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.
"Asymptotic Analysis of the Model for Distribution of High-Tax Payers." Japan J. Indust. Appl. Math. 24 (2) 211 - 218, June 2007.