Quality effects in different advertising models - An impulse control approach

In this paper, we integrate quality as a control variable in three classical dynamic optimal control models of advertising, namely, Nerlove-Arrow, Vidale-Wolfe and Ozga models. Quality refers to design quality, which may deteriorate over time. We assume that decisions in quality improvement can only be made at some exogenously given instants of time, and consequently we use the formalism of impulse optimal control to determine optimal advertising and quality investments. We report numerical results for the three models and discuss the impact of adding quality on the results.