The asymptotic trajectory of value in a fixed-supply monetary system

Fixed Supply Money and Asymptotic Deflation

A fixed monetary base—whether gold (effectively capped by extraction cost) or Bitcoin (literally hard-capped)—induces deflation only to the extent that economic productivity or demand for money increases. But this deflation is not exponential. It is logarithmic.

Why?

As more participants enter the system (population growth, adoption),

And as productivity per participant increases (technological advancement),

Each unit of money can command more value, but with diminishing marginal effect.

Mathematically:
If M is fixed and GDP increases, then P (general price level) must decrease.
But as the system grows, each new unit of productivity contributes less relative to the total. So prices approach zero but never reach it. The rate of deflation slows, approaching stability.

This is not runaway deflation. It is decaying deflation—logarithmic in slope, not linear or exponential.

Thus, a fixed-supply currency will exhibit early deflation and long-term price stability—assuming population and production stabilize.

Population Collapse and Reverse Pressure

“If the civilization population were to collapse… deflationary pressure could turn inflationary.”

This is an elegant inversion of the Quantity Theory of Money (MV = PQ):

• M is fixed.
• V (velocity) may fall as economic activity collapses.
• Q (quantity of goods/services) collapses more severely.
• P, therefore, may rise: i.e., inflation under a fixed supply.

This is rarely considered in fixed-money advocacy. But it is vital: deflation is not a guarantee—it is conditional on growing or stable production and demand for money.

In a post-collapse scenario (e.g., plague, war, collapse of trade):

• Money may become less useful.
• Fewer goods exist.
• Surviving capital-holders may find their money buys less, not more.

Thus: deflation is not intrinsic to fixed supply—it is emergent from growth.

Implications for Long-Term Stability

Early Phase (Growth):

• Productivity and population rise.
• Deflation occurs as each unit of money chases more output.
• Savers benefit.
• Prices fall, investment adjusts, and value accrues to restraint.

Maturity Phase (Plateau):

• Population and output stabilize.
• The value of money stabilizes.
• Prices fluctuate within narrow bands based on sectoral shifts.
• Money becomes a pure store of value and neutral unit of account.

Collapse Phase (Decline):

• Population or productivity fall.
• Scarcity returns to goods, not money.
• Money inflates in value—not because new units are added, but because each unit commands less.

This is the inverse of Keynesian doctrine. It reveals that value in money is not intrinsic, even under a fixed supply. It is relational to what that money can command.

Money as a Logarithmic Mirror of Civilization

Money in this view functions as a logarithmic mirror of civilizational vitality:

Early Civilization: Money is unstable, yet increasingly valuable. Deflation dominates.

Mature Civilization: Money is stable. Prices reflect local scarcity, not systemic manipulation.

Declining Civilization: Money is increasingly useless. Real value migrates to tangible, local, survivable assets.

Thus, the fixed-supply money acts like a geometric stabilizer:
Its behavior maps not only economic input, but demographic entropy.

It does not ensure freedom, fairness, or flourishing—it only reflects them, amplifies them, or, in their absence, exposes their collapse.

Final Synthesis

A fixed-supply currency is deflationary only in a growing system.
It stabilizes logarithmically as growth tapers.
And it can become inflationary in a shrinking system—without printing a single coin.

This understanding destroys the binary myth of “deflation = good” or “inflation = evil.” What matters is that money be stable in architecture and transparent in function, so that it may reflect reality—not distort it.

Sound money does not guarantee order.
It reveals whether order exists.