The US Macro-Learning Curve: Empirical Evidence from Post-War GDP and Productivity Dynamics.

Abstract This paper provides a unified dynamic interpretation of learning curves and aggregate output growth by linking prices, cumulative production, and time through a minimal price–quantity formalism. Starting from a derivation of price as a flow of accumulated value (P ≡ dQ/dt), we show that Wright’s Law and exponential GDP growth emerge as structural consequences of declining unit costs under expanding production. We introduce the expansion rate (R) as a dimensionless measure of growth, characterizing accumulation as a deterministic process unfolding in time. Using 70 years of US FRED data (1947–2024), we empirically validate the framework using OLS regression and rigorous time-series diagnostics. Our results identify a stable continuous expansion rate (R) of 3.05% and a macro-learning rate of 20.8% (structural elasticity, β = 0.3349). The presence of Engle-Granger co-integration (p < 0.0001) confirms that aggregate productivity is a deterministic function of cumulative experience rather than a series of exogenous shocks. This synthesis suggests that GDP growth is fundamentally the "learning curve" of civilization, offering a parsimonious alternative to stochastic growth models and providing a new deterministic tool for forecasting and policy analysis. 1