The competition between legal and illegal firms in the market: Theoretical models and empirical evidence

The main aim of this paper is to study the phenomenon of the coexistence of firms with illegal characteristics and firms showing legal behaviour in developed economies by using an evolutionary competition model known as the Lotka-Volterra equations. Enterprises in a ‘legal system’ obey the extant laws, particularly market rules, while enterprises in an ‘illegal system’ disregard them. Illegal enterprises have a competitive advantage over legal enterprises, yet they cannot survive if legal enterprises disappear completely. The numerical solution of the Lotka-Volterra equations are used to show how there can be a situation of coexistence between legal and illegal enterprises and how state intervention can help reduce illegality in an economic system. This paper outlines a new approach to address the problem of coexistence because it uses non-linear and evolutionary tools to define the competition between legal and illegal firms. The research gap presented in this paper is addressed using the predator-prey scheme to model the competition between legal and illegal firms, which is perceived as the competition between two populations with different fitness levels (survival probabilities). This competition gives rise to three different types of possible equilibrium outcomes: survival of only legal firms, survival of only illegal firms and coexistence of these two types of firms. An empirical analysis of an Italian case study confirms the results of this paper's theoretical model.