The Dynamics of Pareto Distributed Wealth in a Small Open Economy - Matthias Birkner; Niklas Scheuer; Klaus Wälde (Center for Economic Studies and Ifo Institute (CESifo), 2021)
We study a small open economy displaying Pareto-distributed wealth resulting from random death. The government runs a distribution scheme on inheritance. We present the mathematical background that allows to study the dynamics of means. We end up with ordinary differential equations for the mean of age and of individual and government wealth. We also study distributional dynamics analytically. Starting from any distribution of age and wealth, the aggregate distribution converges, both on a transition path towards a steady state and on a transition path towards balanced growth, to an exponential distribution of age and a Pareto-distribution of wealth. The findings are illustrated for different distribution schemes.
Keywords: C61; D31; E21; 330; analytical dynamics of mean and distribution; age and wealth; government budget; stochastic differential equation; Kolmogorov backward equation