Skip to content

Modeling Wealth Distributions

Modeling Wealth Distributions by Bruce Boghosian, professor of mathematics at Tufts University,
Central Bank of Armenia, Dilijan, 2-4PM, August 3, 2017

Today there are six people in the world who have as much combined wealth as half the human population. In 2010, that figure was 388, so we live in a world where wealth is rapidly concentrating. Understanding how and why this is happening, and what if anything needs to be done about it is an interdisciplinary problem that will ultimately involve mathematicians, economists, physicists, political scientists, and specialists in ethics, justice, and public policy.

In the 1990s, a number of physicists began to apply methods of statistical physics to the study of wealth and income distributions. Particular progress was made with a class of agent-based models called “asset-exchange models.” These models represent an economy by a collection of economic agents who exchange wealth in pairwise transactions according to idealized rules.

In this talk, I shall describe recent results obtained using a very simple asset-exchange model with only three free parameters, all of which are motivated by particular features of the society’s microeconomics. The first feature is a measure of the level of redistribution present. The second is the degree to which the society confers an advantage to wealthier agents. The third is a measure of the extent to which there are negative-wealth or “underwater” agents in the economy.

In spite of the simplicity of this model — no advanced mathematics will be used for its description in this presentation — we will see that it has a number of interesting features:

  • It is capable of explaining the actual wealth distribution of the United States between 1989 and the present with remarkable
  • It provides a natural explanation of the phenomenon of oligarchy, in which a finite fraction of a society’s wealth is held by a
    vanishingly small fraction of its population.
  • It relates useful economic metrics, such as “upward mobility,” to the underlying transactional model.

Finally, I shall relate the asset-exchange model described above to transactions between agents based on a stochastic version of
General Equilibrium theory. In doing so, I will explain the origin of the widespread belief that free-market economies are inherently stable, even in the absence of imposed redistribution. I will also explain why this model strongly suggests that this belief is wrong.

Location: Central Bank of Armenia, Dilijan
Duration: 2-4PM

About the presenter: Bruce Boghosian is a professor of mathematics at Tufts University, and President Emeritus of the American University of Armenia. His research on wealth distributions has appeared in, inter alia, Physical Review E, the Journal of Statistical Physics, and Physica A. For the convenience of CBA and AEA members, the most recent of these papers can be temporarily downloaded from the following address

AEA thanks CBA for co-sponsoring and hosting the workshop, and Professor Boghosian for his presentation.