fee in the right place

The v2 model adjusts input for the swap fee when testing the invariant [V2]. In our toy model, fee f=0.003 and effective input Δx_eff=Δx(1−f). Output= y×Δx_eff/(x+Δx_eff). Actual x reserve receives the full input; the retained fee means the unadjusted reserve product increases. It is not correct to remove the fee from reserves and then claim k remains identical.

Declare impact convention

For this lesson, curve impact=1−(no-fee average output/input)/(initial marginal ratio). Fee-inclusive execution shortfall uses the fee-adjusted output/input instead. These two percentages differ; either must be named. Slippage here means additional change between the modeled quote and execution caused by a changed state, not the curve impact already modeled.

Recompute size sensitivity

A larger supplied input travels farther along the curve and worsens average output per input. TVL is aggregate marked value, not the output available at a chosen size. Other pools, routes or hooks are absent; this is not an aggregator quote.

State exclusions

Calculations retain precision and round display only; real onchain integer rounding, gas, fee-on-transfer behavior, MEV and intervening swaps are not simulated. Correct arithmetic provides a conditional estimate, not a guaranteed minimum or safe transaction. LAB03 association in the catalog is downstream and non-gating; this offline lesson does not require deploying a lab.

• Effective input: input after stipulated swap fee adjustment.
• Curve impact: finite no-fee average deviation from initial ratio, under stated convention.
• Fee-inclusive shortfall: comparison including fee.
• Slippage: additional quote/execution change under this lesson's convention.

ILLUSTRATIVE x100 X,y1000 Y,input 10 X,fee 0.3%. Effective 9.97 X. Compare no-fee 10 X and fee-adjusted10 X. Separate larger-input case20 X; no gas or integer contract rounding.

Liquidity-depth chart specification using exact formula; mark10/20 inputs, effective input, average output and fee retention. Different lanes for curve impact, fee-inclusive shortfall and unmodeled slippage.

Conditional outputs and named execution-shortfall comparisons in the fixture.

A guaranteed onchain quote, actual gas/MEV, safe minimum output or complete exit liquidity.

• OBSERVED: FIX-P11-L02 stipulates fee 0.003 and reserves 100/1000.
• INFERRED: output 1000×9.97/109.97 under the toy model.
• UNKNOWN: state at any actual execution.
• INSUFFICIENT EVIDENCE: the modeled output guarantees a real fill.

• Using effective input as actual ending reserve.
• Calling fee effect and slippage the same thing.
• Reporting impact without denominator convention.

Compute fee-adjusted output, ending actual reserves and product. Compute no-fee curve impact and fee-inclusive shortfall for 10 X. Calculate output for 20 X and compare average execution.

Deliver calculations or annotations, claim/source table and limitations. Suggested allocation: study 12 minutes, exercise 8, correction/quiz 10; estimate subject to calibration.

• Declare fee and impact convention.
• Keep full input in actual reserve.
• Round only display.
• Separate modeled curve and later execution.

Fee-adjusted reserve math is reproducible when balances and comparison conventions are explicit; execution still depends on missing state and costs.

• Calculate fee-adjusted constant-product output.
• Separate curve impact, fee effect and later slippage.

P11-L03 after correction review.

NONE in the authoritative catalog. The supplied offline fixture/package is sufficient; no paid feature or unverified Production capability is required. Lab/certification metadata denotes downstream associations, not access gates or live awards.

• [V2] Uniswap v2 core whitepaper (March 2020) — Reserve ratio, constant-product mechanics and input-fee invariant; version-specific, not a live deployment snapshot. Checked 2026-10-01; locator turn14view0.