Market Shares: Some Power Law Results and Observations
AbstractThe 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 InfoPaper provided by Harris School of Public Policy Studies, University of Chicago in its series Working Papers with number 0401.
Date of creation: Jan 2004
Date of revision:
market shares; power law;
Other versions of this item:
- Rajeev Kohli & Raaj Sah, 2005. "Some Patterns of Market Shares of Brands Within and Across Product Categories," Working Papers 11-2005, Singapore Management University, School of Economics.
- Rajeev Kohli & Raaj Sah, 2005. "Some Patterns of Market Shares of Brands Within and Across Product Categories," Working Papers 0604, Harris School of Public Policy Studies, University of Chicago.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Kamel Jedidi & Carl F. Mela & Sunil Gupta, 1999. "Managing Advertising and Promotion for Long-Run Profitability," Marketing Science, INFORMS, vol. 18(1), pages 1-22.
- Kelvin Lancaster, 1990. "The Economics of Product Variety: A Survey," Marketing Science, INFORMS, vol. 9(3), pages 189-206.
- Daniel McFadden, 1986. "The Choice Theory Approach to Market Research," Marketing Science, INFORMS, vol. 5(4), pages 275-297.
- Joseph Persky, 1992. "Retrospectives: Pareto's Law," Journal of Economic Perspectives, American Economic Association, vol. 6(2), pages 181-192, Spring.
- 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.
- 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.
- 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.
- Mark Uncles & Andrew Ehrenberg & Kathy Hammond, 1995. "Patterns of Buyer Behavior: Regularities, Models, and Extensions," Marketing Science, INFORMS, vol. 14(3_supplem), pages G71-G78.
- Ijiri, Yuji & Simon, Herbert A, 1974. "Interpretations of Departures from the Pareto Curve Firm-Size Distributions," Journal of Political Economy, University of Chicago Press, vol. 82(2), pages 315-31, Part I, M.
- Glen L. Urban & Theresa Carter & Steven Gaskin & Zofia Mucha, 1986. "Market Share Rewards to Pioneering Brands: An Empirical Analysis and Strategic Implications," Management Science, INFORMS, vol. 32(6), pages 645-659, June.
- Benoit Mandelbrot, 1963. "New Methods in Statistical Economics," Journal of Political Economy, University of Chicago Press, vol. 71, pages 421.
- Marnik G. Dekimpe & Dominique M. Hanssens, 1995. "Empirical Generalizations About Market Evolution and Stationarity," Marketing Science, INFORMS, vol. 14(3_supplem), pages G109-G121.
- 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.
- Stanley, Michael H. R. & Buldyrev, Sergey V. & Havlin, Shlomo & Mantegna, Rosario N. & Salinger, Michael A. & Eugene Stanley, H., 1995. "Zipf plots and the size distribution of firms," Economics Letters, Elsevier, vol. 49(4), pages 453-457, October.
- Rajiv Lal & V. Padmanabhan, 1995. "Competitive Response and Equilibria," Marketing Science, INFORMS, vol. 14(3_supplem), pages G101-G108.
- Dekimpe, M.G. & Hanssens, D., 1995. "Empirical generalizations about market evolution and stationarity," Open Access publications from Tilburg University urn:nbn:nl:ui:12-358840, Tilburg University.
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