Price of the token

The price of the tokens in Invariant is determined by the ratio of both tokens in the liquidity pool. This ratio is given by the following formula, where:

• $L$ is liquidity,
• $x$ is the unit of the $X$ token,
• $y$ is the unit of the $Y$ token.

The formula fot the price of the token is given as follow:

$$\begin{aligned} \Large p=-\frac{\partial y}{\partial x}=\frac{L^2}{x}=\frac{y}{x}. \end{aligned}$$

Each point on a curve $xy=L^2$ can be parameterized using the variable $p$ in the following way:

$$\begin{aligned} \Large \varphi: (x,y) \longmapsto (\frac{L}{\sqrt{p}},L\sqrt{p}). \end{aligned}$$

More about it, you can learn from our whitepaper