  A microscopic model of aggregation and fragmentation is introduced to
investigate the size distribution of businesses. In the model, businesses are
constrained to comply with the market price, as expected by the customers,
while customers can only buy at the prices offered by the businesses. We show
numerically and analytically that the size distribution scales like a
power-law. A mean-field version of our model is also introduced and we
determine for which value of the parameters the mean-field model agrees with
the microscopic model. We discuss to what extent our simple model and its
results compare with empirical data on company sizes in the U.S. and debt sizes
in Japan. Finally, possible extensions of the mean-field model are discussed,
to cope with other empirical data.
