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Optimal investment in age-structured goodwill

Author

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  • Silvia Faggian

    () (Dept. of Applied Mathematics, University of Venice)

  • Luca Grosset

    () (Dipartimento di Matematica Pura ed Applicata, University of Padua)

Abstract

Segmentation is a core strategy in modern marketing and age-specific segmentation, which is based on the age of the consumers, is very common in practice. A characteristic of age-specific segmentation is the change of the segments composition during time, which may be studied only using dynamic advertising models. Here, we assume that a firm wants to promote and sell a single product in an age segmented market and we model the awareness of this product using an infinite dimensional Nerlove- Arrow goodwill as a state variable. Assuming an infinite time horizon, we use some dynamic programming techniques to solve the problem and 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 the time evolution of the segmentation.

Suggested Citation

  • Silvia Faggian & Luca Grosset, 2009. "Optimal investment in age-structured goodwill," Working Papers 194, Department of Applied Mathematics, Università Ca' Foscari Venezia.
  • Handle: RePEc:vnm:wpaper:194
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    References listed on IDEAS

    as
    1. Faggian, Silvia & Gozzi, Fausto, 2010. "Optimal investment models with vintage capital: Dynamic programming approach," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 416-437, July.
    2. Emilio Barucci & Fausto Gozzi, 2001. "Technology adoption and accumulation in a vintage-capital model," Journal of Economics, Springer, vol. 74(1), pages 1-38, February.
    3. Jean-Pierre Dubé & Puneet Manchanda, 2005. "Differences in Dynamic Brand Competition Across Markets: An Empirical Analysis," Marketing Science, INFORMS, vol. 24(1), pages 81-95, September.
    4. Silvia Faggian & Luca Grosset, 2009. "Optimal investment in age-structured goodwill," Working Papers 194, Department of Applied Mathematics, Università Ca' Foscari Venezia.
    5. E. Barucci & F. Gozzi, 1999. "Optimal advertising with a continuum of goods," Annals of Operations Research, Springer, vol. 88(0), pages 15-29, January.
    6. Silvia Faggian, 2008. "Equilibrium Points for Optimal Investment with Vintage Capital," Working Papers 182, Department of Applied Mathematics, Università Ca' Foscari Venezia.
    7. Barucci, Emilio & Gozzi, Fausto, 1998. "Investment in a vintage capital model," Research in Economics, Elsevier, vol. 52(2), pages 159-188, June.
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    Cited by:

    1. Silvia Faggian & Luca Grosset, 2009. "Optimal investment in age-structured goodwill," Working Papers 194, Department of Applied Mathematics, Università Ca' Foscari Venezia.

    More about this item

    Keywords

    Segmentation; infinite dimensional Nerlove-Arrow goodwill.;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • M37 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Marketing and Advertising - - - Advertising
    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity

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