How Fixed-Amount Transactions and Liquidity Constraints Amplify Wealth Inequality: A Kinetic Model Deviating from the Maximum Entropy Benchmark

TL;DR

This paper models how fixed-amount transactions and liquidity constraints lead to high wealth inequality, deviating from classical maximum entropy predictions, and highlights the poverty trap as a key mechanism.

Contribution

It introduces a minimalist kinetic exchange model incorporating realistic constraints, revealing how inequality emerges without agent heterogeneity or multiplicative advantages.

Findings

Wealth distribution exhibits high inequality with a pauper class and exponential tail.

The poverty trap mechanism causes passive zero-wealth agents to hinder wealth circulation.

Numerical and agent-based simulations confirm the model's predictions.

Abstract

This paper investigates the emergence of wealth inequality through a minimalist kinetic exchange model that incorporates two fundamental economic features: fixed-amount transactions and hard budget constraints. In contrast to the maximum entropy principle, which predicts an exponential Boltzmann-Gibbs distribution with moderate inequality for unconstrained wealth exchange, we demonstrate that these realistic trading rules drive the system toward a highly unequal steady state. We develop a self-consistent mean-field theory, deriving a master equation where agent income follows a Poisson process coupled to the poverty rate. Numerical solution reveals a stationary distribution characterized by a substantial pauper class, high Gini coefficient, and exponential tail--significantly deviating from the maximum entropy benchmark. Agent-based simulations confirm these findings. We identify the poverty trap as the key mechanism: the liquidity constraint creates asymmetric economic agency, where zero-wealth agents become passive recipients, unable to participate in wealth circulation. This work establishes that substantial inequality can emerge spontaneously from equal-opportunity exchanges under basic economic constraints, without requiring agent heterogeneity or multiplicative advantage, providing a mechanistic foundation for understanding poverty as an emergent property of exchange rules.