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Positive Switching Systems and the Wealth Distribution Problem

Author

Listed:
  • Franco Blanchini

    (Università degli Studi di Udine)

  • Daniele Casagrande

    (Università degli Studi di Udine)

  • Patrizio Colaneri

    (Politecnico di Milano
    IEIIT-CNR)

  • Stefanny Ramirez

    (University of Groningen)

  • Dario Bauso

    (University of Groningen
    Università di Palermo)

Abstract

The paper shows how a dynamic model, belonging to the class of positive switching systems, can provide an interesting point of view to the study of the generation and the distribution of wealth in a society. In this model, the evolution of the overall wealth is affected by the way in which individuals share their resources in order to maximize the total income. Different formulations of the corresponding optimal control problem are considered and some general properties are pointed out. Approximated numerical solutions, as well as upper and lower bounds are also investigated. A final section dedicated to an extended numerical analysis yields some qualitative conclusion.

Suggested Citation

  • Franco Blanchini & Daniele Casagrande & Patrizio Colaneri & Stefanny Ramirez & Dario Bauso, 2025. "Positive Switching Systems and the Wealth Distribution Problem," Journal of Optimization Theory and Applications, Springer, vol. 204(2), pages 1-20, February.
    • Handle: RePEc:spr:joptap:v:204:y:2025:i:2:d:10.1007_s10957-024-02579-z
    DOI: 10.1007/s10957-024-02579-z
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    References listed on IDEAS

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    4. Ding, Xiuyong & Liu, Xiu, 2017. "On stabilizability of switched positive linear systems under state-dependent switching," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 92-101.
    5. Judd, Kenneth L., 1985. "Redistributive taxation in a simple perfect foresight model," Journal of Public Economics, Elsevier, vol. 28(1), pages 59-83, October.
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