Statistical properties of business firms structure and growth

– We analyze a database comprising quarterly sales of 55624 pharmaceutical products commercialized by 3939 pharmaceutical firms in the period 1992–2001. We study the probability density function (PDF) of growth in firms and product sales and find that the width of the PDF of growth decays with the sales as a power law with exponent β = 0.20 ± 0.01. We also find that the average sales of products scales with the firm sales as a power law with exponent α = 0.57 ± 0.02. And that the average number products of a firm scales with the firm sales as a power law with exponent γ = 0.42± 0.02. We compare these findings with the predictions of models proposed till date on growth of business firms. In economics there are unsolved problems that involve interactions among a large number of subunits [1–3]. One of these problems is the structure of a business firm and its growth [2,4]. As in many physical models, decomposition of a firm into its constituent parts is an appropriate starting place for constructing a model. Indeed, the total sales of a firm is comprised of a large number of product sales. Previously accurate data on the “microscopic” product sales have been unavailable, and hence it has been impossible to test the predictions of various models. Here we analyze a new database, the Pharmaceutical Industry Database (PHID) which records quarterly sales figures of 55624 pharmaceutical products commercialized by 3939 firms in the European Union and North America from September 1991 to June 2001. We shall see that these data support the predictions of a simple model, and at the same time the data do not support the microscopic assumptions of that model. In this sense, the model has the same status as many statistical physics models, in that the predictions can be in accord with data even though the details of microscopic interactions are not. The assumptions of this simple model given in ref. [5] are as follows: i) Firms tends to organize themselves into multiple divisions once they attain a particular size. ii) The minimum size of firms in a particular economy comes from a broad distribution. iii) Growth rates of divisions are independent of each other and there is no temporal correlation in their growth. With these assumptions the model builds a diversified multi-divisional structure. Starting from a single product evolving