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An elementary proof of the existence of the Leontief inverse

Author

Listed:
  • Conxita Pinyol

    (Department of Economics Universitat Autonoma de Barcelona)

  • Ferran Sancho

    (Department of Economics Universitat Autonoma de Barcelona)

Abstract

We provide a new and simpler proof for the existence and non-negativity of the Leontief inverse that does not rely on advanced mathematics. Instead, we start from an economic condition related to the equilibrium in quantities between demand and supply and proceed using only elementary linear algebra to establish the nature of the inverse.

Suggested Citation

  • Conxita Pinyol & Ferran Sancho, 2022. "An elementary proof of the existence of the Leontief inverse," Economics Bulletin, AccessEcon, vol. 42(2), pages 662-666.
    • Handle: RePEc:ebl:ecbull:eb-22-00104
    as

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    References listed on IDEAS

    as
    1. Ferran Sancho, 2019. "An Armington–Leontief model," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 8(1), pages 1-10, December.
    2. Dietzenbacher, Erik, 2005. "Waste treatment in physical input-output analysis," Ecological Economics, Elsevier, vol. 55(1), pages 11-23, October.
    3. Jeong, Ki-Jun, 1982. "Direct and indirect requirements: A correct economic interpretation of the Hawkins-Simon conditions," Journal of Macroeconomics, Elsevier, vol. 4(3), pages 349-356.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Leontief inverse; viability; linear algebra;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium

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