Production Function in 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 MRW 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 MRW (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. My production function has many policy implications, and the policy recommendations differ among AI-producing countries, rich non-AI-producing countries and poor non-AI-producing countries.