This paper uses novel growth models composed of clusters of heterogeneous agents,andshowsthat limitingbehaviorof one-andtwo-parameterPoisson-Dirichlet models are qualitatively very di?erent. As model sizes grow unboundedly, the coe?cients of variations of extensive variables, such as the number of total clusters, and the numbers of clusters of speci?ed sizes all approach zero in the one-parameter models, but not in the two-parameter models. In the calculations of the coe?cients of variations Mittag-Le?er distributions arise naturally. We show that the distributions of the numbers of the clusters in the models havepower-lawbehavior.
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Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number
CIRJE-F-446.
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