> For the complete documentation index, see [llms.txt](https://the-fedz.gitbook.io/the-fedz/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://the-fedz.gitbook.io/the-fedz/the-fedz-elements-rules-and-tokenomics/private-liquidity-pool/example-private-liquidity-pools-and-open-market-liquidity-pools.md).

# Example: Private Liquidity Pools & Open Market Liquidity Pools

To understand the power and stability of Private Liquidity Pools, let's compare them to ordinary liquidity pools using a visual example.

#### Open Market Liquidity Pool

**Initial State:**

* Total Value: 1000 USD
* Composition: 500 USDT + 500 FUSD

**Scenario: Withdrawal**

* **Withdrawal:** Liquidity providers withdraw 200 USDT.
* **New State:** 300 USDT + 500 FUSD.

**Price Impact:**

* **Initial State Calculation:**
  * K = 500 USDT \* 500 FUSD = 250,000.
* **New State Calculation:**
  * New USDT: 300.
  * FUSD Price: 250,000 / 300 USDT = 833.33 FUSD.
  * Price per FUSD: 300 USDT / 500 FUSD = 0.60 USD per FUSD.

**Result:**

* The FUSD price drops to 0.60 USD, leading to a de-pegging situation due to the imbalance caused by the withdrawal.

#### Private Liquidity Pool

**Initial State:**

* Total Value: 100 USD.
* Composition: 50 USDT + 50 FUSD.

**Withdrawal Rules:**

* Withdrawals or swaps for USDT are not allowed if the FUSD price drops below 1 USD.

**Scenario: Withdrawal**

* **Restricted Actions:** No withdrawal of only USDT or swapping for USDT below 1 USD.
* **New State:** The pool remains balanced.

**Result:**

* The FUSD price remains stable because the system prevents actions that would de-peg it.

#### Power and Incentives

* **Long-Term Semi-Arbitrage:** The price mismatch in ordinary pools creates arbitrage opportunities in private pools, attracting more liquidity to the stable pool.
* **Fedz Incentives:** The Fedz clearing house can subsidize new private LP tokens, further encouraging stability and growth within the private pool.

#### Conclusion

This example demonstrates how Private Liquidity Pools are designed to maintain the stability of FUSD. By restricting certain actions and providing incentives, these pools ensure a stable and reliable environment, especially during high demand periods. This makes them a vital component of The Fedz ecosystem.