Asymptotic analysis of the model for distribution of high-tax payers

TL;DR

This paper uses z-transform techniques to analyze a model of high-tax payer distribution, revealing asymptotic power-law behavior with a critical exponent and universal features in conserved aggregation processes.

Contribution

It provides an asymptotic analysis of the model, identifying critical behavior and coexistence phenomena, extending understanding of distribution patterns in economic models.

Findings

Power-law distribution with exponent -5/2 at critical mass

Critical behavior and scaling relations below threshold

Coexistence of power-law and monopolized member above threshold

Abstract

The z-transform technique is used to investigate the model for distribution of high-tax payers, which is proposed by two of the authors (K. Y and S. M) and others. Our analysis shows an asymptotic power-law of this model with the exponent -5/2 when a total ``mass'' has a certain critical value. Below the critical value, the system exhibits an ordinary critical behavior, and scaling relations hold. Above the threshold, numerical simulations show that a power-law distribution coexists with a huge ``monopolized'' member. It is argued that these behaviors are observed universally in conserved aggregation processes, by analizing an extended model.