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Optimal advertising strategies with age-structured goodwill

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  • Silvia Faggian
  • Luca Grosset

Abstract

The problem of a firm willing to optimally promote and sell a single product on the market is here undertaken. The awareness of such product is modeled by means of a Nerlove–Arrow goodwill as a state variable, differentiated jointly by means of time and of age of the segments in which the consumers are clustered. The problem falls into the class of infinite horizon optimal control problems of PDEs with age structure that have been studied in various papers either in cases when explicit solutions can be found or using Maximum Principle techniques. Here, assuming an infinite time horizon, we use some dynamic programming techniques in infinite dimension to characterize both the optimal advertising effort and the optimal goodwill path in the long run. An interesting feature of the optimal advertising effort is an anticipation effect with respect to the segments considered in the target market, due to time evolution of the segmentation. We analyze this effect in two different scenarios: in the first, the decision-maker can choose the advertising flow directed to different age segments at different times, while in the second she/he can only decide the activation level of an advertising medium with a given age-spectrum. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Silvia Faggian & Luca Grosset, 2013. "Optimal advertising strategies with age-structured goodwill," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(2), pages 259-284, October.
  • Handle: RePEc:spr:mathme:v:78:y:2013:i:2:p:259-284
    DOI: 10.1007/s00186-013-0443-8
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    References listed on IDEAS

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    1. Dieter Grass & Jonathan P. Caulkins & Gustav Feichtinger & Gernot Tragler & Doris A. Behrens, 2008. "Optimal Control of Nonlinear Processes," Springer Books, Springer, number 978-3-540-77647-5, June.
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    4. Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M. & Veliov, Vladimir M., 2006. "Anticipation effects of technological progress on capital accumulation: a vintage capital approach," Journal of Economic Theory, Elsevier, vol. 126(1), pages 143-164, January.
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    Cited by:

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