ODE models of wealth concentration and taxation

TL;DR

This paper uses an ODE model to analyze how different levels of wealth taxation influence the emergence of oligarchs, revealing a bifurcation point where oligarchs form if taxation is too low.

Contribution

It applies a Boghosian et al. model to study wealth concentration, highlighting the critical taxation threshold and its role in oligarch formation.

Findings

Oligarchs emerge when wealth taxation is below a certain threshold.

Taxation of income and capital gains alone cannot prevent oligarch emergence.

The model exhibits a transcritical bifurcation mechanism.

Abstract

We refer to an individual holding a non-negligible fraction of the country's total wealth as an oligarch. We explain how a model due to Boghosian et al. can be used to explore the effects of taxation on the emergence of oligarchs. The model suggests that oligarchs will emerge when wealth taxation is below a certain threshold, not when it is above the threshold. The underlying mechanism is a transcritical bifurcation. The model also suggests that taxation of income and capital gains alone cannot prevent the emergence of oligarchs. This is an article intended for undergraduate students. We suggest several opportunities for students to explore modifications of the model.