# Simple wealth distribution model causing inequality-induced crisis without external shocks

## TL;DR

This paper presents a simple wealth distribution model based on multiplicative processes that naturally leads to inequality-induced crises without external shocks, highlighting the role of intrinsic dynamics and minimal assumptions.

## Contribution

The model demonstrates how extreme inequality and crises can emerge solely from intrinsic multiplicative wealth dynamics, without external shocks or complex interactions.

## Key findings

- High wealth concentration triggers crisis regimes with strong intermittency.
- A small tax bias can slow or halt wealth accumulation and crises.
- The model aligns with Piketty's $r>g$ paradigm and suggests effective class divisions.

## Abstract

We address the issue of the dynamics of wealth accumulation and economic crisis triggered by extreme inequality, attempting to stick to most possibly intrinsic assumptions. Our general framework is that of pure or modified multiplicative processes, basically geometric Brownian motions. In contrast with the usual approach of injecting into such stochastic agent models either specific, idiosyncratic internal nonlinear interaction patterns, or macroscopic disruptive features, we propose a dynamic inequality model where the attainment of a sizable fraction of the total wealth by very few agents induces a crisis regime with strong intermittency, the explicit coupling between the richest and the rest being a mere normalization mechanism, hence with minimal extrinsic assumptions. The model thus harnesses the recognized lack of ergodicity of geometric Brownian motions. It also provides a statistical intuition to the consequences of Thomas Piketty's recent "$r>g$" (return rate $>$ growth rate) paradigmatic analysis of very-long-term wealth trends. We suggest that the "water-divide" of wealth flow may define effective classes, making an objective entry point to calibrate the model. Consistently, we check that a tax mechanism associated to a few percent relative bias on elementary daily transactions is able to slow or stop the build-up of large wealth. When extreme fluctuations are tamed down to a stationary regime with sizable but steadier inequalities, it should still offer opportunities to study the dynamics of crisis and the inner effective classes induced through external or internal factors.