Production Function For Economies With Deployed Self-Learning Technologies (With Empirical Evidences)

This paper introduces a new production function for economies, in which deployed self-learning AI have become meaningful determinant of total output. Building on the Mankiw-Romer-Weil (MRW) framework, the production function separates technologies into deployed non-self-learning technologies and deployed self-learning technologies. Furthermore, the production function separates physical capital, labor forces and human capital based on AI-specificity. The production function is the following: Y(t) = (T(t) [S(t) D(t)] (t)) (KAI(t) 1 KNAI(t) 2) (LAI(t) 1 LNAI(t) 2) (HAI(t) 1 HNAI(t) 2). The most unique feature of the production function is the exponent (t) because (t) is the only exponent whose value is determined by its base; this is the unique recursive feature of the production function. Self-learning AI, which determine the value of (t), also determine whether the economy has production function with decreasing, constant or increasing returns to scale. Mathematical proof shows that, in the proposed production function, singularity is impossible. Empirical evidences from 26 high-income countries show that the proposed production function is very useful in cross-countries analysis; the proposed production function is much more accurate than MRW production function. While MRW production function produces 0.49 correlation among 22 OECD countries in year 1985, the proposed production function produces 0.96 correlation among 26 high-income countries in year 2024. Simulations show that self-learning AI can transition an economy from having production function with decreasing returns to scale to having production function with increasing returns to scale.