A Mathematical Model for the Dynamics of Income Distribution in the Presence of Production

In this paper, a mathematical model is formulated, suitable to explain the evolution of income distribution over a population in the presence of production. The model is conceived from the perspective of complexity. Indeed, the income distribution emerges as the result of a myriad of economic exchanges taking place between individuals. In fact, the aim of the paper is to provide a framework and mathematical tools for the construction and the investigation of models having an exploratory character. The framework is expressed in the form of a system of nonlinear ordinary differential equations, as many as the income classes are, involving transition probabilities. Numerical solutions of these systems are constructed under different assumptions on the law of production and in the presence of different fiscal systems, which provides an example of the versatility of the method.