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A remark on sensitivity in linear programming and Gale-Samuelson nonsubstitution theorem

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Języki publikacji
EN
Abstrakty
EN
The main purpose of this paper is to show that David Gale's result (1960, Lemma 9.3 on sensitivity in linear programming) is not generally valid. In this lemma, additional assumptions, that are instead required, are not made. We give some correct versions of the above mentioned lemma, and with these an elementary proof of the Gale-Samuelson nonsubstitution theorem.
Rocznik
Strony
827--838
Opis fizyczny
Bibliogr. 19 poz.
Twórcy
autor
  • Department of Economics and Quantitative Methods, University of Pavia, via S. Felice, 5, 27100 Pavia, Italy, ggiorgi@eco.unipv.it
Bibliografia
  • ACHAMANOV, S. (1984) Programmation Lineaire. Editions Mir, Moscou.
  • ARROW, K.J. (1951) Alternative proof of the substitution theorem for Leontief models in the general case. In: T.C. Koopmans, ed., Activity Analysis of Production and Allocation. John Wiley, New York, 155-164.
  • BAPAT, R.B. and RAGHAVAN, T.E.S. (1977) Nonnegative Matrices and Applications. Cambridge University Press, Cambridge.
  • BOSE, S. (1972) A new proof of the non-substitution theorem. International Economic Review 13, 183-186.
  • DE GIULI, M.E. (1995) On a theorem of Gale-Hadley-Lancaster and its Economic and Financial Applications. Atti XIX Convegno AMASES, Pugnochiuso, 25-28.9.1995. Cacucci Editore, Bari, 281-290.
  • DE GIULI, M.E., GIORGI, G., MAGGI, M.A. and MAGNANI, U. (2008) Matematica per I’Economia e la Finanza. Zanichelli, Bologna.
  • DE GIULI, M.E. and MAGNANI, U. (1996) Non-substitution theorems for perfect matching problems. In: M. Bertocchi, E. Cavalli and S. Komlosi, eds., Modelling Techniques for Financial Markets and Bank Management. Physica Verlag, Heidelberg, 34-47.
  • FIEDLER, M. and PTÀK, V. (1962) On matrices with nonpositive off-diagonal elements and positive principal minors. Czechoslovak Mathematical Journal, 12, 382-400.
  • GALE, D. (1960) The Theory of Linear Economic Models. McGrawHill, NY.
  • HADLEY, G. (1962) Linear Programming. Addison-Wesley, Reading, Mass.
  • HEAL, G., HUGHES, G. and TARLING, R. (1974) Linear Algebra and Linear Economics. Macmillan, London.
  • KOOPMANS, T.C. (1951) Alternative proof of the substitution theorem for Leontief models in the case of three industries. In: T.C. Koopmans, ed., Activity Analysis of Production and Allocation. John Wiley, New York, 147-154.
  • LANCASTER, K. (1968) Mathematical Economics. Macmillan, London.
  • MAITI, P. (1971) On a theorem in linear programming due to Gale. Indian Statistical Institute, Tech. Report No. Econ /7/71, Calcutta.
  • MANARA, C.F. and NICOLA, P.C. (1967) Elementi di Economia Matematica. Editrice Viscontea, Milano.
  • MURATA, Y. (1977) Mathematics for Stability and Optimisation of Economic System. Academic Press, New York.
  • NICOLA, P.C. (2000) Mainstream Mathematical Economics in the 2(fh Century. Springer, Berlin.
  • PASINETTI, L.L. (1977) On „non-substitution” in production models. Cambridge Journal of Economics, 1, 389-394.
  • SAMUELSON, P.A. (1951) Abstract of a theorem concerning substitutability in open Leontief models. In: T.C. Koopmans, ed., Activity Analysis of Production and Allocation. John Wiley, New York, 142-146.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0055-0031
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