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Beta distributed market shares in a spatial model with an application to the market for audit services


We show that if firms locate on a circle according to a uniform distribution, their market shares will be beta distributed. The result implies that concentration ratios will be skewed. We apply the result to the market for auditing services in the US and show the beta distribution outperforms other relevant distributions.

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The authors thank John Hartigan, Norman Ireland, William Shepherd, and an anonymous referee for valuable comments and Chul Park for research assistance.

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Hviid, M., Villadsen, B. Beta distributed market shares in a spatial model with an application to the market for audit services. Rev Ind Organ 10, 737–747 (1995).

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Key words

  • Concentration indices
  • spatial product differentiation
  • order statistics
  • uniform distribution
  • audit services