Total Output of the Future

This paper develops a theory of growth with self-learning AI. I decompose “technologies” into a non-self-learning component T(t) and a recursive self-learning term (S(t) D(t)) (t), where (t) = 0 + log(S(t) D(t)) links capability gains to deployed self-learning technologies S and data D. I present two complementary production functions. Version 1 highlights distributional channels by separating AI-complementary vs. AI-substitutable labor and human capital. Version 2 is measurement-oriented, mapping the self-learning stock to AI-specific physical capital, labor forces, and human capital, thereby operationalizing S. The model yields sharp regime conditions: with small/approximately constant (t), the economy exhibits a balanced growth path (BGP); when θ(t) becomes large enough to push effective returns above one, growth accelerates. A log-space recursion implies a quadratic bound for log((SD) (t)), establishing no finite-time singularity. The framework produces testable predictions—notably the need for both linear and quadratic terms in log(SD) in empirical specifications—and clarifies bottlenecks: insufficient AI-specific capital or low-quality data can hold down θ(t) and prevent acceleration even with advanced systems. Policy implications follow directly: scale compute and energy, raise HAI, LAI, and improve data governance/quality. The contribution is conceptual and theory-only, positioning the mechanism for subsequent empirical work while providing a tractable structure for cross-country comparisons in an economy increasingly driven by recursive, autonomous innovation.