A Self-Funding Universal Basic Income: The Plain-Language Version
March 2026
This is a non-technical companion to the paper “A Self-Funding Universal Basic Income: Existence Proof for a Stable Monetary Equilibrium” (Zenodo). The full paper contains the mathematical derivations, proofs, and computational verification. This version explains the same content without the math. The open-source codebase is available on GitHub.
What the Paper Does
Every proposal for universal basic income runs into the same question: who pays for it. The answer has almost always been some version of higher taxes — income tax, wealth tax, VAT, carbon tax — and that is where most proposals stall politically or for practicality.
This paper asks a different question. Instead of asking how to fund UBI within the existing monetary system, it asks whether a monetary system can be designed where UBI is the mechanism of money creation itself.
The paper designs such a system — six rules and five parameters — and then asks a precise question: does this system produce a stable equilibrium where the money supply settles at a fixed level, the government has enough revenue to operate, there is enough lending capacity for a functioning economy, and every person receives a guaranteed monthly income?
The answer is yes. The paper proves this by deriving exact algebraic equations for the equilibrium, proving that it is the only possible equilibrium, and proving that the system always converges to it from any starting point. Every numerical result is computationally verified and independently reproducible.
The paper does not argue that this system should be adopted. It does not derive what a coin would be worth in terms of goods and services. It does not model how people would change their behavior. The contribution is narrower and more specific: it is the first formal proof that a self-funding universal basic income admits a stable monetary equilibrium.
The Six Rules
The entire architecture is defined by six rules. Everything that follows — the money supply, government revenue, lending, convergence dynamics — is a mathematical consequence of these rules.
Rule 1: Creation
Every living person receives c coins every month, from birth to death, in the denomination of the country from which they make the claim. The denomination is determined by the person’s physical location at the time of the claim. The coins are deposited directly into the individual’s digital wallet by the protocol. There is no application, no means test, no intermediary. The amount c is the single democratic variable in the system, set by each country’s political process. In the illustrative calibration, c is 2,000 coins per person per month for a US-scale economy with 340 million people. This is the universal basic income. It is also the only way new money enters the system.
Rule 2: Lifespan
Every coin carries a timestamp recording when it was created or last transferred. Coins expire and are permanently destroyed after their lifespan runs out:
Coins held in a regular wallet expire 12 months after their last creation or transfer event. Since self-transfers are not recognized as transfers, the only way to reset the clock is to spend the coin or receive it from someone else.
Coins placed in a vault receive a five-year lifespan. A coin may be vaulted only once — there is a one-time vault flag that prevents re-vaulting.
When a coin is transferred to another person (Rule 4), the original coin is destroyed and the receiver gets newly created coins with a fresh one-year timestamp and no vault history.
Expiration prevents infinite accumulation. The vault mechanism preserves savings. The transfer-refresh mechanism means coins in active use never expire.
Rule 3: The Topper
For every claim made, the government of that denomination automatically receives τ × c additional coins, created by the protocol alongside the individual’s claim. The topper rate τ is fixed permanently by protocol — no legislative action can modify it. At the illustrative value of τ = 0.15, when a person receives 2,000 coins, the government of that denomination simultaneously receives 300 newly created coins. The topper is not taken from the individual’s claim; both are new money. This provides the government with a guaranteed revenue floor that does not depend on economic activity.
Rule 4: The Burn
Every time coins are transferred from one person to a different person, a fraction b is automatically deducted. The sender’s coins are destroyed. The receiver gets newly created coins with fresh timestamps and no vault history, equal to the sent amount minus the burn. Of the burned amount, half is permanently destroyed and half is credited to the government of the sender’s denomination.
The burn rate b is a policy variable set by the government; the illustrative calibration uses b = 0.10 (10%). Self-transfers do not refresh timestamps — you cannot game the system by sending coins to yourself.
Rule 5: Exchange
Each country has its own denomination. A sender can send coins in any denomination they hold. A receiver can only receive coins in the denomination of their physical location. When the denominations differ, the transfer settles through a swap match: a counterpart transfer moving the opposite denomination is matched with the original, so each receiver gets coins in their own denomination from a matched sender. The swap matching infrastructure would need to be independently developed; the paper specifies the rule, not the software. There is no central exchange and no conversion rate set by authority — the exchange rate emerges from swap market supply and demand.
Government accounts are exempt from the location constraint: they can send, receive, and hold coins in any denomination, enabling them to participate as liquidity providers in thin currency pairs.
Rule 6: Claim Identity
A person can only make their own claim. No one else — not the government, not a bank, not a corporation, not another person — can claim on someone else’s behalf. No contract, court order, or government action can redirect or prevent the creation event itself.
This protection applies only to the creation event. Once coins are in a wallet, they are property under the jurisdiction’s laws — they can be spent, saved, lent, seized, or taxed like any other asset. The protocol constrains only itself, not the legal system.
A design principle runs through all six rules: adversarial cooperation. No single actor can optimize their position without generating a benefit for someone else. The burn funds government, but only because people choose to transact. Expiration forces circulation, but the claim guarantees income. Government needs people claiming within its borders but cannot capture or redirect their claims. Banks need depositors to lend, and savers need banks to preserve coins beyond five years. The rules are designed so that conflicting interests produce systemic stability, not despite the conflicts but because of them.
The Five Parameters
The system has five parameters:
c (Monthly claim): Coins per person per month. Set by democratic process. Illustrative value: 2,000.
N (Population): Number of verified identities. Illustrative value: 340,000,000.
τ (Topper rate): Government’s share per claim. Fixed by protocol. Illustrative value: 0.15.
b (Burn rate): Fraction burned per transfer. Policy variable. Illustrative value: 0.10.
v (Velocity): Private-sector transactions per coin per month. Emergent economic variable. Illustrative value: 0.50.
Of these, the topper rate τ and the claim identity rule (Rule 6) are permanently fixed by the protocol and cannot be changed by any government. The claim amount c is set by each country’s democratic process — it determines the scale of the system. The burn rate b is adjustable by government as a monetary policy instrument. Velocity v is not a parameter anyone sets — it emerges from how people actually use the currency.
How the Equilibrium Works
Every month, new money enters the system through two channels: the personal claims (Rule 1) and the topper (Rule 3). Every month, money is destroyed through the burn (Rule 4) and, potentially, through expiration (Rule 2).
But there is a subtlety: government spends its revenue back into the economy. When government pays salaries, buys services, or funds projects, those transfers also trigger the burn. A fraction of government spending survives the burn and re-enters circulation. This fraction is the recycling factor. At a 10% burn rate, approximately 94.7% of government expenditure re-enters the circulating money supply. The equilibrium equation accounts for this: creation plus recycled government spending equals total destruction.
The money supply — the total amount of coins in existence — will stabilize when these two forces balance. This balance point is the steady state.
The paper derives an exact equation for this steady state. The total money supply depends on the claim amount, the population, the topper rate, the burn rate, and velocity. At the illustrative calibration, the nominal money supply comes to $29.5 trillion. For scale, current US M2 is roughly $22 trillion.
The paper then proves two things about this steady state. First, it is unique: for any given set of parameters, there is exactly one equilibrium. There are no alternative steady states the system could settle into. Second, it is globally stable: the system converges to this steady state from any starting point, whether the initial money supply is zero (a fresh launch) or far above the equilibrium (an overshoot).
The convergence follows a simple contraction: each month, the gap between the current money supply and the steady state shrinks by a fixed proportion. Starting from zero, the system reaches 50% of its steady state in about 2 years and 95% in about 9.4 years.
Government Revenue
Government revenue comes from two sources: the topper (Rule 3) and the government’s share of the burn (Rule 4).
At the illustrative calibration, annual government revenue is $10.1 trillion. For reference, current US government spending at all levels is approximately $9.5 trillion after subtracting the estimated cost of the tax collection apparatus (~$0.5 trillion), which would no longer be needed under the architecture. The architecture generates adequate revenue without any additional income tax, wealth tax, corporate tax, or sales tax.
The paper also notes that the reported $10.1 trillion is primary revenue. When the government spends this money, its own transactions trigger the burn, and the government’s share of that burn returns as additional revenue. Through this cascade, the government’s total spending capacity is approximately $10.6 trillion — about 5% higher than the primary revenue figure.
Three Structural Properties
Beyond the numerical results, the paper identifies three structural properties of the equilibrium.
Velocity Invariance
At steady state, government revenue does not depend on velocity — on how fast people spend. This is not an approximation; it is an algebraic identity. If velocity drops (people spend less), the money supply expands because creation continues while destruction slows. The product of velocity and money supply remains constant, and revenue — which depends on that product — is unchanged.
This property holds exactly under the zero-expiration assumption, and approximately with realistic expiration rates (about 10% variation across the practical velocity range). It holds exactly only at steady state. During transitions between steady states (for example, a sudden drop in velocity), revenue temporarily falls before the money supply adjusts. The paper models this explicitly and shows the system recovering.
This is a structural difference from conventional fiscal systems, where government revenue (from sales tax, income tax, corporate tax) is directly exposed to changes in economic activity.
Counter-Cyclical Mechanism
The system has a built-in counter-cyclical stabilizer. During an economic downturn, people transact less. In the current system, this means less tax revenue at exactly the moment government needs to spend more. In this architecture, reduced transactions mean reduced destruction, while creation (the monthly claims) continues unchanged. The money supply automatically expands during downturns without any policy action required.
Decoupled Monetary and Fiscal Policy
The burn rate functions as a monetary policy tool. Raising the burn rate contracts the money supply; lowering it expands it. The paper shows that adjusting the burn rate has negligible impact on government revenue across the practical policy range. This means a government can tighten or loosen monetary conditions without worrying about its budget — a structural separation between monetary and fiscal policy that does not exist in conventional systems.
Lending and Banking
Under this architecture, banks operate on full reserve. Every coin lent is a real coin deposited by a saver. There is no fractional reserve system and no money creation by banks.
People can place coins in personal vaults (preserved for up to 5 years, one-time) or in bank-managed vaults (preserved indefinitely, as long as the vault contract remains active). Banks lend from their vault holdings. At the illustrative calibration — with 68% of the money supply in vaults, 80% of that in bank-managed vaults, and a 77% deployment rate — the lending pool is $12.3 trillion. The current US benchmark is approximately $13.4 trillion.
Every cross-identity transfer creates fresh coins in the receiver’s wallet (Rule 4). Coins received through loan repayment therefore carry no vault history. This means banks cycle fresh coins through lending continuously; a 30-year mortgage requires rolling vault commitments, not a single vault event spanning the loan duration.
Sensitivity and Stress Testing
The paper subjects the equilibrium to extensive sensitivity analysis.
Univariate stress tests vary each parameter individually. Revenue remains constant across the entire tested velocity range — a computational confirmation of the algebraic invariance. Revenue is also approximately invariant to the burn rate, varying by less than 2% across b = 0.05 to 0.15. The lending pool is the binding constraint: it falls below 70% of the current benchmark at high velocity.
A Monte Carlo simulation draws all five parameters simultaneously from triangular distributions across 10,000 runs. Revenue feasibility holds in 98.4% of draws. The full feasibility rate (revenue, lending, and per-capita depth) is 69.7%. These rates describe the fraction of the assumed parameter space that is feasible, not a probability of real-world success.
The paper acknowledges that velocity and vault fraction are drawn independently in the simulation, but are mechanically related in practice (vaulted coins don’t transact). Since revenue is invariant to both, this affects only the lending ratio confidence intervals, not the revenue results.
Supply Chain Burn Cascade
An obvious objection: if every transfer costs 10%, doesn’t a multi-step supply chain compound that cost to economy-killing levels? A product that passes through four intermediaries before reaching the consumer would naively face a cumulative burn of 1 − (1 − 0.10)⁴ = 34.4%.
The paper addresses this through netting efficiency. In practice, businesses in a supply chain can net offsetting transfers — if a supplier and a manufacturer have regular two-way flows, they can settle the net amount rather than the gross. The effective consumer-facing burden depends on both the supply chain depth and the netting efficiency.
At the illustrative calibration with a supply chain depth of 4 and a netting efficiency of 60% (meaning 60% of inter-firm transfers are netted), the effective burden is 15.5% — not 34.4%. At 75% netting efficiency it drops to 9.6%. The paper provides full calibration tables across all combinations of chain depth and netting efficiency.
Whether 15.5% is acceptable depends on what it replaces. The current US system imposes corporate income tax, payroll tax, sales tax, compliance costs, and the deadweight loss of the tax apparatus. The burn replaces all of these with a single, automatic, flat-rate mechanism. Whether the net burden is higher or lower is an empirical comparison the paper does not attempt.
Velocity Floor
A concern with any transaction cost is that it might suppress economic activity to the point where the system breaks. The paper addresses this directly.
Because coins expire if not used (Rule 2), the cost of not transacting — losing the coin entirely — always exceeds the cost of transacting — paying the burn. At a 10% burn rate, spending a coin costs 10%. Not spending it costs 100% when it expires. This creates a structural velocity floor: no matter how high the burn rate (as long as it is below 100%), people will always prefer to spend rather than let coins expire.
This means the burn cannot suppress velocity to zero. The system has a built-in minimum transaction rate driven by the expiration mechanism — a structural property of the rules, not a behavioral assumption.
Velocity Assumptions
The illustrative velocity of 0.50 monthly (6.0 annualized) exceeds current US M2 velocity (~1.3) but is appropriate because this currency is designed to circulate, not to sit as a store of value. M2 includes large deposits and money market funds that rarely transact. The architecture separates circulating coins (which transact at rate v) from vaulted coins (which do not). The relevant comparison is therefore narrower money measures, where velocity is higher. The paper stress-tests across velocities from 0.20 to 0.80 monthly. Revenue is invariant across this entire range. Lending adequacy is the binding constraint at high velocity.
Expiration
The equilibrium equation as derived assumes that no coins expire at steady state — that people and institutions manage their coins actively enough to avoid expiration. The paper addresses this explicitly.
For non-vaulted coins, the probability of a coin remaining untransacted for 12 months is very small (about 0.25%), making wallet expiration negligible.
For personal vault coins ($4.0 trillion at the illustrative calibration), the worst case assumes all eventually expire after their 5-year lifespan. This adds about $67 billion per month of destruction — roughly 8.6% of total monthly inflow. Even at worst-case expiration rates, the reduction in steady-state money supply is approximately 8%, and the velocity invariance of revenue becomes approximate rather than exact (about 10% variation across the practical velocity range).
The qualitative properties — unique steady state, counter-cyclical mechanism, revenue floor from the topper — survive under expiration.
Dynamic Behavior
The paper simulates a velocity shock: velocity drops from 0.50 to 0.30 for 24 months, then recovers. During the shock, the money supply expands (creation exceeds destruction), and revenue temporarily drops from $10.1 trillion to $6.5 trillion annually. When velocity recovers, the money supply gradually contracts back toward the original steady state, and revenue returns to $10.1 trillion.
This illustrates both the counter-cyclical mechanism (money supply expands during the downturn) and the limitation of velocity invariance (revenue is not protected during the transition itself, only at steady state).
Government Fiscal Behavior
The steady-state derivation assumes the government spends all revenue within each period — the balanced-budget case. In practice, the government can deviate from this.
A government that saves a portion of its revenue (runs a surplus) removes coins from active circulation, contracting the money supply below the balanced-budget steady state. A government that spends from accumulated reserves (runs a deficit) injects coins above the steady-state inflow, expanding the money supply. The government can also vault coins under Rule 2, creating a strategic reserve preserved for five years.
The architecture therefore provides three policy instruments: the claim c (scale, set by democratic process), the burn rate b (monetary policy, negligible fiscal side effects), and the government savings rate (conventional fiscal policy, direct impact on the money supply).
What the Paper Does Not Do
The paper is explicit about its limitations. These are not minor gaps — some of them go to the heart of whether the architecture would work in reality.
No price level. The paper derives the nominal money supply and nominal revenue. What a coin is worth in terms of goods and services — the price level — is not derived. All numerical comparisons to current US benchmarks ($29.5T vs M2, $10.1T vs government spending, $12.3T vs lending) assume coins have purchasing power comparable to current dollars. Whether that assumption holds depends on real output, productivity, and expectations — a general equilibrium question the paper identifies as the central open problem. A system can have a perfectly stable nominal equilibrium while hyperinflating. The paper proves nominal stability; real stability remains unproven.
No behavioral modeling. The paper does not model how people would change their work, spending, or saving behavior under this architecture. Velocity is treated as an exogenous parameter for the steady-state derivation, not as a function of incentives.
No transition analysis. The paper assumes a fresh launch from zero. It does not model how an existing economy would transition to this architecture.
No credit market dynamics. Banks operate on full reserve — a significant departure from all existing financial systems. Whether full-reserve lending at the derived scale meets actual credit demand depends on interest rates, maturity transformation, and credit market behavior that the paper does not model.
No implementation specification. The paper specifies the monetary rules but not the technical infrastructure. Identity verification, protocol governance, and software architecture are outside the scope.
No political analysis. Whether this architecture is politically feasible or desirable is not addressed.
The Claim
The conventional approach to UBI asks how to fund it within the existing monetary architecture — through taxation, redistribution, or deficit spending. This paper inverts the question: it designs a monetary architecture where the UBI payment is the mechanism of money creation itself. The monthly claim is not a transfer from one group to another; it is how money enters the system.
This inversion resolves the nominal funding problem — the architecture generates nominal government revenue without any additional taxation beyond the topper and the burn. It does not resolve the real resource question: what the coins buy, how prices adjust, and who bears the real cost of universal income. That question lives in general equilibrium, which is where the next step of this research must go.
The paper’s contribution is specific: it is the first formal demonstration that a self-funding universal basic income admits a unique, globally stable monetary equilibrium. The architecture is the contribution — not a policy recommendation. It is a first step.
All equations are derived from first principles. All numerical results are computationally verified. The full codebase is open source. Every result in the paper can be independently reproduced.
The author welcomes engagement on any aspect of the work — the mathematics, the economic assumptions, implementation questions, or extensions to general equilibrium. The open problems are real and the author does not claim to have all the answers. If the architecture holds up under scrutiny, the next steps require more minds than one.
Frequently Asked Questions
Won’t giving everyone $2,000/month cause massive inflation?
It depends on the price level, which the paper does not derive. What the paper does show is that the nominal money supply converges to a finite, stable value — not an ever-growing one. At steady state, every coin created through monthly claims is matched by a coin destroyed through the burn. Net money creation is zero. Whether the resulting money supply produces inflation, deflation, or price stability depends on real output and productivity — a general equilibrium question that requires further research. The burn rate is available as a monetary policy tool to contract or expand the money supply if needed.
Why would anyone work if they get free money?
The paper does not model labor behavior. This question belongs to the existing UBI literature, which has studied it extensively through dozens of real-world experiments. The paper demonstrates that a self-funding UBI is mathematically feasible, not that UBI is desirable. Whether and how people change their work behavior under universal income is an empirical question outside the paper’s scope.
Isn’t the burn just a tax with a different name?
The burn shares one functional characteristic with taxation — it imposes a cost on participants that funds government. It differs in mechanism: it is a flat-rate, automatic, protocol-level deduction on every inter-identity transfer. There is no filing, no tax code, no assessment, no evasion strategy beyond avoiding transfers entirely. Whether this constitutes “a tax” is a semantic question. The mathematical properties of the system are the same regardless of the label.
Don’t expiring coins destroy people’s savings?
Coins in active use never expire — every transfer creates fresh coins with a new one-year timestamp. Coins placed in a vault are preserved for five years. Bank-managed vaults preserve coins indefinitely. Expiration destroys only coins that no one — holder, bank, or counterparty — touches for the full lifespan. The mechanism targets monetary inertness, not savings. Retirement savings, insurance reserves, and long-term wealth storage all function through the vault mechanism.
What stops someone from creating fake identities to collect multiple claims?
Rule 6 requires a one-to-one mapping between living persons and protocol identities. The identity verification mechanism itself or the privacy-preserving cryptographic mechanisms are external to the architecture — the paper specifies the rule, not the technology. The deterrent is structural: fraud and attack on the protocol could mean permanent disbarment — not just a fine or a penalty, but the permanent loss of $2,000 per month for life and exclusion from the monetary system itself. This is a disproportionate consequence for fraud, by design. The architecture also gives government a direct fiscal incentive to enforce verification, since each verified identity generates revenue through the topper and burn.
Could this actually be implemented?
The paper does not claim it can — at least not without substantial further work. It proves that the mathematical architecture produces a stable equilibrium. Implementation would require universal identity verification, protocol governance, software infrastructure, political will, and a transition framework — none of which are addressed. The paper is an existence proof, not an implementation plan. Whether the gap between mathematical proof and real-world implementation can be bridged is an open question the author does not claim to have answered.
Full paper: https://doi.org/10.5281/zenodo.18830074
Code: https://github.com/a-roy-research/perpetual-coin