FOLLOW THE MECHANISM
- 1Supply
LPs contribute the two reserve assets.
- 2Swap
The input increases one reserve while output reduces the other.
- 3Reprice
The changed reserve ratio changes the next marginal price.
A conceptual sequence. Real implementations can add steps, intermediaries, and conditions.
Inventory becomes the market
An automated market maker holds assets in a pool and uses a rule to determine exchanges. The classic two-asset constant-product model begins with reserves x and y and the relation x × y = k. Buying one asset removes it from the pool while adding the other, changing the ratio and the next quoted price. This is the educational model used here, grounded in Uniswap v2’s historical design. Other AMMs use different curves, ranges, weights or additional mechanisms.
Work through the curve
Ignoring fees, a pool with 100 A and 10,000 B has k = 1,000,000. Adding 10 A leaves 110 A, so the remaining B reserve is 1,000,000 ÷ 110, approximately 9,090.91. The trader receives approximately 909.09 B. The initial marginal price was 100 B per A, while the average received was 90.91. The difference comes from walking along a curved price schedule. The pool never simply multiplies the entire input by its initial spot price.
Fees and arbitrage change the story
With a fee deducted from the trade input, only the effective input determines quoted output, while retained fees can increase reserves. A real protocol may share fees with another recipient. External trading then tends to bring pool prices toward other markets through arbitrage, subject to costs and risk. The pool itself does not know a universally correct market price. Arbitrage trades change LP inventory, connecting the mechanism’s usefulness for traders to the risks borne by inventory suppliers.
Why version and scope matter
Uniswap v3 and v4 allow liquidity over selected price ranges. The full-reserve v2 demonstration does not model their concentrated positions, range exits, hooks or routing. A result from the demo also excludes network fees, token transfer quirks, competing orders and failed execution. It is a balance-conserving model of a pricing mechanism, not a quote from a venue. Inspecting the curve is useful because it shows why small pools and large trades interact so sharply even when every contract behaves as intended.
MAKE IT CONCRETE
Finite reserves
In the no-fee formula, ever-larger inputs approach draining the output reserve but do not reach all of it with any finite input. This is a mathematical property, not evidence that every asset in the pool has value.
FAILURE PATHS & COMMON MISREADINGS
Where the model can break
- A pool ratio is not an external price oracle by itself.
- The v2 model does not describe every AMM or concentrated position.
KEEP EXPLORING