A Quantitative Model for Pricing Gold

This paper introduces a reductionist pricing and calibration framework that treats gold not as an asset but as a metrological invariant—a fixed reference mass used to detect and measure fiat drift. Instead of interpreting nominal price movements as value changes, the model reframes gold as the dimensional anchor that restores unit consistency across macroeconomic variables. Labor provides magnitude, gold provides scale, and fiat expresses drift.

The framework defines three ratio‑based calibration signals:

1. GDP–gold ratio (aggregate output per invariant unit; long‑run anchor ~8:1–10:1)
2. Labor–gold ratio (hours per ounce; empirically stable ~25–35 hours/oz in U.S. data since 1900)
3. Monetary base–gold ratio (liquid base money relative to cumulative physical stock)

These ratios serve as drift detectors that distinguish short‑run nominal volatility from long‑run equilibrium reversion. Gold’s observed “price” becomes a fiat mispricing indicator, not a moving asset. Because gold's above‑ground stock expands slowly (~1.5–2% annually), mirroring long‑run productivity and population trends, it forms a natural invariant for constructing dimensional, cross‑regime valuation frameworks.

The model is explicitly non‑forecasting and non‑ideological: it provides calibration primitives, not trading rules or policy prescriptions. Applications include drift decomposition, equilibrium anchoring, unit‑of‑account consistency checks, and synthetic valuation under fiat expansion.