> For the complete documentation index, see [llms.txt](https://pangeaswap.gitbook.io/pangeaswap/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://pangeaswap.gitbook.io/pangeaswap/en/developers/concept-overview/problem-lazy-liquidity.md).

# Problem : Lazy Liquidity

### Problem of V2 DEX : Lazy Liquidity

Concentrated Liquidity Pool (Uniswap V3 Type) is a **CPAMM** (Constant Product Automated Market Maker) protocol that allows liquidity providers to supply liquidity to specific price ranges. Concentrated Liquidity Pool is designed to solve the problem of “**lazy liquidity**” of the existing DEX (Uniswap V2 Type). Let’s understand what lazy liquidity is by looking at the V2 type AMM model.

### Understanding the Logic of Uniswap V2 Type CPAMM

Uniswap V2 calculates the swap output in such a way that the product of the two assets in the pool is always constant (Constant Product). This can be shown as a formula and a graph below.

$$
X \cdot Y = K
$$

​

![](https://lh6.googleusercontent.com/WbfRFQ4ag2oigjBXqX_ft5QSpkzGCqI9_sLndGFeFZEvbJZgKbEbvilsEaOJv4rgmAONI2AEi-aP_3-jtRAQvGYivj3n_M5eubEqQoaK_89dzw9OP97gFtUrsx2BN0y0PAncFy5pi0bGHlnsN52quA)

Let’s define the price(P) and liquidity(L) as below.

$$
P = \sqrt{\frac{Y}{X}} \ L = \sqrt{XY} = \sqrt {K}
$$

Uniswap V2 type pool always guarantees the same liquidity(L) in all price ranges, so when expressed as a graph, it comes out in the form below.

![](https://lh6.googleusercontent.com/UscQyJ0PzrmCjsGzBlHL2O7JEJhxXvZUW1nyI4-Ve55oEYTxGvpxY_-v4Q23vf9fNr_h7wQPRFI8331sY-0VNm-kc7isnIkK61jTWdWcMXCVWUB5k_hrV9IsyxrLy7zuCHDWuqmZOa4smGR7w8UYvA)

In other words, the Uniswap V2 CPAMM is a model that evenly supplies liquidity over the entire price range from 0 to infinity for token pairs. Although this model has the advantage of being able to provide liquidity for swaps even if the price of the two tokens changes rapidly, in most cases, the token price changes within a specific range (e.g. Pa \~ Pb) as shown above.

![](https://lh6.googleusercontent.com/t49e7tI0kFaHJvpQ7FywWaYrhqClAVyev-RPoUp7H6l9V1y9w-FdmNThDpOL5xP4L3ojQlJyfmEY_XDJnij4zSvqt7g1PIT9j65r6ieedRnAlqVdX3vtlz_xHdbPBlvriU9OBNQ1AWpRi8KxbRbaow)

The liquidity that is supplied to the section (Pa\~Pb) where the actual transaction occurs and is actively used for the swap is called **Active Liquidity**. And the liquidity that is supplied to the section (0\~Pa,Pb\~∞) where the transaction does not occur and is not used for swaps is called **Lazy Liquidity**.

Pairs such as stablecoin pairs with stable prices(e.g. USDT-DAI) or KLAY-aKLAY, which have a high correlation between the values of the two tokens, are traded only in a very narrow price range. Which makes most of the liquidity provided by LPs lazy liquidity.

By supplying liquidity in a concentrated manner through the Concentrated Liquidity Pool, it is possible to reduce lazy liquidity not used in transactions as above and activate more liquidity to be used for transactions.


---

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