The Inequity of Consumption-Based Tax Systems

TL;DR

This paper investigates the fairness of consumption-based tax systems using a kinetic wealth-exchange framework (a Yard-Sale variant) with $N$ agents, flat tax rate $\lambda$, and redistribution to the bottom $\tau$ fraction of wealth-sorted agents. It compares universal versus targeted redistribution and employs both the Gini coefficient $G$ and the Palma index $P$ to quantify inequality, highlighting that $P$ is more sensitive to extreme wealth concentrations. The results show that consumption taxes are intrinsically regressive, with the bottom 40% bearing a disproportionate burden at most $\lambda$, and that meaningful inequality reduction under redistribution only emerges at high tax rates with near-perfect targeted transfers; no Laffer-curve is observed. The study emphasizes that the definition of “optimal” redistribution is metric-dependent and that policy implications hinge on the chosen inequality or revenue objective, suggesting careful design of tax and transfer mechanisms beyond simple flat consumption taxes. $\lambda$-dependent dynamics and the tail-focused Palma index provide a nuanced view of how fiscal policy can interact with wealth distributions in complex economies.

Abstract

This study examines the lack of redistributive effectiveness of consumption-based tax systems with respect to social fairness. Through numerical simulations, we explore the wealth exchanges among economic agents subject to flat consumption taxes, comparing universal redistribution with optimal targeted approaches. The results demonstrate that consumption taxes exhibit inherent regressivity, disproportionately burdening the poorest 40% of households who contribute over half of total tax revenue for most tax rates. The findings challenge the equity of consumption taxes and provide quantitative insights for designing more fair fiscal policies.

Figures (10)

• Figure 1: (a) Wealth distributions (log-log scale) for two systems that have the same Gini index $G = 0.375$. (b) Lorenz curves of the same systems. The Palma indices vary more than 10%, $P_A = 1.467$ and $P_B=1.671$. Simulation parameters: $\lambda=0.79$ and $\tau=0.9$ (A), $\lambda=0.37$ and $\tau=0.22$ (B).
• Figure 2: Top: tax revenues ($\Lambda$) as functions of time for two rates, $\lambda = 0.01$ (left) and $0.06$ (right). Bottom: tax paid by each class. The gray lines represent the measures at each MCS, while black, cyan, and red lines indicate averages over $10^3$ steps. Note the different vertical scales.
• Figure 3: Proportion of wealth paid in taxes for each class. The tax rates are in the legend of the figure and universal redistribution ($\tau = 1$) is considered.
• Figure 4: Temporal evolution of the Gini coefficient under low-tax regimes ($\lambda = 0.01$ and $\lambda = 0.06$).
• Figure 5: Relationship between inequality measures and taxation outcomes. (Left) Scaling behavior between Palma and Gini indices, showing superlinear growth ($P \sim G^\alpha$). (Right) Dependence of Palma index on tax revenue ($\Lambda$).