Optimal Resource Allocation with Time-varying Marketing Effectiveness, Margins and Costs

The importance of optimal marketing communications mix decisions is well-recognized by both marketing scholars and practitioners. A significant volume of work has addressed the problem of dynamic marketing mix optimization assuming constant effectiveness of marketing instruments. However, the effectiveness of marketing communications varies over time for a variety of reasons. Moreover, due to factors such as inflation or deflation in media prices and/or raw material inputs, there can be differential changes in the costs of communications and/or margins on the good (or service) sold over time. The academic literature offers little normative direction on how time-varying marketing effectiveness and costs drive optimal marketing-mix levels and their relative allocation. The authors shed light on these issues by solving a monopoly firm's finite horizon dynamic marketing communications mix optimization problem involving two marketing instruments with time-varying parameters, i.e., the marketing effectiveness parameters, media costs, and product margin are all allowed to vary over time. First, they find that the structure of the solutions is similar to that of the classic Nerlove-Arrow model, for a completely general nature of time-varying effectiveness. Second, their model can be used by managers to exactly determine whether and when to switch their marketing-mix emphasis (defined by the marketing element receiving the dominant portion of the budget) over a finite planning horizon. In sum, the authors expand knowledge on optimal allocation of marketing resources with time-varying effectiveness. They also extend their solution to incorporate multiple (more than two) marketing instruments.