Dynamic control of low-carbon efforts and process innovation considering knowledge accumulation under dual-carbon policies

Governments frequently implement carbon trading (CT) and carbon subsidy (CS) policies for encouraging enterprises to engage in low-carbon efforts (LCE) and reduce emissions, ultimately aiming for sustainable development in environmental and economic realms. In response, enterprises increase their investments in process innovation (PI) to balance revenue generation and cost reduction while simultaneously accumulating knowledge. Exploring the relation between LCE and PI is crucial to guide enterprises in effectively balancing these inputs, as well as to examine the role of government regulations on carbon emissions in motivating enterprises to enhance their efforts. This study proposes a dynamic optimal control model integrating PI and LCE within the dual-carbon policy framework, considering the effect of knowledge accumulation (KA). Moreover, it evaluates changes in inputs and benefits under profit-optimal and social welfare-optimal conditions. Finally, a comparative analysis is conducted using numerical simulation and emulation. The findings indicate complementary and substitution effects between the two inputs: the KA effect enhances input stability, and the impact of social incentives consistently outweighs that of monopoly incentives. Furthermore, CT and CS policies exhibit cross-impacts on enterprise returns and the two inputs.