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Market Shares: Some Power Law Results and Observations

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  • Raaj Sah
  • Rajeev Kohli

Abstract

The authors report an empirical regularity in the market shares of brands. They propose a theoretical explanation for this observed regularity and identify additional consequences of their explanation. Empirical testing of these consequences supports the proposed explanation. The empirical regularity is obtained using cross-sectional data on market shares of brands in 91 product categories of foods and sporting goods sold in the United States. In total, the data set has 1171 brands. The key feature of the empirical regularity is that, in each category, the difference between pairs of successively-ranked market shares forms a decreasing series. In other words, the decrease in the market share between two successively-ranked brands becomes smaller as one progresses from higher-ranked to lower-ranked brands. The observed patterns of market shares are represented by the power law to a remarkable degree of accuracy, far surpassing the fits typically observed in predictive models of market shares. The authors then propose an explanation for the regularity in terms of a model of consumer purchases. At the heart of this model is a special case of the well-known Dirichlet-multinomial model of brand purchases. This special case corresponds to Bose-Einstein statistics, and has an intuitive implication that the purchase probability of a brand is proportional to the number of units of that brand already purchased. A notable feature of the model is that it considers multiple product categories, and allows for the entry and exit of brands over time. The authors then describe, and test using the data set, two predictions of the proposed model regarding patterns of market shares across product categories. For both of these predictions, which appear counterintuitive, the authors report reasonable empirical support. Overall, there appears to be good evidence supporting the proposed model and the observed regularities. The authors discuss some potential implications of the regularities for marketing practice and research. They also offer an interpretation of the previously known square-root relationship between market share and the order of entry of firms into an industry.

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Bibliographic Info

Paper provided by Harris School of Public Policy Studies, University of Chicago in its series Working Papers with number 0401.

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Date of creation: Jan 2004
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Handle: RePEc:har:wpaper:0401

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Keywords: market shares; power law;

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References

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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. 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.
  3. 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.
  4. Benoit Mandelbrot, 1963. "New Methods in Statistical Economics," Journal of Political Economy, University of Chicago Press, vol. 71, pages 421.
  5. Frank M. Bass, 1995. "Empirical Generalizations and Marketing Science: A Personal View," Marketing Science, INFORMS, vol. 14(3_supplem), pages G6-G19.
  6. 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.
  7. 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.
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Cited by:
  1. Hisano, Ryohei & Mizuno, Takayuki, 2011. "Sales distribution of consumer electronics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(2), pages 309-318.

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