Synergy and Effectiveness Evaluation of Carbon Policy and Government Subsidies: Variational Inequality Model Based on Supply Chain Network

To address environmental challenges, governments globally have implemented a range of carbon reduction policies. Based on their mechanisms of action, this study categorizes these policies into regulatory (e.g., carbon taxes and cap-and-trade) and supportive measures (e.g., production cost subsidies, low-carbon technology subsidies, and low-carbon product subsidies). By integrating these approaches, six distinct policy combinations were identified. A supply chain network equilibrium model, incorporating manufacturers, retailers, and demand markets, was developed using variational inequality theory to assess the effectiveness of these combinations. Numerical simulations were conducted with a modified projection algorithm, and the Borda method was applied to evaluate equilibrium outcomes, specifically production levels and emission reductions, under each policy combination, revealing synergies between policies. The analysis revealed three key findings: (1) Among supportive policies, the combination of low-carbon product subsidies with regulatory policies is the most effective, while production cost subsidies are relatively weaker; (2) carbon tax policies combined with supportive policies outperform carbon trading; (3) a higher intensity of regulatory policies enhances the incentive effects of supportive policies. This research offers valuable guidance for governments seeking to design evidence-based policy portfolios that effectively balance emission reduction goals with economic development priorities.