A Theory of Endogenous Growth Through Public AI Infrastructure and Digital Crowding-In

In this paper, we formulate a new endogenous growth framework designed for the artificial intelligence era. We theorize AI as a hybrid production factor, possessing the non-rivalrous properties of public knowledge and the rivalrous constraints of computing power. By endogenizing the role of public finance, the model demonstrates that strategic government investment in digital infrastructure and AI-specialized human capital acts as a primary catalyst for the marginal productivity of private capital. We derive the Theorem of Digital Optimality, identifying the optimal allocation of tax revenue between physical hardware and intangible intelligence. Our findings suggest that in an AI-driven economy, public spending generates a significant crowding-in effect, shifting the private investment frontier upward. The model warns that failure to optimize these public inputs leads to digital secular stagnation, in which the lack of sovereign digital platforms bottlenecks private-sector innovation.