A sustainable dynamic optimization model of pricing and advertising in the presence of green innovation investment

Due to the increasing greenhouse effect and global warming, ecological and environmental protection issues are growing tremendously. The Paris Agreement and other international agreements have been enacted to slow down the increase in carbon emissions to prevent it from degrading the ecosystem. With the increasing consumer awareness of environmental protection and environmental regulatory pressures, firms must integrate carbon emissions concerns into decision-making. This paper analyzes a joint dynamic pricing, green innovation investment, and advertising model under the cap-and-price mechanism. The demand rate is multiplicatively related to the selling price and goodwill. The profit-maximizing problem is considered over an infinite horizon. Specifically, we assume that the stock of goodwill grows with green innovation and advertising efforts but depreciates by a constant proportion each period. Numerous theoretical results have been established to expand our comprehension of the problem. Moreover, we present several explications corresponding to these structural properties, characterizing the effects of critical parameters on optimal decisions. Finally, some numerical illustrations and explanations of the concepts of sensitivity analysis are presented to obtain managerial insights, followed by concluding remarks and future research.