Eur. Phys. J. B 21, 447-453 (2001)
https://doi.org/10.1007/s100510170188

Models for the size distribution of businesses in a price driven market

Department of Mathematical Sciences, Brunel University, Uxbridge, Middlesex UB8 3PH, UK

Corresponding author: ^a rene.dhulst@brunel.ac.uk

Received: 10 January 2001
Revised: 12 March 2001
Published online: 15 June 2001

Abstract

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 US and debt sizes in Japan. Finally, possible extensions of the mean-field model are discussed, to cope with other empirical data.