Optimizing green technology diffusion through advertising and referral incentives in heterogeneous markets

This study develops a continuous-time optimal control model to examine how firms should dynamically allocate advertising and referral incentives during the diffusion of sustainable technologies in heterogeneous markets. The model distinguishes between early adopters and the mainstream market, allowing the two groups to differ in spontaneous adoption, advertising responsiveness, word-of-mouth intensity, and referral responsiveness. To better reflect the economic conditions of green technology markets, the framework incorporates diminishing-return marketing effects, a time-varying unit contribution margin, explicit control bounds, and an overall budget constraint. The analysis yields three main findings. First, optimal advertising is generally front-loaded, as its marginal value declines with increasing market saturation. Second, referral incentives tend to follow a stage-dependent path, strengthening first and then receding as the balance between installed-base expansion and market saturation shifts over time. Third, advertising and referral incentives are dynamically complementary rather than statically interchangeable. By integrating consumer heterogeneity, nonlinear marketing response, dynamic profitability, and financial feasibility into a unified diffusion-control framework, this study provides a theory-driven normative benchmark for dynamic marketing resource allocation in sustainable technology diffusion.