  We address the issue of the distribution of firm size. To this end we propose
a model of firms in a closed, conserved economy populated with
zero-intelligence agents who continuously move from one firm to another. We
then analyze the size distribution and related statistics obtained from the
model. Our ultimate goal is to reproduce the well known statistical features
obtained from the panel study of the firms i.e., the power law in size (in
terms of income and/or employment), the Laplace distribution in the growth
rates and the slowly declining standard deviation of the growth rates
conditional on the firm size. First, we show that the model generalizes the
usual kinetic exchange models with binary interaction to interactions between
an arbitrary number of agents. When the number of interacting agents is in the
order of the system itself, it is possible to decouple the model. We provide
some exact results on the distributions. Our model easily reproduces the power
law. The fluctuations in the growth rate falls with increasing size following a
power law (with an exponent 1 whereas the data suggests that the exponent is
around 1/6). However, the distribution of the difference of the firm-size in
this model has Laplace distribution whereas the real data suggests that the
difference of the log sizes has the same distribution.

General Finance