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Mathematical Economics

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Abstract

I. The steady course on which mathematical economics has held for the past four decades sharply contrasts with its progress during the preceding century, which was marked by several major scientific accidents. One of them occurred in 1838, at the beginning of that period, with the publication of Augustin Cournot’s Recherches sur les principes mathématiques de la théorie des richesses. By its mathematical form and by its economic content, his book stands in splendid isolation in time; and in explaining its data historians of economic analysis in the first half of the nineteenth century must use a wide confidence interval.

This chapter was originally published in The New Palgrave: A Dictionary of Economics, 1st edition, 1987. Edited by John Eatwell, Murray Milgate and Peter Newman

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Bibliography

  • Allais, M. 1943. A la recherche d’une discipline économique. Paris: Imprimerie Nationale.

    Google Scholar 

  • Anderson, R.M. 1978. An elementary core equivalence theorem. Econometrica 46: 1483–1487.

    Article  Google Scholar 

  • Arrow, K.J. 1951. An extension of the basic theorems of classical welfare economics. In Proceedings of the second Berkeley symposium on mathematical statistics and probability, ed. J. Neyman, 507–532. Berkeley: University of California Press.

    Google Scholar 

  • Arrow, K.J. 1953. Le rôle des valeurs boursières pour la répartition la meilleure des risques. Econométrie, Paris: Centre National de la Recherche Scientifique, 41–48.

    Google Scholar 

  • Arrow, K.J., and G. Debreu. 1954. Existence of an equilibrium for a competitive economy. Econometrica 22: 265–290.

    Article  Google Scholar 

  • Arrow, K.J., and F.H. Hahn. 1971. General competitive analysis. San Francisco: Holden-Day.

    Google Scholar 

  • Arrow, K.J., and M.D. Intriligator. (ed.). 1981–5. Handbook of mathematical economics, Vols I, II and III. Amsterdam: North-Holland Publishing Company.

    Google Scholar 

  • Aumann, R.J. 1964. Markets with a continuum of traders. Econometrica 32: 39–50.

    Article  Google Scholar 

  • Balasko, Y. 1986. Foundations of the theory of general equilibrium. New York: Academic.

    Google Scholar 

  • Brouwer, L.E.J. 1912. Über Abbildungen von Mannigfaltigkeiten. Mathematische Annalen 71: 97–115.

    Article  Google Scholar 

  • Brown, D.J., and A. Robinson. 1972. A limit theorem on the cores of large standard exchange economies. Proceedings of the National Academy of Sciences of the USA 69: 1258–1260.

    Article  Google Scholar 

  • Cournot, A. 1838. Recherches sur les principes mathématiques de la théorie des richesses. Paris: L. Hachette.

    Google Scholar 

  • Debreu, G. 1951. The coefficient of resource utilization. Econometrica 19: 273–292.

    Article  Google Scholar 

  • Debreu, G. 1952. A social equilibrium existence theorem. Proceedings of the National Academy of Sciences of the USA 38: 886–893.

    Article  Google Scholar 

  • Debreu, G. 1959. Theory of value: An axiomatic analysis of economic equilibrium. New York: Wiley.

    Google Scholar 

  • Debreu, G. 1970. Economies with a finite set of equilibria. Econometrica 38: 387–392.

    Article  Google Scholar 

  • Debreu, G. 1974. Excess demand functions. Journal of Mathematical Economics 1: 15–21.

    Article  Google Scholar 

  • Debreu, G. 1977. The axiomatization of economic theory. Unpublished lecture given at the University of Bonn, 22 April 1977.

    Google Scholar 

  • Debreu, G. 1982. Chapter 15: Existence of competitive equilibrium. In eds. K.J. Arrow, and M.D. Intriligator (1981–5).

    Google Scholar 

  • Dierker, E. 1974. Topological methods in Walrasian economics. Berlin: Springer.

    Book  Google Scholar 

  • Dierker, E. 1975. Gains and losses at core allocations. Journal of Mathematical Economics 2: 119–128.

    Article  Google Scholar 

  • Dierker, E. 1982. Chapter 17: Regular economies. In eds. K.J. Arrow, and M.D. Intriligator (1981–5).

    Google Scholar 

  • Edgeworth, F.Y. 1881. Mathematical psychics. London: Kegan Paul.

    Google Scholar 

  • Gale, D. 1956. The closed linear model of production. In Linear inequalities and related systems, ed. H.W. Kuhn and A.W. Tucker. Princeton: Princeton University Press.

    Google Scholar 

  • Hicks, J.R. 1939. Value and capital. Oxford: Clarendon.

    Google Scholar 

  • Hildenbrand, W. 1974. Core and equilibria of a large economy. Princeton: Princeton University Press.

    Google Scholar 

  • Hildenbrand, W. 1982. Chapter 18: Core of an economy. In eds. K.J. Arrow and M.D. Intriligator (1981–5).

    Google Scholar 

  • Kakutani, S. 1941. A generalization of Brouwer’s fixed point theorem. Duke Mathematical Journal 8: 457–459.

    Article  Google Scholar 

  • Koopmans, T.C. (ed.). 1951. Activity analysis of production and allocation. New York: Wiley.

    Google Scholar 

  • Lyapunov, A.A. 1940. Sur les fonctions-vecteurs complètement additives. Izvestiia Akademii Nauk SSSR 4: 465–478.

    Google Scholar 

  • Mantel, R. 1974. On the characterization of aggregate excess demand. Journal of Economic Theory 7: 348–353.

    Article  Google Scholar 

  • Mas-Colell, A. 1985. The theory of general economic equilibrium: A differentiable approach. Cambridge: Cambridge University Press.

    Google Scholar 

  • McKenzie, L.W. 1954. On equilibrium in Graham’s model of world trade and other competitive systems. Econometrica 22: 147–161.

    Article  Google Scholar 

  • Minkowski, H. 1911. Theorie der konvexen Körper. Gesammelte Abhandlungen, Leipzig and Berlin: Teubner, Vol. II, 131–229.

    Google Scholar 

  • Nash, J.F. 1950. Equilibrium points in n-person games. Proceedings of the National Academy of Sciences of the USA 36: 48–49.

    Article  Google Scholar 

  • Neumann, J. von. 1937. Über ein ökonomisches Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes. In Ergebnisse eines mathematischen Kolloquiums, Vol. 8, 73–83.

    Google Scholar 

  • Pareto, V. 1896–1897 Cours d’économie politique. Lausanne: Rouge.

    Google Scholar 

  • Pareto, V. 1909. Manuel d’économie politique. Paris: Giard.

    Google Scholar 

  • Pareto, V. 1911. Economie mathématique. In Encyclopédie des sciences mathématiques, Paris: Gauthier- Villars, Vol. I(4), 591–640.

    Google Scholar 

  • Robinson, A. 1966. Non-standard analysis. Amsterdam: North-Holland.

    Google Scholar 

  • Samuelson, P.A. 1947. Foundations of economic analysis. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Sard, A. 1942. The measure of the critical points of differentiable maps. Bulletin of the American Mathematical Society 48: 883–890.

    Article  Google Scholar 

  • Scarf, H. 1962. An analysis of markets with a large number of participants. In Recent advances in game theory, ed. H. Scarf. Princeton: Princeton University Press.

    Google Scholar 

  • Scarf, H. 1973. (With the collaboration of T. Hansen) The computation of economic equilibria. New Haven: Yale University Press.

    Google Scholar 

  • Scarf, H. 1982. Chapter 21: The computation of equilibrium prices: An exposition. In eds. K.J. Arrow, and M.D. Intriligator (1981–5).

    Google Scholar 

  • Scarf, H.E., and J.B. Shoven. 1984. Applied general equilibrium analysis. Cambridge: Cambridge University Press.

    Google Scholar 

  • Shubik, M. 1959. Edgeworth market games. In Contributions to the theory of games, Annals of mathematical studies 40, vol. IV. Princeton: Princeton University Press.

    Google Scholar 

  • Smale, S. 1981. Chapter 8: Global analysis and economics. In eds. K.J. Arrow, and M.D. Intriligator (1981–5).

    Google Scholar 

  • Sonnenschein, H. 1973. Do Walras’ identity and continuity characterize the class of community excess demand functions? Journal of Economic Theory 6: 345–354.

    Article  Google Scholar 

  • Vind, K. 1964. Edgeworth-allocations in an exchange economy with many traders. International Economic Review 5: 165–177.

    Article  Google Scholar 

  • von Neumann, J. 1928. Zur Theorie der Gesellschaftsspiele. Mathematische Annalen 100: 295–320.

    Article  Google Scholar 

  • von Neumann, J., and O. Morgenstern. 1944. Theory of games and economic behavior. Princeton: Princeton University Press.

    Google Scholar 

  • Wald, A. 1935. Über die eindeutige positive Lösbarkeit der neuen Produktionsgleichungen. Ergebnisse eines mathematischen Kolloquiums 6: 12–20.

    Google Scholar 

  • Wald, A. 1936a. Über die Produktionsgleichungen der ökonomischen Wertlehre. Ergebnisse eines mathematischen Kolloquiums 7: 1–6.

    Google Scholar 

  • Wald, A. 1936b. Über einige Gleichungssysteme der mathematischen Ökonomie. Zeitschrift für Nationalökonomie 7: 637–670.

    Article  Google Scholar 

  • Walras, L. 1874–1877. Eléments d’économie politique pure. Lausanne: L. Corbaz.

    Google Scholar 

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Debreu, G. (1987). Mathematical Economics. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95121-5_1083-1

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  • DOI: https://doi.org/10.1057/978-1-349-95121-5_1083-1

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  • Online ISBN: 978-1-349-95121-5

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Chapter history

  1. Latest

    Mathematical Economics
    Published:
    23 March 2017

    DOI: https://doi.org/10.1057/978-1-349-95121-5_1083-2

  2. Original

    Mathematical Economics
    Published:
    25 November 2016

    DOI: https://doi.org/10.1057/978-1-349-95121-5_1083-1