Inequality assessment in a dynamic framework with heterogenous agents

We propose a method to carry out an inequality assessment in a dynamic and cross sectional framework, by applying the dynamic version of a suitable inequality index, such as the Gini coefficient, as a function of time. We use our methodology to a setup where the optimal value functions is the individuals’ income flows while the initial conditions characterize their level of wealth. When the Hamilton–Jacobi– Bellman system of equations can be solved in closed form, the monotone path of the income distribution is established. Extending the model according to a government intervention gives the possibility to study, first policy for reducing income inequality under a specific exogenous target, and second to minimise income inequality across individuals.