The Distribution of Business Firms Size, Stochasticities, and Self-organized Criticality

Introduction: Decades ago, it has been noticed that the distribution of the size of business firms is "almost always highly skewed and its upper tail resembles the Pareto distribution (i.e. is a power law)".1 This old and intriguing observation is still true today (Figure 1) and is clearly a robust pattern. Since firms engaged in very different activities contribute to build this distribution, this suggests the existence of long range effects in the economy. Skew distributions are very common. They are found in subjects as varied as astrophysics, biology, economics, geophysics, linguistics, etc... They are sometimes referred to as 1/f distributions2, as they seem to correspond to power laws distributions. Their origin and interpretations on the other hand are far less clear. 1/f is a signature for "Self-Organized Criticality".3 Self-Organized Criticality suggests that the distribution has a dynamical origin. An explanation for the distribution of business size firms, which does not have the potential to "explain" the ubiquity of power law distributions is intrinsically unsatisfactory. This criticism applies to "explanations" of the business size distribution too deeply rooted in economic assumptions.