An analogy of the size distribution of business firms with Bose-Einstein statistics

We approach the size distribution of business firms by proposing an analogy of the firms' ranking with a boson gas, identifying the annual revenue of the firms with energy. We found that Bose-Einstein statistics fits very well to the empirical cumulative distribution function for the firms' ranking for different countries. The fitted values for the temperature-like parameter are compared between countries and with an index of economic development, and we found that our results support the hypothesis that the temperature of the economy can be associated with the level of economic development of a country. Moreover, for most of the countries the value obtained for the fugacity-like parameter is close to 1, suggesting that the analogy could correspond to a photon gas in which the number of particles is not conserved; this is indeed the case for real-world firms' dynamics, where new firms arrive in the economy and other firms disappear, either by merging with others or through bankruptcy.