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On Continuous-Time Optimal Advertising Under S-Shaped Response

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  • Fred M. Feinberg

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    (University of Michigan Business School, 701 Tappan St., Ann Arbor, Michigan 48109)

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    Abstract

    Continuous-time monopolistic models of advertising expenditure that rely on strict response concavity have been shown to prescribe eventual spending at a constant rate. However, analyses of discrete analogs have suggested that S-shaped response (convexity for low expenditure levels) may allow for the periodic optima encountered in actual practice. Casting the dynamic between advertising and sales in a common format (an autonomous, first-order relationship), the present paper explores extensions along three dimensions: an S-shaped response function, the value of the discount rate, and the possibility of diffusion-like response. Supplementing the treatment by Mahajan and Muller (1986), a flexible class of S-shaped response models is formulated for which it is demonstrated that, in contrast to findings in the literature on discretized advertising models, continuous periodic optima cannot be supported. Further, a set of conditions on the advertising response function are derived, that contains and extends that suggested by Sasieni (1971). Collectively, these results both suggest a set of baseline properties that reasonable models should possess and cast doubt on the ability of first-order models to capture effects of known managerial relevance.

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    File URL: http://dx.doi.org/10.1287/mnsc.47.11.1476.10246
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 47 (2001)
    Issue (Month): 11 (November)
    Pages: 1476-1487

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    Handle: RePEc:inm:ormnsc:v:47:y:2001:i:11:p:1476-1487

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    Related research

    Keywords: Advertising Models; Optimal Control; Contagion; Diffusion Models; S-Shaped Response;

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    Cited by:
    1. Toker Doganoglu & Daniel Klapper, 2006. "Goodwill and dynamic advertising strategies," Quantitative Marketing and Economics, Springer, vol. 4(1), pages 5-29, March.
    2. Mesak, Hani I. & Ellis, T. Selwyn, 2009. "On the superiority of pulsing under a concave advertising market potential function," European Journal of Operational Research, Elsevier, vol. 194(2), pages 608-627, April.
    3. Huang, Jian & Leng, Mingming & Liang, Liping, 2012. "Recent developments in dynamic advertising research," European Journal of Operational Research, Elsevier, vol. 220(3), pages 591-609.
    4. Eftichios S. Sartzetakis & Anastasios Xepapadeas & Emmanuel Petrakis, 2009. "The Role of Information Provision as a Policy Instrument to Supplement Environmental Taxes: Empowering Consumers to Choose Optimally," Working Papers 2009.46, Fondazione Eni Enrico Mattei.
    5. Villas-Boas, Sofia B & Villas-Boas, Miguel, 2006. "Learning, Forgetting, and Sales," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt7td275hv, Department of Agricultural & Resource Economics, UC Berkeley.
    6. Beltran-Royo, C. & Zhang, H. & Blanco, L.A. & Almagro, J., 2013. "Multistage multiproduct advertising budgeting," European Journal of Operational Research, Elsevier, vol. 225(1), pages 179-188.

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