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A Turnpike Theorem in the Closed Dynamic Leontief Model with a Singular Matrix of Capital Coefficients


  • Roman Kiedrowski


The paper refers to the well-known Tsukui turnpike theorem on convergence of optimal growth trajectories in the closed dynamic Leontief model to the maximum balanced growth trajectory, called turnpike. In the original proof of this theorem, the assumption that the matrix B of capital coefficients is non-singular plays an essential role. For many reasons this assumption, very convenient for theoretical analysis, is not always satisfied in input-output systems built for empirical purposes. This paper fills the gap between theory and empirical studies, presenting a proof that convergence of optimal trajectories towards the turnpike is also a characteristic feature of the closed Leontief model in the case when matrix B is singular. The general idea of the proof is based on the approximation of a singular matrix B by an infinite sequence of non-singular matrices.

Suggested Citation

  • Roman Kiedrowski, 2001. "A Turnpike Theorem in the Closed Dynamic Leontief Model with a Singular Matrix of Capital Coefficients," Economic Systems Research, Taylor & Francis Journals, vol. 13(2), pages 209-222.
  • Handle: RePEc:taf:ecsysr:v:13:y:2001:i:2:p:209-222
    DOI: 10.1080/09537320120064885

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    Cited by:

    1. Dobos, Imre, 2007. "Egy megjegyzés Bródy András: Leontief zárt dinamikus modellje című dolgozathoz
      [A note on András Bródys study entitled Leontiefs closed dynamic model"]
      ," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(11), pages 1004-1011.


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