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The Dynamics of Pareto Distributed Wealth in a Small Open Economy

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  • Matthias Birkner
  • Niklas Scheuer
  • Klaus Wälde

Abstract

We study a small open economy displaying Pareto-distributed wealth resulting from random death. The government runs a distribution scheme on inheritance. We present the mathematical background that allows to study the dynamics of means. We end up with ordinary differential equations for the mean of age and of individual and government wealth. We also study distributional dynamics analytically. Starting from any distribution of age and wealth, the aggregate distribution converges, both on a transition path towards a steady state and on a transition path towards balanced growth, to an exponential distribution of age and a Pareto-distribution of wealth. The findings are illustrated for different distribution schemes.

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  • Matthias Birkner & Niklas Scheuer & Klaus Wälde, 2021. "The Dynamics of Pareto Distributed Wealth in a Small Open Economy," CESifo Working Paper Series 9058, CESifo.
    • Handle: RePEc:ces:ceswps:_9058
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    2. Matthias Birkner & Niklas Scheuer & Klaus Wälde, 2023. "The dynamics of Pareto distributed wealth in a small open economy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(2), pages 607-644, August.
    3. Berenice Anne Neumann & Niklas Scheuer, 2024. "The Impact of Bequest Taxation on Wealth Inequality - Theory and Evidence," Research Papers in Economics 2024-05, University of Trier, Department of Economics.

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    More about this item

    Keywords

    analytical dynamics of mean and distribution; age and wealth; government budget; stochastic differential equation; Kolmogorov backward equation;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

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