Skip to main content
Log in

The generalized Leontief input-output model and its application to the choice of new technology

  • Economic And Financial Equilibria
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

The Leontief input-output model is generalized and formulated as a generalized linear complementarity problem. Conditions for existence of solutions are given, and solution techniques are reviewed. An application of the model to choosing new technologies is suggested.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. T.S. Barker, Foreign trade in multisectional models, in:Input-Output Techniques, eds. A. Brody and A.P. Carter (North-Holland, New York, 1972).

    Google Scholar 

  2. R. Chandrasekaran, A special case of the complementary pivot problem, Opsearch 7 (1970) 263–268.

    Google Scholar 

  3. R.W. Cottle and G.B. Dantzig, A generalization of the linear complementarity problem, J. Combinatorial Theory 8 (1970) 79–90.

    Google Scholar 

  4. R.W. Cottle and A.F. Veinott, Polyhedral sets having a least element, Math. Progr. 3 (1972) 238–249.

    Google Scholar 

  5. G.B. Dantzig, Optimal solution of Leontief model with substitution, Econometrica 23 (1955) 295–302.

    Google Scholar 

  6. A.A. Ebiefung, The generalized linear complementarity problem and its applications, Ph.D. Dissertation, Clemson University, Clemson, SC 29634 (1991).

    Google Scholar 

  7. A.A. Ebiefung, On existence of solutions and solvability for the generalized linear complementarity problem, submitted for publication (1991).

  8. A.A. Ebiefung and M.M. Kostreva, Global solvability of generalized linear complementarity problems and a related class of polynomial complementarity problems, inRecent Advances in Global Optimization, eds. C. Floudas and P. Pardalos (Princeton University Press, Princeton, NJ, 1992) pp. 102–124.

    Google Scholar 

  9. A.A. Ebiefung and M.M. Kostreva,Z- matrices and the generalized linear complementarity problem, Tech. Report #608, Department of Mathematical Sciences, Clemson University, Clemson, SC 29634 (1991).

    Google Scholar 

  10. M. Fiedler and V. Pta'k, On matrices with nonpositive off-diagonal elements and positive principal minors, Czech. Math. J. 12 (1962) 382–400.

    Google Scholar 

  11. C.E. Lemke, Mathematical programming course notes, Mathematical Sciences Department, Rensselaer Polytechnic Institute, Troy, NY (1973).

    Google Scholar 

  12. W.W. Leontief, The choice of technology, Sci. Amer. (June 1985) 37–45.

  13. W.W. Leontief,The Structure of the American Economy, 1919–1935 (Oxford University Press, New York, 1949).

    Google Scholar 

  14. W.W. Leontief,Input-Output Economics (Oxford University Press, New York, 1966).

    Google Scholar 

  15. W.W. Leontief and F. Daniel, Air pollution and the economic structure: Empirical results of input-output computations, in:Input-Output Techniques, eds. A. Brody and A.P. Carter (North-Holland, New York, 1972).

    Google Scholar 

  16. O.L. Mangasarian, Generalized linear complementarity problems as linear programs, Oper. Res. Verfahren 31 (1979) 392–402.

    Google Scholar 

  17. R.E. Miller and P.D. Blair,Input-Output Analysis (Prentice-Hall, Englewood Cliffs, NJ, 1985).

    Google Scholar 

  18. K.G. Murty,Linear Complementarity, Linear and Nonlinear Programming (Heldermann, Berlin, 1988).

    Google Scholar 

  19. B.P. Szanc, The generalized complementarity problem, Ph.D. Thesis, Rensselaer Polytechnic Institute, Troy, NY (1989).

    Google Scholar 

  20. A. Tamir, Minimality and complementarity properties associated withZ- andM-functions, Math. Progr. 7 (1974) 17–31.

    Google Scholar 

  21. A. Tamir, An application ofZ-matrices to a class of resource allocation problems, Manag. Sci. 23 (1976) 317–323.

    Google Scholar 

  22. L. Vanderberghe, B.L. De Moor and J. Vanderwalle, The generalized linear complementarity problem applied to the complete analysis of resistive piecewise-linear circuits, IEEE Trans. Circuits and Syst. 11 (1989) 1382–1391.

    Google Scholar 

  23. R. Wu and C. Chen, On the application of input-output to energy issues, Energy Econ. (January 1990) 71–76.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ebiefung, A.A., Kostreva, M.M. The generalized Leontief input-output model and its application to the choice of new technology. Ann Oper Res 44, 161–172 (1993). https://doi.org/10.1007/BF02061065

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02061065

Keywords

Navigation