A constraint on the dynamics of wealth concentration

Abstract

In [1] the authors show that under minimal hypothesis, in a free, growing economy the wealth concentration as measured by the Gini coefficient G t is bounded to reach its maximum, G t → 1. Under their hypothesis the wealth growth is on average proportional to the wealth itself, thus leaving no room for a salary component independent of the individual's wealth. In addition, the state of zero wealth is absorbing, meaning that once an individual loses all its wealth, it is forced to remain in that state. Here we further generalize the result of [1], introducing a salary component of wealth growth and thus allowing for the possibility to escape from the state of zero wealth. We arrive at the same conclusions of the previous study, unless a minimum salary component is introduced and kept proportional to the average wealth.