This study investigates how a profit-maximizing firm can jointly optimize its pricing, advertising efforts, and inventory replenishment strategies over a finite planning horizon under the cap-and-price regulatory framework. Our theoretical results demonstrate that cap-and-price regulation enables governments to effectively control emissions, offering an effective policy tool to balance economic development and environmental protection. Numerical examples reveal that goodwill and regulatory parameters significantly influence a firm’s behavior. More frequent replenishment allows firms to fine-tune pricing and advertising strategies at the cost of higher replenishment and emission-related expenses. We alsofind that Cap-and-Trade yields the highest profit and moderate emissions, benefiting from trading flexibility and balanced incentives. In contrast, firms adopt aggressive strategies without regulation, producing the highest emissions and lowest profits. Furthermore, as carbon penalties internalize emission costs, firms may face higher operating costs, leading to rising prices or reduced advertising efforts. Such responses can affect brand image and weaken customer loyalty, underscoring the importance of integrated and adaptive decision-making in regulated markets. The proposed model offers valuable insights for high-emission sectors, supporting integrated decisions under environmental constraints. Finally, we conclude the study with insights derived from the theoretical analysis and numerical experiments and suggest directions for future research.
