Moony’s primary price discovery mechanism is an onchain pricing curve - a deterministic exponential function encoded within the Moony Reserve smart contract. Unlike traditional market-based price discovery that relies on order books or liquidity pools, the pricing curve calculates the price of MNY based solely on the current circulating supply. As tokens enter circulation through unlocking, the price rises along a mathematically defined trajectory. As tokens are redeemed and removed from circulation, the price falls along the same curve in reverse.
The exponential model creates predictable incentive structures: gradual price appreciation during early adoption, accelerating value capture as the network matures, and a natural ceiling at maximum supply. Early participants benefit from lower entry prices while later participants contribute proportionally more capital to the reserve - capital that backs the redemption value of all circulating tokens. This mechanism applies symmetrically to both unlocking and redemption, enforced by immutable onchain code with no administrative override capability. All transaction outcomes are independently verifiable using the formulas documented below.
Spot Price
The spot price represents the instantaneous price per MNY token at any given circulating supply level - a continuous mathematical function with no bid-ask spread and no dependence on external liquidity. It is defined by an exponential equation with three immutable constants:
P(S)- spot price in USDF at supply level SS- current circulating supply of MNY tokense- Euler’s number (~2.71828), the base of the natural exponential function
The exponential form ensures that the rate of price change is proportional to the current price itself - creating smooth, continuous appreciation without discontinuities at any supply level.
Constants
Three immutable constants parameterize the curve to produce an initial price of ~0.01 USDF and a terminal price of 1,000,000 USDF at maximum supply (21M MNY):
a = 11400.230149967394933471Amplitude constant - scales the curve to reach $1,000,000 USDF at maximum supply.
b = 0.000000877175273521Initial price coefficient - sets the starting price at a × b ≈ $0.01 USDF when supply is near zero.
c = 0.000000877175273521Growth rate - controls how rapidly price increases with supply. Note: c = b by design, which simplifies integral calculations.
Price at Supply Milestones
Reference prices at key supply milestones, computed directly from the spot price formula:
| Circulating Supply | Spot Price (USDF) |
|---|---|
| 0 | 0.01 |
| 1,000,000 | 0.02 |
| 5,000,000 | 0.80 |
| 10,000,000 | 64.50 |
| 15,000,000 | 5,180 |
| 20,000,000 | 415,000 |
| 21,000,000 | 1,000,000 |
Transaction Pricing
The spot price tells you the current price per token, but you cannot simply multiply it by the quantity you want - because each token you buy slightly increases the price of the next one. Instead, the total cost is computed by integrating the spot price function across the full range of the transaction. The formulas below handle this automatically: two for buying (cost and tokens received), two for selling (value and tokens required).
Cost to Buy Tokens
Given a token quantity to acquire, this formula computes the total USDF cost - the definite integral from current supply to new supply:
S₀- circulating supply before the purchase (currentSupply)S₁- circulating supply after the purchase (S₀ + tokensToBuy)- Since b = c by design, the coefficient (a · b / c) simplifies to
a
The computed cost always exceeds (spot price × quantity) because each successive token in the transaction is priced marginally higher than the previous. This price impact is an inherent property of pricing curves and scales with transaction size relative to total supply.
Tokens Bought for Value
When participants specify a USDF amount to spend (the typical case), this inverse function determines the exact quantity of MNY received:
T- tokens received (tokensBought)V- USDF amount the participant wishes to spendS₀- circulating supply before the purchaseln- natural logarithm, the inverse of exponentiation (e^x)
The logarithmic term arises from inverting the exponential cost function. Because the natural log is the inverse of e^x, this formula algebraically solves for the supply endpoint that yields exactly the specified cost when integrated from S₀.
Value from Selling Tokens
The same logic applies in reverse when redeeming tokens. Tokens return to the reserve, supply decreases, and USDF is released:
S₀- circulating supply before the redemptionS₁- circulating supply after the redemption (S₀ - tokensToSell)- Returns the gross redemption value before protocol fees are applied
The mathematical symmetry between acquisition and redemption ensures that the reserve always holds sufficient USDF to honor all outstanding redemptions at current curve prices. This is a fundamental solvency invariant - the value locked in the reserve exactly equals the redemption value of all circulating tokens.
Tokens Required for Value
When participants specify a desired USDF amount to receive, this inverse function computes the MNY required to redeem. It operates on reserve value rather than supply:
T- tokens required to sell (tokensToSell)V₀- total USDF currently locked in the reserveV₁- reserve balance after redemption (V₀ - valueToReceive)ln- natural logarithm, the inverse of exponentiation (e^x)
This formulation uses the reserve’s locked value as the state variable rather than circulating supply. The two are mathematically equivalent due to the one-to-one correspondence between supply levels and cumulative reserve value.
Secondary Market Dynamics
The formulas above govern transactions directly with the Moony Reserve. But MNY may also trade on external markets (DEXs, exchanges) where prices are set by supply and demand rather than the pricing curve. How do these two pricing systems interact? The Reserve’s guaranteed liquidity creates a powerful anchoring effect through arbitrage:
Arbitrageurs acquire MNY from the Reserve at the lower curve price, then sell on the secondary market at the elevated price. This increases Reserve supply (raising the curve price) while adding sell pressure to the secondary market (lowering its price), converging the two.
Arbitrageurs purchase MNY on the secondary market at the discounted price, then redeem at the Reserve for the higher curve value. This adds buy pressure to the secondary market (raising its price) while decreasing Reserve supply (lowering the curve price), converging the two.
This arbitrage mechanism establishes the Reserve as both a price floor and ceiling for external markets. Any price gap exceeding transaction costs becomes an opportunity that arbitrageurs will exploit until equilibrium is restored, keeping MNY prices across all markets tethered to the deterministic curve.
Discrete Implementation
The formulas above are mathematically exact, but how does the smart contract actually compute them? Direct calculation of exponentials and logarithms onchain is computationally expensive. Instead, the Moony Reserve precomputes all curve values at regular supply intervals and stores them in lookup tables. Transaction pricing reduces to table lookups with linear interpolation - efficient and producing identical results every time.
Lookup Tables
The implementation maintains two parallel data structures, each precomputed from the continuous formulas at fixed supply intervals:
Spot price P(S) evaluated at each discrete supply level. Used for displaying current market price.
The integral of P(S) from 0 to each supply level. Enables O(1) transaction cost computation by subtracting values at transaction boundaries.
Precision
The lookup tables are configured to balance storage efficiency against interpolation accuracy:
Each table entry represents the curve value at supply S = i × 100. Interpolation error remains below 0.01%.
Internal calculations use 128-bit integers with 18 decimal scaling for precision. The MNY token uses 10 decimal places.
Covers all supply levels from 0 through the 21,000,000 MNY maximum in 100-token increments.
These tables are fully deterministic and independently verifiable. Any implementation can regenerate the complete table contents from the constants and formulas documented above and verify equivalence with the deployed contract data.