Research on China’s Sustainable Economic Development and Peak Carbon Achievement Issues—Expanded Solow-based Modeling Analysis

China’s early achievement of carbon peaking is systematic and pioneering, driving energy and economic transformation and upgrading as well as high-quality development under goal-oriented frameworks. Therefore, based on an extended Solow model, energy consumption and carbon dioxide emissions are incorporated into the model for empirical analysis to explore the relationship between carbon peaking and China’s sustainable economic development. The study reveals that the elasticity of energy consumption to economic growth is relatively significant, while carbon dioxide acts as a “negative input” to economic growth, with a significantly negative elasticity. The carbon peaking target will accelerate the green and low-carbon transformation of the economic development model, continuously enhancing China’s capacity for sustainable economic development. Based on the empirical analysis results, recommendations are proposed, including accelerating the optimization of the energy consumption structure and leveraging the supportive role of technological innovation; vigorously promoting energy conservation and emission reduction strategies and improving the institutional framework for low-carbon development; fostering low-consumption and environmentally friendly production methods and restructuring the economic framework towards low-carbon practices; and gradually refining the carbon trading market mechanism to advance the construction and operation of the carbon market.