When there is a trade in a pool, the pool collects a trade fee. The trade fee is denominated in the input token. Each pool has its own trade fee set based on the underlying assets.
In addition, liquidity providers can stake their LP tokens in the appropriate farms to earn additional BEETS liquidity mining incentives.
As the pool collects fees, your Beethoven X Pool Tokens automatically collect fees because they represent your proportional share of the pool.
Let's say Alice, Bob, Chuck, and Diana all provide liquidity in the same pool starting out worth $100. After some time, it has earned many trade fees and is now worth $200. The pool itself grows while their proportional shares stay the same.
In general the AMM logic determines the prices that traders pay. For example, Weighted Pools, use a constant product formula and Stable Pools, use a StableSwap formula.
Beethoven X allows for the creation of self-balancing index funds. Instead of paying a portfolio manager to continuously rebalance the fund, as investors do with an ETF, liquidity providers collect fees as traders rebalance the trading pools. This works because market actors are incentivized to rebalance the portfolio to take advantage of arbitrage opportunities.