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# Constant Product Market Maker
Liquidity pools on GnoSwap utilize the **Constant Product Formula** to achieve deterministic pricing of any token in a pool, ensuring that trades can occur at any price within the range of (0, ∞). Liquidity pools maintain a constant ***k*** value, which is the product of ***x*** and ***y***, representing the quantity of **token x** and **token y** in the pool, respectively. This mechanism results in the following formula:
$$
x \*y=k
$$
When a trade occurs in a pool, the values of ***x*** and ***y*** change. Let's assume that **∆** represents the change in the quantity of a token. If a trader sells **∆*****x*** amount of **token x**, the pool receives **∆*****x*** amount of **token x** and pays out **∆*****y*** amount of ***token***** y** (minus the swap fee) as the output in a way that satisfies the equation below:
$$
(x+∆x)(y-∆y)=k
$$
Based on the above formula, we can plot a graph that illustrates changes in token reserves in a pool after a trade.
To illustrate this concept, let's consider a scenario where Pool A holds 10 $GNOT and 10,000 $USDC. If Alice wishes to exchange 1 $GNOT for $USDC in Pool A, an equation reflecting the current reserves and **∆x** (change in $GNOT) is set up as follows:
$$
k = 10\*10,000 = 100,000 = (10+1)(10,000-∆y)
$$
Solving for ∆y, we get:
$$
∆y = 10,000-(100,000/11) = 909.090909...
$$
Therefore, we can expect Alice would receive 909.090909... $USDC if she were to sell 1 $GNOT in Pool A.
When adding liquidity to an existing pool, liquidity providers must deposit an amount of **token x** and **token y** that is proportional to the current ***x : y*** ratio in the pool. Once liquidity is added, the value of ***k*** adjusts to the new values of ***x*** and ***y***.
As ***k*** is proportional to the liquidity of the pool, this structure can be seen as a virtual order book where liquidity is evenly distributed across the entire price range.
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