The rapid increase of wealth inequality in the past few decades is a most disturbing social and economic issue of our time. In order to control, and even reverse that surge, its origin and underlying mechanisms should be revealed. One of the challenges in studying these mechanisms is to incorporate realistic individual dynamics in the population level in a self-consistent manner. Our theoretical approach meets the challenge by using interacting multi-agent master-equations to model the dynamics of wealth inequality. The model is solved using stochastic multi-agent iterated maps. Taking into account growth rate, return on capital, private savings and economic mobility, we were able to capture the historical dynamics of wealth inequality in the United States during the course of the 20th century. We show that the fraction of capital income in the national income and the fraction of private savings are the critical factors that govern the wealth inequality dynamics. In addition, we found that economic mobility plays a crucial role in wealth accumulation. Notably, we found that the major decrease in private savings since the 1980s could be associated primarily with the recent surge in wealth inequality and if nothing changes in this respect we predict further increase in wealth inequality in the future. However, the 2007–08 financial crisis brought an opportunity to restrain the wealth inequality surge by increasing private savings. If this trend continues, it may lead to prevention, and even reversing, of the ongoing inequality surge.
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