In this paper, I intend to reconstruct the invisible hand notion created by Classical Political Economy and, in special, by Adam Smith, in order to circumscribe its significance, conceptually and formally. In the text, meanwhile, this concept do not designate the best coordination of agents plans, all of them endowed with perfect rationality, but the self-organization process inherent to the competition of capitals. After a section where this concept is discussed historically, I construct a time oriented model that requires, immediately, a formalization of capital mobility process which occurs in face of profit variations in the productive sectors. Then, the required formalization is done applying the so called replication dynamics that were constructed in the field of mathematic biology to represent the reproduction and competition process of certain animals' species.
invisible hand; replication dynamics; competition of capitals; market self-organization
