Dynamic Optimal Control Models in Advertising: Recent Developments

This paper presents a review of recent developments that have taken place in the area of dynamic optimal control models in advertising subsequent to the comprehensive survey of the literature by Sethi in 1977. The basic problem underlying these models is that of determining optimal advertising expenditures and possibly other variables of interest over time for a firm or a group of competing firms under consideration. This optimization is done subject to some dynamics that define how these variables translate into sales and in turn, into profits. The purpose of this update is twofold. On the one hand, new contributions in the areas already treated in the earlier survey are reviewed. On the other hand, new trends in the advertising literature since 1977, such as quality as an additional marketing instrument, cumulative sales models, pulsing advertising, and advertising as a part of corporate models of the firm, are discussed. The models covered in this update are organized under six headings: models with capital stocks generated by advertising, price, and quality, sales-advertising response models, cumulative sales models for durable goods, models with more than one state variables in the advertising process, models incorporating interaction with other functional areas, and competitive models. The discussion involves specifications, methods used, results, empirical validation, if any, and their economic significance. The survey concludes with suggestions for extensions and future directions of research.