A predator-prey economic system of tax evasion and corrupt behavior

The goal of this research is to study an economic system characterized by the coexistence of tax evading citizens with corrupt auditors (public officials), that is a system of predators-preys, i.e. corrupts and not, evaders and not. We show that citizens choose non-corrupt behavior when their utility exceeds a threshold level with respect to an optimal progressive tax rate. On the other hand, auditors choose non-corrupt behavior if their utility is higher than a certain threshold level depending on the fines and probabilities of being sanctioned. Being aware of this situation, a government or central authority must study a dynamic evolutionary economic system (a generalized predator-prey model) by analyzing all possible steady states of this economic system. The stability of the steady states depends on the crucial parameters of the model, namely: i) a socially negative impact exerted by corrupt public officials or auditors on the evolution of the economic society, ii) the impact of the social weight of the citizens who pay taxes on corrupt auditors, iii) the behavior of imitation of the agents when perceiving the possibilities of being sanctioned or not, and iv) the inertia and feedback of the corrupt system (dishonest behavior and tax evasion). We conclude by highlighting the importance of bifurcations or qualitative changes in the parameters of this economic system to fight corruption and evasion.