Understanding the optimal strategy of carbon labelled product advertising delivery: A dynamic differential equation analysis

In the rapidly evolving landscape of sustainable marketing, the advertising of carbon labelled products represents a critical intersection of environmental awareness and marketing strategy. Existing studies have mainly discussed optimization strategies for content and forms of advertising. Less attention has been paid to optimization strategies related to the quantity of advertising delivery. Setting an advertiser's optimal advertising intensity is a problem that has puzzled researchers for a long time. To this end, we investigate the optimal strategy for advertising delivery based on a differential equation analysis of advertising dynamics to maximize market size for advertisers with regard to carbon labelled products. We first show that the vitality index can reflect the carryover effect of advertisers, and that there exists an optimal advertising intensity to maximize market size if competition is not taken into account. We then find that current and global solutions of optimal strategies are consistent, from which we can determine the sustainability of an advertiser's carbon labelled product market by calculating the equilibrium vitality index. Moreover, we provide numerical experiments that illustrate the quantitative relationship that exists between greenness and the proportion of green consumers jointly determining the feasibility of the optimal strategy and the sustainability of advertisers in management practices. This research not only charts a course for optimal advertising strategy but also equips managers with data-driven tools to navigate the complexities of eco-conscious marketing.