New Production Function (which is Supported by Empirical Evidences) for an Economy with Deployed Self-Learning Technologies

The purpose of this paper is to introduce a new production function that takes into account self-learning AI, which can improve itself and therefore productivity without any additional human capital or labor, even though it still requires physical capital. The difference between my production function and any other existing production function is that my production function separates technologies into self-learning and non-self-learning technologies. The value of exponent for the self-learning technologies depends on the value of its base and this is the unique recursive feature of my production function. Unlike in the Mankiw-Romer-Weil production function, in my production function, technology and labor force are separated and this is allowed because I make the technology endogenous. My production function leads to only two possibilities, which are an economy that is in balanced growth path (BGP), and an economy that is in accelerating growth path. The determining factor that decides whether an economy is in BGP or not is the exponent for the self-learning technologies in my production function. If the sum of all exponents is less or equal to 1, then the economy is in BGP, which is consistent with Mankiw-Romer-Weil (1992). If the sum of all exponents is greater than 1, then the economy is in accelerating growth path, which is consistent with Romer (1986). There is no steady state in my production function. I also rule out the possibility of singularity. I support my production function with empirical evidences that confirm that my production function is quite accurate and quite useful for cross-countries comparison. Furthermore, I conduct simulations that show how the U.S economy will transition from balanced growth path to accelerating growth path.