Semi-Endogenous Growth with Automation and A.I: Representative Household vs. Social Planner

Heng-Fu Zou ()

No 794, CEMA Working Papers from China Economics and Management Academy, Central University of Finance and Economics

Abstract: We develop a unified, utility-based model of semi-endogenous growth in which a representative household (RH) and a social planner (SP) face identical feasibility and knowledge constraints, and in which automation/A.I. directly performs a fraction of research tasks. The framework is deliberately parsimonious-one state (the stock of ideas) and one intensive choice (the research share)-so mechanisms are transparent and results come in closed form. First, in a competitive reduced-form environment we solve RH and SP side-by-side, prove equivalence for growth, and derive a closed-form balanced-growth research share that cleanly separates levels (chosen by the research share) from rates (pinned by the idea law and the evolution of research effort). Second, we place automation inside R&D via a task aggregator and obtain a single organizing iden tity that links long-run idea growth to the growth of machine and human research capacity. Two closures-ideas-riding A.I. and “exogenous A.I. drift†-deliver testable expressions for per-capita growth and a simple sustainability condition under demographic headwinds. Off the balanced growth path, we provide an exact transition decomposition, including a reallocation term from the diffusion of automation. Third, embedding a Romer variety-expansion sector reveals a static markup wedge and a dynamic knowledge wedge; a minimal policy pair-a user-price subsidy for intermediates and an R&D prize/ wage subsidy-decentralizes the planner. The resulting toolkit offers suffcient statistics for measurement and policy design.

Pages: 20 pages
Date: 2025-10-22
New Economics Papers: this item is included in nep-gro and nep-upt
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