Methodology
RTM Live Simulator
The Relative Theory of Money is a formal mathematical framework proving that only one class of monetary systems achieves spatial and temporal symmetry. This page documents the derivation, the simulation implementation, and all underlying assumptions.
Theoretical Foundation
The Relative Theory of Money (Théorie Relative de la Monnaie) was formalized by Stéphane Laborde in 2010. Its central theorem proves that for a monetary system to treat all participants equally — regardless of when they join or leave — newly created monetary units must be distributed equally to every living member.
This equal distribution is called the Universal Dividend (UD). The theory defines a growth rate c that determines how much new money enters the system each period. For a human lifespan of approximately 80 years, the optimal rate converges to roughly 10% per year.
The key insight: in fiat systems, money enters via bank lending (credit creation), benefiting borrowers and financial institutions first. RTM replaces this asymmetric mechanism with a symmetric one where every participant receives the same share of new money creation.
Core Formulas
Universal Dividend Recurrence
UD(t+1) = UD(t) + c² × (M(t) / N(t+1))UD(t) — Universal Dividend at time t
c — Growth rate (annual, e.g., 0.10 for 10%)
M(t) — Total money supply at time t
N(t+1) — Number of active members at time t+1
Money Supply Evolution
M(t+1) = M(t) + UD(t+1) × N(t+1)The total money supply grows by exactly the aggregate Universal Dividend — the sum of all individual UD payments. No money is created outside this mechanism.
Initial Conditions
UD(0) = c × M(0) / N(0)The initial Universal Dividend is set as the growth rate times the per-capita money supply. In our simulation, M(0) = N × 1000 (each member starts with 1000 units).
Optimal Growth Rate
c = ln(ev) / (ev / 2) ≈ 0.10Where ev is average life expectancy (~80 years). This ensures that over a complete human lifetime, no generation accumulates a disproportionate monetary advantage. The simulator allows adjusting c from 1% to 20% to observe sensitivity.
Symmetry Properties
Spatial Symmetry
At any given moment, every member receives the same Universal Dividend. There is no privileged position in the network. Unlike fiat systems where proximity to the central bank confers advantage, RTM distributes new money identically to all participants.
Temporal Symmetry
A person entering the system today receives the same relative share of the money supply as someone who entered 40 years ago. The growth rate c is calibrated so that over one human lifetime, the relative monetary position converges. No generation is structurally advantaged over another.
Implementation
The simulator iterates the recurrence relation year by year:
function simulateRTM({ members, growthRate, years, initialMoneySupply }) {
let M = initialMoneySupply; // M(0)
let UD = growthRate * M / members; // UD(0)
let cumulative = 0;
for (let y = 0; y <= years; y++) {
cumulative += (y === 0) ? 0 : UD;
record(y, M, UD, cumulative);
// Apply RTM recurrence:
const nextUD = UD + growthRate² × (M / members);
M += nextUD × members;
UD = nextUD;
}
}Full source: simulation.ts on GitHub
Assumptions & Limitations
Constant member count
The simulation holds N constant. In reality, members join and leave over time. The RTM formula handles this via N(t+1) in the denominator, but for clarity the simulator lets you set a fixed population.
No external economic factors
The model is purely monetary — it does not account for productivity growth, trade dynamics, or fiscal policy. It isolates the effect of the money creation mechanism itself.
Deterministic model
No randomness or volatility is modeled. This is intentional — the purpose is to demonstrate the mathematical invariants, not to simulate market behavior.