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We address the issue of the distribution of firm size. To this end we proposea model of firms in a closed, conserved economy populated withzero-intelligence agents who continuously move from one firm to another. Wethen analyze the size distribution and related statistics obtained from themodel. Our ultimate goal is to reproduce the well known statistical featuresobtained from the panel study of the firms i.e., the power law in size (interms of income and/or employment), the Laplace distribution in the growthrates and the slowly declining standard deviation of the growth ratesconditional on the firm size. First, we show that the model generalizes theusual kinetic exchange models with binary interaction to interactions betweenan arbitrary number of agents. When the number of interacting agents is in theorder of the system itself, it is possible to decouple the model. We providesome exact results on the distributions. Our model easily reproduces the powerlaw. The fluctuations in the growth rate falls with increasing size following apower law (with an exponent 1 whereas the data suggests that the exponent isaround 1/6). However, the distribution of the difference of the firm-size inthis model has Laplace distribution whereas the real data suggests that thedifference of the log sizes has the same distribution.

Firm dynamics in a closed, conserved economy: A model of size distribution of employment and related statistics