2012 | 9(13) | 55-74
Article title

Some reasons why we should teach matrices to students of economics

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The paper makes up the second part of the series of articles aimed at establishing the usefulness of matrices in the study of contemporary economic sciences. The series was initiated by the present author in his previous article of this subject (Rybicki, 2010). The items chosen to be presented here concern applications of (operating with) matrices in the field of welfare economics and to the description dynamics of economic systems. The first class of matrices we discuss serves as tools for indicating the inequalities of distributions of (finite) commodity bundles (and as devices to “equalize” these distributions). Other considered families of matrices consist of transition matrices of Markov chains. The presented statements are of an elementary character – they are intended to help students feel (and believe in) some uniformity of the content of lectures on mathematics and economics and (in a wider sense) operations research.
Physical description
  • Arnold B. (1987). Majorization and the Lorenz Order: A Brief Introduction. Springer Verlag. Berlin–Heidelberg–New York–Paris–Tokyo.
  • Birkhoff G. (1946). Tres observaciones sobre al algebra lineal. Univ. Nac. Tucuman Rev. Ser A.5. Pp. 147-151.
  • Dalton H. (1920). The measurement of the inequality of incomes. Economic Journal 30. Pp. 348-361.
  • Feller W. (1966). Wstęp do rachunku prawdopodobieństwa. PWN. Warszawa.
  • Fisz M. (1967). Rachunek prawdopodobieństwa i statystyka matematyczna. PWN. Warszawa.
  • Hardy G., Littwood J., Polya G. (1929). Some Simple Inequalities Satisfying by Convex Functions. Mess. of Math. 58. Pp. 145-152.
  • Kilhstrom R.E., Mirman L.J. (1974). Risk Aversion with Many Commodities. Journal of Economic Theory. Vol. 8. Str. 361-388.
  • Kingman J.F.C. (1972). Regenerative Phenomena. J. Willey & Sons Ltd. London–New York–Sydney–Toronto.
  • Le Breton M. (1991). Stochastic Orders In Welfare Economics. In: K. Mosler, M. Scarsini (Eds.). Stochastic Orders and Decision Under Risk. Inst. of Math. Statistics. Lecture Notes – Monograph Series. Vol. 19. Pp. 190-206.
  • Lorenz M. (1905). Methods of measuring the concentration of wealth. Publ. of the American Statistical Association 9. Pp. 209-219.
  • Marshall A.W., Olkin J. (1979). Inequalities: Theory of Majorization and Application. Academic Press. New York.
  • Mosler K., Scarsini M. (Eds.) (1991). Stochastic Orders and Decision Under Risk, Inst. Of Math. Statistics. Lecture Notes – Monograph Series. Vol. 19. Hayward. California.
  • Muirhead R. (1903). Some methods applicable to identities and inequalities of symmetric algebraic functions of n letters. Proceedings of the Edinburg Math. Society 21. Pp. 144-157.
  • Nermuth M. (1993). Different Economic theories with the Same Formal Structures: Risk, Inequality, Information Structures etc. In: E. Diewert, K. Spremann,
  • F. Stehling (Eds.). Mathematical Modelling. Springer Verlag. Pp. 271-277.
  • Phelps R. (1966). Lectures on Choquet’s Theorem, D. Van Nostrand Company Inc. Princeton. New Jersey. Toronto–New York–London.
  • Rosenblatt M. (1967). Procesy stochastyczne. PWN. Warszawa.
  • Rybicki W. (2010). Kilka powodów dla których opowiadamy studentom ekonomii o macierzach. Didactics of Mathematics 7(11). Wrocław University of Economics. Pp. 109-126.
  • Rybicki W. (2012). Further Examples of the Appearance of Matrices (and Role They Play) in the Course of the Economic Education. Didactics of Mathematics (this issue).
  • Rybicki W. (2013). The Role of Matrices in the Contemporary Education of Students of Economics – Further Remarks and Examples of Applications – the paper prepared for the publication in Didactics of Mathematics 10(14).
  • Schmeidler D. (1979). A Bibliographical Note on Theorem of Hardy. Littlewood and Polya. Journal of Economic Theory 20. Pp. 125-128.
  • Schur J. (1923). Über eine klasse von mittel-bildungen mit anwendungen die determinaten. Theorie Sitzungsber Berlin Math. Gesalschaft 22. Pp. 9-20.
  • Shaked M., Shanthikumar J. (1993). Stochastic Orders and Their Applications. Academic Press. New York.
  • Szekli R. (1995). Stochastic Ordering and Dependence in Applied Probability. Springer Verlag. New York.
  • Winkler G. (1980). Choquet Order and Simplices. Springer-Verlag. Berlin–Heidelberg–New York–Tokyo.
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Publication order reference
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