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The dynamics of Pareto distributed wealth in a small open economy

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Listed:
  • Matthias Birkner

    (Johannes Gutenberg University Mainz)

  • Niklas Scheuer

    (Johannes Gutenberg University Mainz)

  • Klaus Wälde

    (CESifo
    IZA)

Abstract

We study a small open economy with labor, capital accumulation, random death, taxation and a government budget balanced in the long run. We offer methods that provide ordinary differential equations for means and analytical expressions for densities. The latter is achieved by solving stochastic differential equations analytically and deriving the density from this solution. Starting from any distribution, the aggregate distribution converges, both on a transition path towards a steady state and on a transition path towards balanced growth, to a Pareto-distribution. We provide an intuitive economic interpretation for a stationary long-run density with an infinite mean in an economy on a balanced growth path. We also show how government tax policy can lead to non-monotonic links between the equilibrium growth rate of the economy and risk aversion of households.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:joecth:v:76:y:2023:i:2:d:10.1007_s00199-022-01471-z
    DOI: 10.1007/s00199-022-01471-z
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    1. 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.
    2. 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; Wealth; Government budget; Stochastic differential 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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