Pricing Formula

Virtual Liquidity Pool

The trading of Power adopts AMM's constant product formula. Here, we introduce the concept of a 'virtual liquidity pool'. This liquidity pool doesn't actually exist; we use this concept to explain the calculation of the price of Power.

Suppose Liquidity(ETH)Liquidity(ETH) and Liquidity(Power)Liquidity(Power) are the ETH amount and the Power amount in the Virtual Liquidity Pool respectively. We adopt the AMM's constant product formula: Liquidity(ETH)×Liquidity(Power)=kLiquidity(ETH) \times Liquidity(Power) = k to determine the price of Power and the ETH cost.

Total Supply, Initial Liquidity and kk

The Topic Power price starts from 0.001 ETH. The Subtopic Power price starts from 1 Topic Power.

When a Topic is launching, its Total Supply is determined by the popularity of the Topic. Typically, it ranges between 5,000 and 50,000, with 10,000 being the most common.

Initially, the total supply of Power is all in the virtual liquidity pool, Liquidityinitial(Power)=TotalSupplyLiquidity_{initial}(Power) = TotalSupply

From this, we can derive that Liquidityinitial(ETH)=0.001×TotalSupplyLiquidity_{initial}(ETH)=0.001\times TotalSupply

k=Liquidityinitial(ETH)×Liquidityinitial(Power)=0.001×TotalSupply2k=Liquidity_{initial}(ETH)\times Liquidity_{initial}(Power)=0.001\times TotalSupply^2

The price of Topic Power is 0.001×(TotalSupplyLiquidity(Power))2ETH0.001 \times \left(\frac{TotalSupply}{Liquidity(Power)}\right)^2 \, \text{ETH}

We set a Subtopic's total power supply to be 1/20 of its Topic's total power supply. For example, if the total supply of a topic power is 10,000, each of its Subtopic will have a 500 total supply.

Thus, the price of Subtopic Power is 0.0025×(TotalSupplyLiquidity(Power))2Topic Power0.0025 \times \left(\frac{TotalSupply}{Liquidity(Power)}\right)^2 \, \text{Topic Power}

Buying Process

Assuming a user purchases xx Power with yy ETH (or xx Subtopic Power with y Topic Power), based on the AMM's constant product formula (Liquidity(ETH)+y)×(Liquidity(Power)x)=k(Liquidity(ETH)+ y)\times (Liquidity(Power)-x) = k, we'd get

x=Liquidity(Power)kLiquidity(ETH)+yx=Liquidity(Power) - \frac{k}{Liquidity(ETH) + y}, and the average price of this transaction would be yx\frac{y}{x}

Selling Process

Similarly, if a user sell xx Power, and would get yy ETH (or sell xx Subtopic Power and get y Topic Power),

y=Liquidity(ETH)kLiquidity(Power)+xy=Liquidity(ETH) - \frac{k}{Liquidity(Power) + x}, and the average price of this transaction would be yx\frac{y}{x}

The above calculation doesn't include trading fee. For details on these fees, please refer to Trading Fee.

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