Did you know? A decentralised exchange can change a token’s price as part of processing your own trade, even if nobody else places an order at the same time. The reason is that many automated market makers price trades from the assets already held in their liquidity pools. Trading changes those reserves, and the next unit can have a different price from the first.
Imagine Alicia, Kai Kai and Tricia running a fictional school science-club exchange desk. Its cupboard contains ten ART prize credits and 100 classroom dollars. Students can exchange dollars for ART under a published formula. Alicia asks what happens if she buys most of the available ART. Tricia explains that removing scarce ART while adding dollars changes the pool’s asset ratio. Under the stated formula, each additional ART unit becomes harder to obtain.
This introduces a useful idea called price impact. It is not inherently evidence of fraud or a broken blockchain; it is often a mathematical consequence of trading against limited liquidity.
Quick answer: in a classic constant-product automated market maker, the reserves of two assets follow a rule commonly written x × y = k in an idealised fee-free illustration. A swap changes those reserve quantities, so the marginal price moves as the trade proceeds. Larger trades relative to available pool depth generally cause more price impact. Fees, concentrated liquidity and different protocol versions modify the exact calculation. A wallet’s preliminary quote is not a promise that future market state will remain unchanged.
This conversational guide explains how blockchain technology works through reserves, pool pricing, trade size, price impact, slippage, liquidity providers, fees and actual received amounts. All arithmetic uses fictional school credits rather than real market recommendations.
Choose Your Reading Route
- Why a liquidity pool is different from a seller’s order book
- What the constant-product formula means
- A larger trade moves further along the curve
- Why a pool never provides a simple fixed price for unlimited quantity
- Price impact and slippage are not identical
- Fees change the simple formula
- Concentrated liquidity changes where the depth exists
- Frequently asked questions
- Primary sources and related reading
Why a liquidity pool is different from a seller’s order book
An ordinary exchange may match a buyer with another participant who has placed a sell order at a specified price. An automated market maker can instead let the buyer transact directly with a smart contract holding a pool of assets under predefined exchange rules.
The pool needs assets supplied by liquidity providers or another authorised funding mechanism. Those reserves are not invented when a trade occurs. The contract calculates how much one asset can be received in exchange for another, applying its actual formula, fees and conditions.
In the science-club model, there is no student behind the counter secretly deciding each quote. The class agrees on a mathematical rule and stocks the cupboard with ART and imaginary dollars. Any permitted trader can interact with that same inventory.
This makes trading possible without requiring a matching seller to click “accept” at precisely the same moment. It also means the size and balance of the cupboard determine the available terms.
The Uniswap guide to how its protocol works explains that swaps trade against pool reserves, while price follows an algorithm appropriate to the protocol version.
The beginner question is which assets are in this particular pool, in what quantities, and under which pricing rule? The token’s global market-cap number cannot answer it.
What the constant-product formula means
A common introductory automated market maker uses two asset reserves, labelled x and y, with a constant-product relationship written x × y = k when ignoring trading fees and certain implementation details.
Suppose the fictional pool contains ten ART credits and 100 classroom dollars. The product of the reserves is 10 × 100 = 1,000, so k is 1,000 in this simplified arithmetic model.
If someone adds ten classroom dollars to obtain ART, the pool now has 110 classroom dollars. To preserve the simplified product, it would have 1,000 ÷ 110, or about 9.0909 ART credits remaining. The trader receives roughly 0.9091 ART rather than one whole ART.
The starting ratio suggested ten dollars per ART, but spending ten dollars obtained less than one ART because the exchange price moves along the curve as the trade changes reserves. The calculation deliberately ignores fees.
Real implementations use exact integer arithmetic and protocol-specific safeguards, so simple classroom division is not an operational quote. Uniswap V2’s pricing documentation explains the underlying constant-product model and how fees affect execution.
The mathematical habit is to distinguish the initial marginal ratio from the average price of the whole trade. That difference is central to understanding price impact.
A larger trade moves further along the curve
Now compare two imaginary purchases from the same initial pool with ten ART and 100 classroom dollars. In the fee-free classroom model, spending one dollar results in about 0.0990 ART, while spending fifty dollars gives about 3.3333 ART.
The second buyer does not receive five ART even though the starting ratio was ten dollars each. The larger trade changes the pool’s dollar and ART reserves much more substantially.
This is why the *size of the trade relative to available liquidity* matters. The same 50-dollar purchase would have far less relative impact in a pool with a vastly larger balanced reserve under a comparable formula.
Price impact should not be confused with a surprise service fee. It is a consequence of the changing reserve ratio within the pricing mechanism. Fees can be charged on top and can also affect the exact outcome.
For students, imagine the school has only ten rare science-prize tickets. Acquiring half of them is economically different from buying one ticket from an inventory of a thousand.
The Uniswap price-impact guide identifies pool depth and trade size as key determinants. It is a good way to interpret a large warning without assuming every price movement was caused by an attacker.
Why a pool never provides a simple fixed price for unlimited quantity
A fixed price sign can make sense when an ordinary retailer promises to sell a stated stock under a published policy. A constant-product AMM behaves differently. Its available reserves and formula establish a curved relationship between quantity and price.
As a trader attempts to obtain an increasingly large fraction of a finite reserve, the exchange terms become progressively less favourable in the idealised constant-product model. That characteristic helps prevent a single finite-input trade from completely draining one reserve under ordinary mathematical conditions.
This is not a universal promise that a pool can never lose funds. Smart-contract vulnerabilities, unusual token rules, administrator powers and other risks can affect the system independently of its pricing curve.
The correct statement is narrower: a classic constant-product formula prices successively larger trades against the changing reserves, so the amount obtainable for a given input is not simply the displayed marginal price multiplied by the whole desired quantity.
That makes the user’s expected output and its allowable minimum particularly important. An attractive price shown for one unit does not guarantee the same average price for one hundred units.
A careful interface should distinguish the current spot estimate, the trade’s expected average execution amount and any additional costs.
Price impact and slippage are not identical
Price impact commonly refers to the change caused by the user’s own proposed trade relative to the pool’s starting price or liquidity. Slippage concerns the difference between an expected and executed result, potentially including price impact and market changes while the transaction waits.
Uniswap’s developer glossary separates the two: price impact is linked to order size relative to liquidity, while slippage captures execution deviations that can reflect both that impact and changes before inclusion.
Some wallet interfaces use these words differently or combine them in estimates. Readers should therefore inspect the exact definitions and the transaction’s permitted limits rather than assume one percentage always means the same thing.
For the school club, buying several ART credits changes the desk’s reserve ratio even if no one else trades. That is ordinary price impact. If Kai Kai buys first while Alicia’s request is pending, the pool can move again before her transaction executes, changing her expected result.
A minimum-output condition can prevent an execution outside the stated boundary, but the request may then revert rather than deliver the originally quoted amount.
The main teaching point is to read three separate fields: starting price, expected output for this trade size, and minimum output authorised.
Fees change the simple formula
Real pools can collect fees for swaps, and their precise implementation affects how much of the input is used to calculate the output, how reserves are updated and how the pool compensates providers.
The mathematical model x × y = k is a useful starting point, but the actual contract may apply fees and rounding that make the direct classroom calculation insufficient for a live trade. Depending on the version, the product can stay constant or increase under fee-accounting effects.
Different pools for the same token pair can have different fee tiers or other settings. That can change both price and provider economics even when the token contracts themselves are identical.
A user’s complete cost can also include Ethereum gas and, where relevant, additional application or routing fees. These are separate from price impact. A wallet should not combine them into a vague “exchange difference” without explaining the components.
For the science-club desk, imagine a small administration charge per exchange. The charge is distinct from the fact that buying ART changes the cupboard’s remaining reserves.
Read Why Network Fees Change When It Gets Busy for network processing cost. The price curve and gas fee describe different parts of the user experience.
Concentrated liquidity changes where the depth exists
Newer Uniswap designs include concentrated liquidity, in which a liquidity provider can allocate capital to a selected price range rather than supporting every possible price across the entire curve in the same way as an older full-range pool.
The Uniswap overview explains that V3 and V4 use price-range-based liquidity positions, while the constant-product relationship operates within relevant ranges.
This can improve capital efficiency when the market price remains inside a heavily funded range. It also means that available liquidity can change as the price moves across boundaries and different providers become active or inactive.
An article saying “every Uniswap pool always contains two fixed reserves with precisely the V2 formula for every price range” would therefore be inaccurate. The precise version, pool settings and current liquidity distribution matter.
For the classroom analogy, imagine the school has many exchange volunteers available at common price ranges but fewer volunteers willing to exchange at extreme prices. A large request can pass through areas with very different depth.
The underlying literacy lesson remains: a headline price alone does not reveal how much can be traded at nearby prices or who provides that liquidity.
Who supplies the assets in the pool?
Liquidity providers deposit eligible assets under the protocol’s rules, receiving a position or entitlement to a share of pool activity. Their assets are what enable traders to swap without directly matching an individual counterparty order.
In the fictional school club, Alice and Tricia place ART credits and classroom dollars into the exchange cupboard. Students trade against that shared inventory under the published formula. The providers’ holdings change in composition as trades occur.
In Uniswap V2, liquidity providers receive fungible pool shares. V3 represents individual concentrated-liquidity positions through NFTs, while V4 has its own position accounting structure. These differences matter when explaining how providers track ownership and fees.
The Uniswap protocol glossary describes liquidity providers and pool reserves. It also makes clear that providers take on price risk while potentially earning trading fees.
A liquidity-provider position is not the same as holding a bank deposit with guaranteed principal. Its value changes with the underlying assets, trading activity and applicable smart-contract rules.
A good educational article therefore separates the trader, liquidity provider, pool contract and any protocol governance arrangements rather than implying the user’s swap is simply a transfer to a central merchant.
Why liquidity-provider value can change
When traders use a constant-product pool, the proportion of each asset held by the pool changes. A liquidity provider owns an interest in those changing reserves under the relevant contract rules.
Suppose the price of ART rises sharply in outside markets. Traders interacting with the pool may remove ART while adding more of the other asset until the pool price better reflects external markets. The liquidity provider’s position can end up holding less ART and more of the other token than before.
That change can cause the position to perform differently from simply holding the original token quantities in a wallet. Educational material often describes this as impermanent loss or divergence loss, but the exact outcome depends on fees, prices, range and withdrawal timing.
The Uniswap V2 guide to understanding returns explains this relationship under a simple constant-product model.
The word impermanent should not be read as a promise that every loss automatically reverses. Market prices, fees and the timing of withdrawal can make the final economic outcome uncertain.
For our school analogy, a provider might start with five ART and fifty dollars, then end with a different mix after student exchanges. The inventory composition changed without the provider personally accepting every trade.
Different pools can show different prices
The same exact token pair may exist in several pools with different reserve balances, fee tiers or liquidity ranges. A centralised exchange can also have its own order book and market participants.
As a result, the same token may have different observed prices on different venues at the same moment. Arbitrage can sometimes help bring prices closer together when an economic opportunity exists, but fees, execution risk and available liquidity can prevent perfect equality.
Suppose the science club has two exchange desks. Desk Blue holds ten ART and 100 classroom dollars, while Desk Green holds ten ART and 120 dollars. The initial ratios differ. Students may try to exchange through one or the other, but each trade changes the relevant inventory and resulting quote.
A person comparing the two figures needs to know the exact asset, network, pool or order book, timestamp and trade size. Two different contract tokens using the same symbol should not be mistaken for the same asset.
For the dedicated reader’s guide, see Why the Same Token Has Different Prices on Exchanges.
The important principle is a price is a quotation emerging from a venue’s specific state, not a universal number floating above all exchanges.
Why a pool’s price should not always be treated as a trusted oracle
A smart contract may need a price to determine collateral, rewards or another high-impact action. Using an AMM’s immediate spot ratio can be risky if that pool is thinly funded or its price can be influenced by relatively small trades.
An on-chain value can be correctly calculated from the pool’s current reserves and still be unsuitable as the truth about a broader market. The contract’s arithmetic and the reliability of the underlying reference are separate questions.
Imagine a school programme valuing every art-club award from one unusual trade at a tiny exchange desk. The resulting number may faithfully reflect that desk while poorly representing the school’s intended standard valuation.
Robust pricing systems can consider multiple sources, averaging, update rules and other protections appropriate to the application’s threat model. There is no universal guarantee that one design fits every asset or use.
This concern also connects to flash loans, which can provide large temporary liquidity within one atomic transaction and change what certain actors are economically able to do during an operation.
For deeper evidence concepts, see Why an Oracle Can Deliver Incorrect Data. A real blockchain price observation is not automatically the right price for every purpose.
Why transaction ordering matters to the final output
The user may read an AMM quote at one moment, then another participant’s trade is included first. Because the pool’s reserves have changed, the initial quote can no longer predict exactly what the later transaction would receive.
This is not necessarily an error in the pool’s code. The contract can be working exactly as programmed against the current state.
Order-dependent pricing can also create MEV opportunities in which participants seek an advantageous position around other transactions. Understanding that risk requires examining the accepted ordering rather than merely seeing a changing quote.
A properly designed wallet can explain estimated output and the boundaries authorised by the signed request. It should distinguish ordinary price impact from additional state changes between quotation and execution.
If the transaction cannot satisfy a minimum-output requirement, it may revert. The user might receive no swapped tokens while still incurring network processing costs according to the chain’s rules.
Read Why Transaction Ordering Can Change a Trade for the focused MEV and sequencing explanation.
A pool price is not proof of market capitalisation or cash backing
A thin pool can produce a token price that a market-data service later multiplies by a much larger circulating supply to estimate market capitalisation. That calculation does not imply the pool holds cash equal to the resulting valuation.
Suppose a fictional ART pool has 100 classroom dollars and ten ART tokens. A separate issuer has 10,000 ART units outstanding. Applying the small pool’s marginal price to every outstanding token could produce a large number, even though the particular pool contains only its own reserves.
The difference between pool liquidity, market valuation and issuer treasury assets is essential for financial literacy. One asset price displayed in a wallet cannot guarantee that every holder could sell all units at that price.
The issuer’s real-world backing or redemption rights also need independent evidence. A pool is a trading mechanism, not automatically a custodian legally promising cash at par.
For the related lesson, read Why Token Market Cap Is Not Cash in the Treasury.
The useful habit is to record pool reserves, quoted trade outcome, circulating supply and issuer assets in separate columns.
A fictional experiment with three trade sizes
Start with ten imaginary ART credits and 100 classroom dollars in a fee-free constant-product pool. Calculate k as 1,000. Keep this as the baseline for all three experiments.
In round one, Alicia adds ten dollars. The pool’s dollar reserve becomes 110, and the ART reserve must become approximately 9.0909. Alice receives about 0.9091 ART.
Reset the pool. In round two, Kai Kai adds fifty dollars. The dollar reserve becomes 150; the ART reserve becomes approximately 6.6667. He receives about 3.3333 ART. Notice that five times the dollar input does not produce five times Alice’s output.
Reset once more. In round three, Tricia adds only one dollar. The new ART reserve is approximately 9.9010, so she receives about 0.0990 ART. Her trade has a much smaller relative price impact.
Ask students to compare each average exchange rate with the original simple ratio of ten dollars per ART. Then discuss why a more deeply funded pool would show different results for the same trade sizes.
Finally introduce an additional fee and explain why the simplified results would no longer be exact. The exercise teaches the formula without encouraging live swaps or financial speculation.
Seven checks before interpreting a liquidity-pool quote
1. Which assets and chain? Identify the exact token contracts and network rather than relying on logos or a ticker.
2. Which pool and version? A V2-style full-range formula, concentrated-liquidity pool or other AMM may use different execution rules and fees.
3. How much liquidity is relevant? The reserves and active price-range liquidity determine the trade’s price impact.
4. What quantity are you trading? The average execution price for a large trade is not necessarily the same as the initial marginal quote.
5. What fees apply? Separate pool trading fees, application charges and network gas.
6. What might change before inclusion? Other accepted transactions can alter reserves and make a previously accurate quote outdated.
7. Which outcome was actually authorised and received? Compare the expected output, signed minimum and final accepted asset movement.
This checklist helps explain a pool’s behaviour without treating a calculator, explorer or promotional chart as a guaranteed trading offer.
Frequently asked questions
Why does a liquidity pool price change after a trade?
A swap changes the pool’s asset reserves, and the pricing formula uses those reserves to determine subsequent exchange amounts.
What is an automated market maker?
An AMM is a system in which smart contracts and defined mathematical rules permit swaps against supplied liquidity rather than requiring a direct matching order for every trade.
What does x × y = k mean?
In a classic constant-product example, x and y represent two asset reserves, and k describes the invariant used to calculate their relationship, ignoring fees and other protocol-specific details.
Why do larger trades get worse prices?
Larger trades relative to available liquidity move further along the pricing curve, so their average execution amount can differ more from the initial marginal price.
Is price impact a trading fee?
No. Price impact arises from the trade’s effect on pool pricing. Fees are additional charges defined by the pool or service.
Is slippage the same as price impact?
They are related but different concepts. Slippage describes deviation between expected and executed outcomes, while price impact is the effect of the trade size on available pricing.
Do all Uniswap pools use the identical V2 formula everywhere?
No. Protocol versions and concentrated-liquidity designs have different details. The constant-product intuition still applies within relevant liquidity ranges under the particular implementation.
Who owns the pool’s assets?
Liquidity providers supply assets under the pool contract’s rules and hold associated positions or claims; the pool itself controls reserves for permitted operations.
Can liquidity providers lose value?
Yes. Their positions can change composition and value with trading and market prices, even when they receive fees.
Why can the same token have different prices on two pools?
Different reserve balances, fee tiers, active liquidity and trade timing can produce different quotes for the same exact asset.
Does a pool price prove my tokens can all be sold at that price?
No. The pool has finite reserves. A large trade may move the price significantly, and restrictions or fees may further affect proceeds.
What should students remember?
A liquidity-pool quote is generated from available reserves and a specific trade size. Trading changes those reserves, so a price is not an unlimited fixed promise.
Primary sources and related reading
The Uniswap Developer Guide explains swaps, reserves and how V2, V3 and V4 differ. Uniswap V2 Pricing documents the classic constant-product relationship. Uniswap Price Impact and the Uniswap Glossary distinguish price impact, slippage and available liquidity.
For deeper eduKateSG study, continue to Automated Market Maker Arithmetic: Read the Pool Before Calling It a Price, Why the Same Token Has Different Prices on Exchanges, Why Transaction Ordering Can Change a Trade and Why Token Market Cap Is Not Cash in the Treasury.
The lasting lesson is a pool’s price is a mathematical consequence of the assets available, the trade size, and the rules of that particular contract. Read those conditions before turning a quotation into a conclusion.