The Interplay Between Green Product Production and Advertising Investment Under Green Reputation

Establishing a green reputation reduces environmental impacts, gains recognition and increases production efficiency. We develop a stochastic optimal control model for monopolies and stochastic differential game models for duopoly and twotier supply chains. These models involve the sales of green products, the green reputation of products, and comprehensive capital stock. The model is transformed into the Hamilton–Jacobi–Bellman (HJB) equation (system). By solving the HJB equation (system), we obtain the analytical results and draw the following meaningful management conclusions: (i) Under a green reputation, the advertising and production investments of green products mutually promote each other when the firm's emissions decrease and the sales margin increases. (ii) Improving the green supply chain structure will increase the capital stock, green reputation, and sales of firms. However, as we modify our assumptions, the model becomes more complex, and analytical results cannot be obtained. We hence develop a machine learning algorithm based on the deep Galerkin method (DGM) to help solve it. We find that high sales profit margins can offset the investment constraints imposed by competitors' market presence and emission levels, thereby stimulating advertising investment. Finally, we use data from two electric vehicle firms to estimate our model and compare it with two econometric models. We show that our model performs better or equivalently in fitting. Our research aims to help engineering managers and firm executives use the green reputation to guide production planning and investment management.