Future Directions and Conclusions

The set of mechanisms that we have considered up to now explains quite well both ends of the distribution of firm’s sizes. Indeed, while the average growth rate of firm’s asset values, the intensity of firm’s births and the hazard rate of a firm’s sudden death accurately explain the behavior of the population of large firms, the introduction of a lower threshold below which firms disappear (by lack of efficiency, for instance) explains the behavior of the population of small firms. Everything is not perfect however. In many countries, like France and India amongst others, the population of medium size firms exhibits an anomalous behavior. One usually speaks of the “missing middle” phenomenon to describe the fact there is a deficit of firms of intermediate sizes. Our model, while already quite versatile, does not account for this country-specific stylized fact. The reason is in fact rather simple. To a large extent, the “missing middle” phenomenon could be explained by the strong propensity of large firms to merge with firms which are still small but present a promising potential. This should yield a depletion of the population of medium size firms. In addition to the mechanisms in terms of birth, death and random growth which have been considered in the previous chapters, we envision that the next level of development of a complete mathematical theory of firms needs to take into account the mechanism of mergers between firms (referred to as M&A for “merger and acquisition”), as well as it symmetric, the phenomenon of creation of spin-off firms born from parent firms which outsource a part of their existing business as separate units. For this, the long tradition in physics concerning the investigation of the processes of coagulation (merger) and of fragmentation (spin-off) could provide a fertile reservoir of ideas and techniques (Aldous, 1999; Leyvraz, 2003).