A dynamical model of company growth

摘要

A theoretical method based on the concept of “system-size expansion” isapplied to the study of a nonlinear stochastic model of company growth, which treats the populations C and E, of the capital resources of the company and the number of employees, as interacting entities. These populations are assumed to have upper limits, Cmax and Emax, as determined by the conditions prevailing in the market. Analytical expressions for the time evolution of both stochastic and deterministic aspects of the model are derived. An interesting feature of the model lies in the appearance of a “critical phenomenon”, in the nature of a phase transition, in the system when a certain parameter ξ of the problem approaches its critical value ξc. Finally, the nonlinearity of the model enables us to exploit the asymptotic expressions for the various quantities pertaining to the system for evaluating certain finite-size effects as well.