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Optimal advertising and pricing in a class of general new-product adoption models

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  • Helmes, Kurt
  • Schlosser, Rainer
  • Weber, Martin

Abstract

In [21], Sethi et al. introduced a particular new-product adoption model. They determine optimal advertising and pricing policies of an associated deterministic infinite horizon discounted control problem. Their analysis is based on the fact that the corresponding Hamilton–Jacobi–Bellman (HJB) equation is an ordinary non-linear differential equation which has an analytical solution. In this paper, generalizations of their model are considered. We take arbitrary adoption and saturation effects into account, and solve finite and infinite horizon discounted variations of associated control problems. If the horizon is finite, the HJB-equation is a 1st order non-linear partial differential equation with specific boundary conditions. For a fairly general class of models we show that these partial differential equations have analytical solutions. Explicit formulas of the value function and the optimal policies are derived. The controlled Bass model with isoelastic demand is a special example of the class of controlled adoption models to be examined and will be analyzed in some detail.

Suggested Citation

  • Helmes, Kurt & Schlosser, Rainer & Weber, Martin, 2013. "Optimal advertising and pricing in a class of general new-product adoption models," European Journal of Operational Research, Elsevier, vol. 229(2), pages 433-443.
    • Handle: RePEc:eee:ejores:v:229:y:2013:i:2:p:433-443
    DOI: 10.1016/j.ejor.2013.02.035
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    References listed on IDEAS

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    1. Trichy V. Krishnan & Dipak C. Jain, 2006. "Optimal Dynamic Advertising Policy for New Products," Management Science, INFORMS, vol. 52(12), pages 1957-1969, December.
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    3. Frank M. Bass & Trichy V. Krishnan & Dipak C. Jain, 1994. "Why the Bass Model Fits without Decision Variables," Marketing Science, INFORMS, vol. 13(3), pages 203-223.
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    6. repec:dau:papers:123456789/3445 is not listed on IDEAS
    7. Kumar, Subodha & Sethi, Suresh P., 2009. "Dynamic pricing and advertising for web content providers," European Journal of Operational Research, Elsevier, vol. 197(3), pages 924-944, September.
    8. Bass, Frank M, 1980. "The Relationship between Diffusion Rates, Experience Curves, and Demand Elasticities for Consumer Durable Technological Innovations," The Journal of Business, University of Chicago Press, vol. 53(3), pages 51-67, July.
    9. S. P. Sethi & A. Prasad & X. He, 2008. "Optimal Advertising and Pricing in a New-Product Adoption Model," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 351-360, November.
    10. Russell, Thomas, 1980. "Comments on "The Relationship between Diffusion Rates, Experience Curves, and Demand Elasticities for Consumer Durable Technological Innovations."," The Journal of Business, University of Chicago Press, vol. 53(3), pages 69-73, July.
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    Cited by:

    1. Régis Chenavaz & Corina Paraschiv & Gabriel Turinici, 2017. "Dynamic Pricing of New Products in Competitive Markets: A Mean-Field Game Approach," Working Papers hal-01592958, HAL.
    2. Schlosser, Rainer & Chenavaz, Régis Y. & Dimitrov, Stanko, 2021. "Circular economy: Joint dynamic pricing and recycling investments," International Journal of Production Economics, Elsevier, vol. 236(C).
    3. Ghobadi, Somayeh Najafi- & Bagherinejad, Jafar & Taleizadeh, Ata Allah, 2021. "A two-generation new product model by considering forward-looking customers: Dynamic pricing and advertising optimization," Journal of Retailing and Consumer Services, Elsevier, vol. 63(C).
    4. Karray, Salma & Martín-Herrán, Guiomar, 2022. "The impact of a store brand introduction in a supply chain with competing manufacturers: The strategic role of pricing and advertising decision timing," International Journal of Production Economics, Elsevier, vol. 244(C).
    5. Chenavaz, Régis Y. & Eynan, Amit, 2021. "Advertising, goodwill, and the Veblen effect," European Journal of Operational Research, Elsevier, vol. 289(2), pages 676-682.
    6. Régis Chenavaz & Corina Paraschiv & Gabriel Turinici, 2021. "Dynamic Pricing of New Products in Competitive Markets: A Mean-Field Game Approach," Dynamic Games and Applications, Springer, vol. 11(3), pages 463-490, September.
    7. Chenavaz, Régis Y. & Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M., 2020. "Modeling the impact of product quality on dynamic pricing and advertising policies," European Journal of Operational Research, Elsevier, vol. 284(3), pages 990-1001.
    8. Schlosser, Rainer, 2015. "Dynamic pricing and advertising of perishable products with inventory holding costs," Journal of Economic Dynamics and Control, Elsevier, vol. 57(C), pages 163-181.
    9. Fuxiao Lu & Guowei Liu & Jianxiong Zhang & Wansheng Tang, 2016. "Benefits of partial myopia in a durable product supply chain considering pricing and advertising," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(10), pages 1309-1324, October.
    10. Régis Chenavaz & Sajjad M. Jasimuddin, 2017. "An analytical model of the relationship between product quality and advertising," Post-Print hal-01685892, HAL.
    11. Kurt Helmes & Rainer Schlosser, 2015. "Oligopoly Pricing and Advertising in Isoelastic Adoption Models," Dynamic Games and Applications, Springer, vol. 5(3), pages 334-360, September.
    12. Helmes, Kurt L. & Schlosser, Rainer, 2013. "Dynamic advertising and pricing with constant demand elasticities," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2814-2832.

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