Based on the panel data of 285 cities in China from 2000 to 2019, this paper searches the number of patent applications related to urban artificial intelligence from five dimensions: algorithm, data, computing power, application scenario and related technology. Combining the two perspectives of industrial upgrading and rationalization, we analyze the internal influence theory of the research topic from the theoretical and empirical perspectives. The results show that artificial intelligence is not only conducive to industrial upgrading, but also significantly inhibit the deviation of industrial structure from equilibrium, which is conducive to industrial rationalization. In addition, the conclusion of this paper is still valid after a series of robustness tests, such as eliminating the samples of central cities, winsorize treatment and instrumental variables method. Through the heterogeneity test, it is found that the promoting effect of artificial intelligence on industrial upgrading is more obvious in big cities and cities with high level of industrial upgrading. The internal mechanism test results show that artificial intelligence promotes industrial upgrading by promoting technological innovation. In cities with a high degree of marketization and Internet development, the role of artificial intelligence in promoting industrial upgrading can be strengthened. The research conclusions of this paper will be conducive to accelerating the development of artificial intelligence to promote industrial upgrading, and provide a useful reference for realizing high-quality development.

Based on the “centripetal force” and “centrifugal force” of the intermolecular distance model in physics, this article establishes a worthwhile and original mathematical model to analyze the influence of the distribution of cities on urban labor productivity. We incorporate the crowding parameter into the local spillover model and demonstrate the existence of the optimal intercity distance. In addition, we estimate the optimal intercity distance for urban economic efficiency by using data from Chinese prefecture-level cities. Judging from the deviation between the actual average distance and the optimal average distance in each region, the cities in the eastern region are overcrowding, and the cities in the central and western regions are too sparse. Findings in this study carry several important policy implications. For areas in the central and western regions with large administrative areas and large populations, it would be appropriate to increase the number of prefecture-level cities and industrial density through industrial transfer and development. This approach is conducive not only to improving the economic efficiency of the central and western cities and reducing the congestion of eastern cities but also to accommodating the radiation effect of the city on rural areas and achieving the goal of common prosperity.

Based on the externality theory, this paper estimates the city size threshold of specialized agglomeration and diversified agglomeration. We find that when the urban population is below 1.25 million, specialized agglomeration is more advantageous for improving urban labor productivity. When the urban population exceeds 0.9 million, diversified agglomeration is more advantageous for improving urban labor productivity. Moreover, Specialized agglomeration of small and medium-sized cities is more likely to play the role of Marshall-Arrow-Romer externality within the spillover radius of regional central cities. One important policy suggestion is that for areas with small administrative regions and small population, it is better to increase the level of specialized agglomeration through industrial transfer, and for areas with large administrative regions and large population, it is better to increase the level of diversified agglomeration through industrial introduction, so as to further improve the urban economic efficiency.