Curve Math

How printing works?

The pricing mechanism in Printr.Money follows a bonding curve formula.

This formula determines token prices based on supply and virtual reserves. The goal is to create a smooth and predictable price increase as more tokens enter circulation.

Expression

The expression for the curve is:

$$f(x) = \frac{MP(x + a)}{M - (x + a)}$$

where:

• M = Maximum token supply

• P = Base price factor

• x = New supply added

• a = Virtual reserve (used to smooth pricing)

The function applies within this range:

$$0 \leq x < M - a$$

How It Works

Price Calculation

• The numerator MP(x + a) represents the virtual reserve multiplied by the new supply.

• The denominator M - (x + a) prevents the price function from exceeding the total supply limit.

• The result is a dynamically increasing price curve that rises as supply nears its maximum.

Properties of the Curve

• Supply-Driven Price Increases: Prices rise as users mint more tokens, following the supply curve.

• Liquidity Smoothing: The virtual reserve a reduces sudden price jumps when users add new tokens.

• Supply Constraints: The function only works within valid supply limits, maintaining ecosystem stability.

The expression provides us a reliable pricing model for printed tokens while providing stability through the token's lifecycle.