## Introduction to Constant Product AMMs We are going to look at the constant product AMM, a type of decentralized exchange, and what we call *liquidity*. We can see how an AMM works by looking at a graph of a constant product function. This graph shows all possible combinations of tokens in the pool. The function used for the constant product AMM is defined as: ``` x * y = L ^ 2 ``` Where: * x = amount of token X * y = amount of token Y * L = liquidity **Example:** In this example, we see an AMM where: * x = 200 * y = 200 * L = 200 This means the liquidity of the AMM is 200, and all combinations of token X and token Y that satisfy the function `x * y = L ^ 2` are valid. **How does the curve determine the amount of token that goes out in a trade?** Let's look at a trade scenario where we begin with an AMM with 200 token X and 200 token Y. If a trader adds 200 tokens Y, the AMM will move to the point on the curve where the x-coordinate is 100 and the y-coordinate is 400. This means that the AMM will have to remove 100 token X from the pool to maintain the constant product. The difference between the initial value of Y and the new value of Y determines how much token Y goes out. **What is L?** L represents the *liquidity* of the AMM. The bigger the L value, the bigger the curve gets and the more smooth it becomes. This means that traders will get a better price for the same amount of token. **Example:** If we start with an AMM where x = 400 and y = 400, and L = 400, adding 200 tokens X results in x1 = 600 and y1 = 266.6666667. In this case, the amount of token Y removed from the pool (dY) will be 133.3333333. We can see that as L increases, the amount of token Y that can be acquired for the same amount of token X increases.