> For the complete documentation index, see [llms.txt](https://elephanteth.gitbook.io/elephant.money/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://elephanteth.gitbook.io/elephant.money/liquidity-management-stability.md). # Liquidity Management (Stability) Stability & Growth By Design
### Stable growth design Elephant Eth Money was designed with price stability and growth in mind. This is achieved through the implementation of two passive systems to address liquidity depth (price stability) and price appreciation (growth) simultaneously. The buyback system and front office (token buyers) drive price appreciation by removing ELEPHANT/ETH tokens from the LP. The transaction fees on UNI and graveyard rebalances build liquidity depth by continuously adding more LP tokens to the ELEPHANT/WETH liquidity pool. ## Stability In AMMs (like UNI) the token price is determined by the ratio of two assets in the LP and when a buy or sell occurs this creates a change in the ratios moving the price up or down. ### AMM Liquidity Fundamentals The AMM uses a formula called the Constant Product Formula to make sure the two assets in the LP always stay at a 50/50 value ratio. When the pool becomes out of balance the AMM rebalances the "price" back to a 50/50 ratio constantly. By increasing the liquidity depth through the addition of more LP tokens this creates more depth in the liquidity pool, meaning it now takes more capital to move the price To keep things simple I will not use the formula but I will show the results of how the AMM works in a simplified manner. ### Example For this example the price of TRUNK is at $1.00 and the liquidity pool is TRUNK/DAI. For this example the LP has $1000 USD value \ \ 500 TRUNK/ 500 DAI LP If someone buys 20 TRUNK, this swap would be routed through the DAI side. Adding more DAI to the pool and removing the equivalent value in TRUNK from the pool. \ \ DAI in, TRUNK out\ \ The pools balance has now shifted. 480 TRUNK / 520 DAI LP \ \ The AMM then rebalances the prices back to a 50/50 ratio.\ \ Now there are only 480 TRUNK in the LP but the value need to equal to the other side of the pair (520 DAI). So the AMM adjusts the price of TRUNK to maintain the 50/50 value ratio. \ \ And what does this look like? \ \ 520/480 = **$1.083 (+8.3%)**\ \ $1.083 is the new price of 1 TRUNK and now the pool value is back to 50/50 value ratio. Now let's look at this same transaction with *Deeper Liquidity*.\ \ For this example the LP has $10,000 USD value and TRUNK is at $1.00\ \ 5000 TRUNK / 5000 DAI LP \ \ 20 TRUNK purchased with 20 DAI\ \ This adds 20 DAI to the LP and removes 20 TRUNK After the purchase LP ratio is at: 5020 DAI / 4980 TRUNK The AMM will rebalance by adjusting the price of TRUNK to make sure both assets are at a 50/50 value ratio. \ \ 5020/4980 = **1.008** new TRUNK Price **(+0.8%)**\ \ So we can see from this example a $20 buy moved the price 8c with a $1000 USD value LP while that same $20 transaction with a $10,000 USD value LP failed to move the price 1c. Furthermore, these principles work in reverse as well. So on the flip side removing DAI from the LP and adding more TRUNK (selling) will have a declining effect on the price. As you can see from the example above increasing liquidity depth helps to increase price stability, the benefit of this is it allows holders to move medium to large size positions in and out of ELEPHANTETH token without it causing a huge price impact to the upside or downside. ## Growth The Elephant Eth Money ecosystem utilizes a strategic combination Elephant buybacks and purchases by holders to drive long-term price appreciation for ELEPHANTETH token.