# Wealth Distribution Models with Regulations: Dynamics and Equilibria

## TL;DR

This paper examines how social protection policies influence wealth distribution dynamics and stability in agent-based economic models, highlighting the long-term effects of policy removal on inequality and system hysteresis.

## Contribution

It introduces an analysis of social protection policies within wealth exchange models and explores their impact on stability, mobility, and inequality, including effects of policy interruptions.

## Key findings

- Regulations can enhance economic mobility and reduce inequality.
- Removing social protection leads to increased and persistent inequality.
- Policy interruptions cause long-lasting changes and potential irreversibility in wealth distribution.

## Abstract

Simple agent based exchange models are a commonplace in the study of wealth distribution in an artificial economy. Generally, in a system that is composed of many agents characterized by their wealth and risk-aversion factor, two agents are selected sequentially and randomly to exchange wealth, allowing for its redistribution. Here we analyze how the effect of a social protection policy, which favors agents of lower wealth during the exchange, influences stability and some relevant economic indicators of the system. On the other hand, we study how periods of interruption of these policies produce, in the short and long term, changes in the system. In most cases, a steady state is reached, but with varying relaxation times. We conclude that regulations may improve economic mobility and reduce inequality. Moreover, our results indicate that the removal of social protection entails a high cost associated with the hysteresis of the distribution of wealth. Economic inequalities increase during a period without social protection, but also they remain high for an even longer time and, in some extreme cases, inequality may be irreversible, indicating that the withdrawal of social protection yields a high cost associated with the hysteresis of the distribution of wealth.