Cybernetics and Systems Analysis

, Volume 46, Issue 5, pp 729–736 | Cite as

Optimal normalized structure of demand and value added in a productive leontief model1

  • P. I. StetsyukEmail author
  • L. B. Koshlai


The problem of finding normalized vectors of demand and value added in a productive Leontief model is solved. These vectors maximize the national income. It is shown that if the Leontief matrix is productive and indecomposable, then an optimal normalized structure is determined by positive components of the eigenvectors that correspond to maximum eigenvalues of some symmetric matrices. The results of test calculations for a seven-branch matrix are presented.


Leontief matrix static Leontief model extremum quadratic problem eigenvalues and eigenvectors 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    V. V. Leontief, Selected Works, Vols. 1–3 [in Russian], Ekonomika, Moscow (1966).Google Scholar
  2. 2.
    M. V. Mikhalevich and I. V. Sergienko, Modeling a Transition Economy. Models, Methods, Information Technologies [in Russian], Naukova Dumka, Kyiv (2005).Google Scholar
  3. 3.
    I. V. Sergienko, M. V. Mikhalevich, P. I. Stetsyuk, and L. B. Koshlai, “Models and information technologies for decision support during structural and technological changes,” Cybern. Syst. Analysis, 45, No. 2, 187–203 (2009).zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    H. Bortis, Institutions, Behaviour and Economic Theory. A Contribution to Classical-Keynesian Political Economy, Cambridge University Press, Cambridge (1997).Google Scholar
  5. 5.
    H. Bortis, “Keynes and the classics: Notes on the monetary theory of production,” in: L.-P. Rochon and S. Rossi (eds), Modern Theories of Money. The Nature and Role of Money in Capitalist Economies, Edward Elgar: UK, USA (2003), pp. 411–474.Google Scholar
  6. 6.
    S. A. Ashmanov, An Introduction to Mathematical Economics [in Russian], Nauka, Moscow (1984).Google Scholar
  7. 7.
    P. I. Stetsyuk, L. B. Koshlai, and A. V. Pilipovskii, “On the problem of optimal relation between demand and value added in Leontief models,” Teoriya Optym. Rishen’, No. 9, 136–143 (2010).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  1. 1.V. M. Glushkov Institute of CyberneticsNational Academy of Sciences of UkraineKyivUkraine

Personalised recommendations