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Some Patterns of Market Shares of Brands Within and Across Product Categories

  • Rajeev Kohli

    ()

    (Columbia University)

  • Raaj Sah

    ()

    (School of Economics and Social Sciences, Singapore Management University)

This paper: (i) reports an empirical regularity in the market shares of brands; (ii) presents a theoretical framework for understanding the observed regularity; (iii) adduces additional empirical consequences of the framework, which are some counterintuitive relationships among market shares of brands across different product categories; and (iv) presents empirical evidence for these consequences, thus providing additional support for the theoretical framework. Our cross-sectional data on market shares consists of 1171 brands in 91 product categories of foods and sporting goods sold in the US. If we assign a lower rank to a brand with a higher market share, then the key empirical regularity is that, in each category, the ratio of market shares between two successively-ranked brands becomes smaller as one progresses from higher-ranked to lower-ranked brands. The power law represents these patterns well, in an absolute sense, and better than an alternative model, namely, the exponential form, which has been studied in the literature but without having been compared to any alternative. The latter form predicts that the ratio of the market shares of any two successively ranked brands is a constant. We present some potential implications of our findings for marketing practice and research. We also offer an interpretation of the previously known square-root relationship between market share and the order of entry of firms into an industry. The theoretical framework that we present for understanding the patterns reported here shares its foundation with that of the familiar Dirichlet-multinomial paradigm of brand purchases. This framework has some intuitive interpretations; it accommodates multiple product categories; and it allows for the entry and exit of brands over time.

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Paper provided by Singapore Management University, School of Economics in its series Working Papers with number 11-2005.

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Length: 36 pages
Date of creation: Mar 2005
Date of revision:
Publication status: Published in SMU Economics and Statistics Working Paper Series
Handle: RePEc:siu:wpaper:11-2005
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  1. Gurumurthy Kalyanaram & William T. Robinson & Glen L. Urban, 1995. "Order of Market Entry: Established Empirical Generalizations, Emerging Empirical Generalizations, and Future Research," Marketing Science, INFORMS, vol. 14(3_supplem), pages G212-G221.
  2. Benoit Mandelbrot, 1963. "New Methods in Statistical Economics," Journal of Political Economy, University of Chicago Press, vol. 71, pages 421.
  3. Brock, W A, 1999. "Scaling in Economics: A Reader's Guide," Industrial and Corporate Change, Oxford University Press, vol. 8(3), pages 409-46, September.
  4. Christensen, Laurits R & Jorgenson, Dale W & Lau, Lawrence J, 1975. "Transcendental Logarithmic Utility Functions," American Economic Review, American Economic Association, vol. 65(3), pages 367-83, June.
  5. Chung, Kee H & Cox, Raymond A K, 1994. "A Stochastic Model of Superstardom: An Application of the Yule Distribution," The Review of Economics and Statistics, MIT Press, vol. 76(4), pages 771-75, November.
  6. Frank M. Bass, 1995. "Empirical Generalizations and Marketing Science: A Personal View," Marketing Science, INFORMS, vol. 14(3_supplem), pages G6-G19.
  7. Peter M. Guadagni & John D. C. Little, 1983. "A Logit Model of Brand Choice Calibrated on Scanner Data," Marketing Science, INFORMS, vol. 2(3), pages 203-238.
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