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Dynamic advertising and pricing with constant demand elasticities

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  • Helmes, Kurt L.
  • Schlosser, Rainer

Abstract

In this paper we analyze a stochastic dynamic advertising and pricing model with isoelastic demand. The state space is discrete, time is continuous and the planing horizon is allowed to be finite or infinite. A dynamic version of the Dorfman–Steiner identity will be derived. Explicit expressions of the optimal advertising and pricing policies, of the value function and of the optimal advertising expenditures will be given. The general results will be used to analyze the case of impatient customers. Furthermore, particular time inhomogeneous models and homogeneous ones with and without discounting will be examined. We will study the social efficiency of a monopolist's optimal policies and the consequences of specific subsidies. From a buyer's perspective, our analysis reveals that waiting – when looking at (immediate) expected prices – is never profitable should two or more units be available. But we will also prove that the sequence of average sales prices is monotone decreasing. Moreover, the techniques applied to solve the discrete stochastic advertising and pricing problem will be used to solve a related deterministic control problem with continuous state space.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:dyncon:v:37:y:2013:i:12:p:2814-2832
    DOI: 10.1016/j.jedc.2013.08.004
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    References listed on IDEAS

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    1. 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.
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    6. Stiglitz, Joseph E, 1976. "Monopoly and the Rate of Extraction of Exhaustible Resources," American Economic Review, American Economic Association, vol. 66(4), pages 655-661, September.
    7. 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.
    8. Gustav Feichtinger & Richard F. Hartl & Suresh P. Sethi, 1994. "Dynamic Optimal Control Models in Advertising: Recent Developments," Management Science, INFORMS, vol. 40(2), pages 195-226, February.
    9. Wedad Elmaghraby & P{i}nar Keskinocak, 2003. "Dynamic Pricing in the Presence of Inventory Considerations: Research Overview, Current Practices, and Future Directions," Management Science, INFORMS, vol. 49(10), pages 1287-1309, October.
    10. Bagwell, Kyle, 2007. "The Economic Analysis of Advertising," Handbook of Industrial Organization, in: Mark Armstrong & Robert Porter (ed.), Handbook of Industrial Organization, edition 1, volume 3, chapter 28, pages 1701-1844, Elsevier.
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    Citations

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    Cited by:

    1. Chenavaz, Régis Y. & Leocata, Marta & Ogonowska, Malgorzata & Torre, Dominique, 2022. "Sustainable tourism," Journal of Economic Dynamics and Control, Elsevier, vol. 143(C).
    2. 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.
    3. Jørgensen, Steffen & Zaccour, Georges, 2019. "Optimal pricing and advertising policies for a one-time entertainment event," Journal of Economic Dynamics and Control, Elsevier, vol. 100(C), pages 395-416.
    4. Schlosser, Rainer, 2017. "Stochastic dynamic pricing and advertising in isoelastic oligopoly models," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1144-1155.
    5. Schlosser, Rainer, 2016. "Joint stochastic dynamic pricing and advertising with time-dependent demand," Journal of Economic Dynamics and Control, Elsevier, vol. 73(C), pages 439-452.
    6. 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.
    7. Lihao Lu & Qinglong Gou & Wansheng Tang & Jianxiong Zhang, 2016. "Joint pricing and advertising strategy with reference price effect," International Journal of Production Research, Taylor & Francis Journals, vol. 54(17), pages 5250-5270, September.
    8. Rainer Schlosser, 2016. "Stochastic dynamic multi-product pricing with dynamic advertising and adoption effects," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 15(2), pages 153-169, April.

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    More about this item

    Keywords

    Dynamic advertising and pricing; Optimal deterministic and stochastic control; Dorfman–Steiner identity; Constant demand elasticities;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D42 - Microeconomics - - Market Structure, Pricing, and Design - - - Monopoly
    • M37 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Marketing and Advertising - - - Advertising

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