The Dynamic Persuasive and Informative Advertising Strategy of a Two-Part Tariff Monopolist with Advertising Spillover Effects

Though the two-part tariff is a widely adopted pricing strategy, research on it is lacking. In this paper, we establish a model of a two-part tariff product with persuasive advertising, informative advertising, and process innovation using optimal control theory. We apply Taylor’s theorem to analyze the properties of the nonlinear dynamic system and the shooting method to solve the numerical problem. We find that the pricing strategy is consistent with a two-part tariff in the static state, with price affected only by process innovation. The relationship between the two types of advertisements is affected by the advertising spillover effect, which represents the similarity of the roles of the two types of advertisements. The more similar the roles of the advertisements are, the more likely they are to be supplemented. Meanwhile, the advertising spillover effect also indicates the quality of an advertisement. The firm with the higher advertising spillover effect is more likely to attract consumers, reducing marginal costs. Therefore, a firm should either diversify its advertisements or invest only in the one with the highest advertising spillover effect. The shooting method converges well and the numerical solution indicates that our model has a unique saddle point equilibrium.