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Some Demand Functions in a Duopoly Market with Advertising

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Functional Equations and Inequalities

Part of the book series: Mathematics and Its Applications ((MAIA,volume 518))

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Abstract

Some general models of demand functions S(p1, p2, v1, v2), in a duopoly market of a single product, depending on the prices p 1 and p 2 and advertising expenditures v 1 and v 2 of the two duopolists are presented. The models are derived using functional equations techniques. Additive or multiplicative changes in the prices and/or advertising expenditures are assumed to lead to independent additive or multiplicative increments in sales, which depend on several combinations of prices and/or advertising expenditures. Eight different models are obtained which show either independent or combined effects (interactions) of prices and advertising expenditures. We also consider an unlimited or fixed demand market. For these types of models, the equilibrium strategy for the duopoly, Cournot and Stackelberg cases, are obtained and one example is given. Finally, some least squares methods of estimation of the model parameters are discussed.

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics and Computational Sciences, University of Cantabria and University of Castilla-La Mancha, Ciudad Real, Spain

    Enrique Castillo

  2. Department of Economics and Department of Business Administration, University of Cantabria, Spain

    Jose Maria Sarabia

  3. Department of Business Administration, University of Cantabria, Spain

    Ana Mercedes Gonzalez

Authors
  1. Enrique Castillo
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  2. Jose Maria Sarabia
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  3. Ana Mercedes Gonzalez
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© 2000 Springer Science+Business Media Dordrecht

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Castillo, E., Sarabia, J.M., Gonzalez, A.M. (2000). Some Demand Functions in a Duopoly Market with Advertising. In: Functional Equations and Inequalities. Mathematics and Its Applications, vol 518. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4341-7_3

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  • DOI: https://doi.org/10.1007/978-94-011-4341-7_3

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5869-8

  • Online ISBN: 978-94-011-4341-7

  • eBook Packages: Springer Book Archive

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