The Generalized Sethi Advertising Model

We propose a flexible yet tractable dynamic advertising model called the generalized Sethi model to capture different market penetration rates across various media and markets via advertising. Specifically, the generalized Sethi model employs a Cobb-Douglas production function of advertising expenditure and the untapped market share with constant returns to scale. It encompasses some standard dynamic advertising models as particular cases. Moreover, the model's flexibility does not compromise its tractability. We demonstrate it by showing single- and multifirm advertising problems involving Nash and Stackelberg games to admit closed -form expressions for the firms' optimal advertising strategies and value functions under the generalized model. Sensitivity analysis of the model parameters also yields novel economic insights regarding the firms' optimal advertising strategies and value functions.