Other Authors on Mathematical Economics

  • Reghinos D. Theocharis


There are a number of other authors who must receive some mention in this book. These are authors who, during the period under discussion, either found it appropriate to use occasionally some simple mathematics and formulas in order to construct one or more of their arguments, or expressed views on the usefulness of the mathematical method in economic analysis.


Political Economy Mathematical Economic Simple Mathematic Algebraic Formula Compound Interest 
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Notes and References

  1. 1.
    J.-G. Courcelle-Seneuil, Traité théorique et pratique d’Économie Politique, Paris: Guillaumin, 1858; 2nd edn, Paris: Amyot, 1867.Google Scholar
  2. 12.
    J.-G. Courcelle-Seneuil, Traité théorique et pratique des opérations de Banque, fourth edition, Paris: Guillaumin, 1864, pp. 500–1, 510–11, 548–65.Google Scholar
  3. 13.
    E. Laspeyres, Wechselbeziehungen zwischen Volksvermehrung und Höhe des Arbeitslohns, Heidelberg: Akademische Verlagshandlung von J. C. B. Mohr, 1860.Google Scholar
  4. 22.
    H. D. Macleod, The Theory and Practice of Banking, vol. 1, London: Longman, Brown, Green & Longmans, 1855, pp. 189–97.Google Scholar
  5. 22a.
    H. D. Macleod, The Elements of Political Economy, London: Longman etc., 1858;Google Scholar
  6. 22b.
    H. D. Macleod, On the Definition and Nature of the Science of Political Economy, Cambridge and London: Macmillan, 1862; also see ‘On the Definition and Nature of the Science of Political Economy’, Report of the thirty-second meeting of the British Association for the Advancement of Science, London, 1863(a), pp. 159–61.Google Scholar
  7. 22c.
    H. D. Macleod, A Dictionary of Political Economy: Biographical, Bibliographical, Historical, and Practical, vol. 1, London: Longman etc., 1863(b), pp. 573–81.Google Scholar
  8. 22d.
    H. D. Macleod, The Elements of Economics, London: Longman Green, vol. I, 1881, pp. 223–5, 256–60, 309–16; vol. II, 1886, pp. 80–5.Google Scholar
  9. 22e.
    H. D. Macleod, The Elements of Banking, London: Longmans etc., 1882, pp. 83–91.Google Scholar
  10. 22f.
    The works of 1858, 1862 and 1863 are listed in Jevons’s bibliography; see W. S. Jevons, The Theory of Political Economy, fifth edn, New York: Kelley, 1965, pp. 331–2.Google Scholar
  11. 23.
    F. A. Hayek, ‘Macleod, Henry Dunning’, Encyclopaedia of the Social Sciences, vol. 10, 1933, p. 30.Google Scholar
  12. 38.
    W. S. Jevons, The Theory of Political Economy, London and New York: Macmillan, 1871, p. 17, where he wrote: ‘In more recent years, Mr. McLeod has applied algebraic formulae to economical questions, especially to Banking.’ Jevons’s citation refers to Macleod, 1855 and 1863.Google Scholar
  13. 40.
    Jevons, 1965, pp. xxvii–xxviii. Jevons, ibid., p. xxxii, makes the additional comment that ‘Mr. H. D. Macleod has the merit at least of mentioning Cournot’s work, but he misspells the name of the author, and gives only the title of the book (the Recherches), which he had probably never seen.’ On Macleod and his influence on Jevons, see: R. M. Robertson, ‘Jevons and his Precursors’, Econometrica, vol. 19, 1951, pp. 237–8; Robertson, ibid., p. 239, says that ‘MacLeod’s only mathematical passages are concerned with the computation of yields on bills in the portfolios of commercial banks’.CrossRefGoogle Scholar
  14. 41.
    R. Jennings, Natural Elements of Political Economy, London: Longman, Brown, Green & Longman, 1855.Google Scholar
  15. 41a.
    On Jennings see: F. Y. Edgeworth, ‘Jennings, Richard’, Palgrave’s Dictionary of Political Economy, vol. II, London: Macmillan, 1906, pp. 473–4; W. S. Jevons, 1871, p. 18; see also Jevons, 1965, pp. 55–7; R. M. Robertson, 1951, pp. 234–7, 239.Google Scholar
  16. 48.
    J. Benner, Theorie Mathématique de l’Économie Sociale ou Éléments Nouveaux d’Économie Politique, Genève: Imprimerie Vaney, 1855. The only copy I could trace is found at the ‘Bibliothèque Publique et Universitaire, Genève’.Google Scholar
  17. 48a.
    It is interesting to note that in both Jevons’s and Fisher’s bibliographies of works on mathematical economics the book is wrongly listed as ‘1856. Benner. Theórie mathématique de l’économie politique‘. See Jevons, 1879, p. 304; Fisher, 1960 [1897], p. 178. The title (but not the date) of the work is correctly listed in Boccardo’s bibliography as ‘Théorie mathématique de l’économie sociale; 1 vol. in 8vo, Ginevra, 1856’. See G. Boccardo, ‘Matematica applicata all’ Economia politica’, Dizionario delia Economia Politica e del Commercio, cost teorico come pratico, vol. III, Torino: S. Franco, 1859, p. 244.Google Scholar
  18. 58.
    J. B. Cherriman, ‘Recherches sur les principes Mathématiques de la Théorie des Richesses, par Augustin Cournot, Recteur de l’ Académie et Professeur de la Faculté des Sciences de Grenoble. Paris: Hachette, 1838’, The Canadian Journal of Industry, Science and Art, new series, vol. 9, 1857, pp. 185–94.Google Scholar
  19. 58a.
    On this, see: R. W. Dimand, ‘An Early Canadian Contribution to Mathematical Economics: J. B. Cherriman’s 1857 Review of Cournot’, Canadian Journal of Economics, vol. 21, 1988, pp. 610–16;CrossRefGoogle Scholar
  20. 58b.
    C. D. W. Goodwin, Canadian Economic Thought, Durham, NC: Duke University Press, 1961, pp. 75, 116–18;Google Scholar
  21. 58c.
    R. D. Theocharis, ‘A Note on the Lag in the Recognition of Cournot’s Contribution to Economic Analysis’, Canadian Journal of Economics, vol. 23, 1990, pp. 923–33.CrossRefGoogle Scholar
  22. 62.
    G. Boccardo, ‘Matematica applicata all’Economia Politica’, Dizionario della Economia Politica e del Commercio cosí teorico come pratico, Torino: S. Franco, vol. 3, 1859, pp. 241–4.Google Scholar
  23. 63.
    G. Boccardo, ‘Aritmetica politica’, Dizionario etc., vol. 1, 1857, pp. 190–2.Google Scholar
  24. 80.
    Boccardo, 1859, pp. 244 and 244n., where he cites ‘Sur les institutions de prévoyance, ecc. par M. Hubbard’. Its full title is N. G. Hubbard, De l’organisation des sociétés de prévoyance ou de secours mutuels, Paris, 1852.Google Scholar
  25. 81.
    G. Boccardo, ‘Matematica applicata all’ Economia Politica’, Dizionario della Economia Politico, e del Commercio, 3rd edn, vol. 2, Torino, 1881, pp. 216–20.Google Scholar
  26. 82.
    L. Walras, ‘Éléments d’économie politique pure, Lausanne, 1874’.Google Scholar
  27. 83.
    W. S. Jevons, ‘The Theory of Political Economy, London, 1874’.Google Scholar
  28. 84.
    S. F. Lacroix, ‘Traité élémentaire du calcul des Probabilités, Parigi, 1833’.Google Scholar
  29. 85.
    G. Dufour, ‘Delle Imposte. Genova, 1861’.Google Scholar
  30. 86.
    E. Morpurgo, ‘La statistica e le scienze sociali. Firenze, 1872’.Google Scholar
  31. 87.
    A. Favaro, ‘Giornale degli Economisti. Padova, Agosto, 1875’.Google Scholar
  32. 88.
    G. Boccardo, ‘Del metodo in Economia Politica’, Giornale degli Economisti, vol. 1, 1875, pp. 110–30; see pp. 127–30. Also by the same, ‘Dell’applicazione dei Metodi Quantitivi alle scienze economiche, statistiche e sociali. Saggio di logica economica — Prefazione al II volume’, Biblioteca dell’ Economista, ser. 3, vol. II, Torino: Unione Tipogafico-editrice, 1878, pp. I–LXXII; see esp. pp. XX–LXXII. Also his ‘L’economia politica odierna come scienza e come ordinamento sociale — Introduzione generale’, Biblioteca dell’ Economista, ser. 3, vol. I, Torino: Unione Tipogafico-editrice, 1876, p. 31.Google Scholar
  33. 89.
    G. Boccardo (ed.), Biblioteca dell’ Economista, ser. 3, vol. II, Torino: Unione Tipogafico-editrice, 1878, pp. 1–1388.Google Scholar
  34. 90.
    G. Boccardo, ‘Lavori pubblici’, Dizionario etc., vol. 3, 1859, pp. 652–3.Google Scholar
  35. 91.
    K. Marx, Das Kapital, Vol. I, Hamburg: Otto Meissner, 1867; references are to the English translation: K. Marx, Capital, Vol. I, Moscow: Foreign Languages Publishing House.Google Scholar
  36. 91a.
    On Marx and mathematical economics, see: L. Smolinski, ‘Karl Marx and Mathematical Economics’, Journal of Political Economy, vol. 81, 1973, pp. 1189–1204;CrossRefGoogle Scholar
  37. 91b.
    J. Zeleny, The Logic of Marx, Oxford: Blackwell, 1980, pp. 89–102.Google Scholar
  38. 102.
    K. Marx, Mathematische Manuskripte, (ed. W. Endemann), Kronberg: Scriptor Verlag, 1974. On this, see also: Smolinski, 1973; Zeleny, 1980.Google Scholar
  39. 103.
    A.-E. Cherbuliez, Précis de la science économique et de ses principales applications, 2 vols, Paris: Guillaumin, 1862.Google Scholar
  40. 107.
    C. Le Lièvre, Le travail et le prêt a intérêt, Paris: Guillaumin, 1865, pp. 53–7.Google Scholar
  41. 108.
    A. W. Marget, The Theory of Prices: A Re-examination of the Central Problems of Monetary Theory, London: P. S. King, 1938, p. 10.Google Scholar
  42. 109.
    W. Roscher, Die Grundlagen der Nationalökonomie, Stuttgart und Tübingen: Cotta’scher Verlag, 1854, book II, ch. 3.Google Scholar
  43. 113.
    F. Bowen, The Principles of Political Economy, Applied to the Condition, the Resources and the Institutions of the American People, Boston: Little, Brown and Co., 1856.Google Scholar
  44. 117.
    É. Levasseur, La Question de l’Or, Paris: Guillaumin, 1858.Google Scholar
  45. 121.
    C. Jellicoe, ‘The Bank of England; its present Constitution and Operations’, Quarterly Journal of the Statistical Society, vol. XIX, London, 1856, pp. 272–83.Google Scholar
  46. 122.
    Jellicoe, p. 281. It should be noted that this author also used some uninteresting simple mathematics in two other studies which appeared in the period under discussion. See: C. Jellicoe, ‘On the Contrivances required to render Contingent Reversionary Interests Marketable Securities’, The Assurance Magazine, vol. II, London, 1852, pp. 159–66; by the same, ‘On the true meaning of Liability in a System of Direct Taxation’, The Assurance Magazine and Journal of the Institute of Actuaries, vol. III, London, 1853, pp. 1–7.Google Scholar
  47. 123.
    R. Price, Observations on reversionary payments; on schemes for providing annuities for widows, and for persons in old age; on the method of calculating the values of assurances on lives; and on the national debt. To which are added four essays; also an appendix, London, 1771.Google Scholar
  48. 125.
    R. Price, Observations ... etc, 4th edn, London, 1783, vol. ii, pp. 32–7.Google Scholar
  49. 126.
    J. H. T. du Villard de Durand, Recherches sur les Rentes, les Emprunts et les Remboursements, Paris et Genève, 1787.Google Scholar
  50. 126a.
    Excerpts are published in W. J. Baumol and S. M. Goldfeld, Precursors in Mathematical Economics: An Anthology, London, 1968, pp. 153–4.Google Scholar
  51. 128.
    F. Callet, Tables portatives de Logarithmes, Paris: Didot, 1783, pp. 32–40.Google Scholar
  52. 129.
    H. C. Emmery, Pont d’ Ivry, en bois, sur piles en pierre, traversant la Seine, près du confluent de la Marne, Paris: Carilian Goeury, 1832, pp. 262–86.Google Scholar
  53. 131.
    D. Jones, On the Value of Annuities and Reversionary Payments, 2 vols, London: Baldwin & Cradock, 1843.Google Scholar
  54. 132.
    * C. Jellicoe, ‘On the Contrivances required to render Contingent Reversionary Interests Marketable Securities’, The Assurance Magazine, vol. II, London, 1852, pp. 159–66. We have already referred to Jellicoe in the chapter on the ‘equation of exchange’ theorists. For the meaning of the asterisk, see note 144 below.Google Scholar
  55. 133.
    * W. Farr, ‘The Income and Property Tax’, Quarterly Journal of the Statistical Society, vol. XVI, London, 1853, pp. 1–44, esp. pp. 19 seq.Google Scholar
  56. 134.
    * P. Hardy, ‘An Exposé of the Fallacy, “That it is just to tax Temporary Annuities at the same rate as Perpetual Annuities”’, The Assurance Magazine and Journal of the Institute of Actuaries, vol. III, London, 1853, pp. 195–204.Google Scholar
  57. 135.
    A. C. Courtois, Des opérations de Bourse, Paris: Guilaumin, 1855.Google Scholar
  58. 136.
    C. Le Touzé, Traité théorique et pratique du change, des arbitrages et des matières d’or et d’argent, Paris: Guilaumin, 1859.Google Scholar
  59. 137.
    A.-P. Violeine, Tables pour faciliter les calculs des probabilités sur la vie humaine tels que rentes viagères, assurances etc., Paris, Mallet Bachelier, 1859.Google Scholar
  60. 138.
    F. Thoman, Theory of Compound Interest and Annuities with Logarithmic Tables, London: John Weale, 1859.Google Scholar
  61. 139.
    E. Pereire, Tables de l’intérêt composé, des annuités et des rentes viagères, Paris, 1860.Google Scholar
  62. 140.
    * T. Wittstein, Mathematische Statistik und deren Anwendung auf Nationalökonomie und Versicherungs-Wissenschaft, Hannover: Hanhn’sche Hofbuchhandlung, 1867.Google Scholar
  63. 141.
    * P. Gray, ‘On the Rate of Interest in Loans payable by Instalments’, Journal of the Institute of Actuaries and Assurance Magazine, vol. xi, London, 1869, pp. 91–102 and 182–9.Google Scholar
  64. 142.
    H. Charlon, Théorie mathématique des opérations financières, Paris: Gauthier Villars, 1869.Google Scholar
  65. 143.
    * H. Lefèvre, Traité théorique et pratique des valeurs mobilières et des opérations de bourse, Paris: Lachaud, 1870; a part of it has also been published separately as * Théorie élémentaire des opérations de bourse, Paris, 1870.Google Scholar
  66. 144.
    I. Fisher, [1897] 1960, pp. 179 and 181; W. S. Jevons, The Theory of Political Economy...; with Notes and an extension of the Bibliography of Mathematical Economic Writings by H. Stanley Jevons, fourth edition, London: Macmillan, 1924, pp. 330 and 333. See also Jevons, 5th edn, 1965, pp. 330 and 333.Google Scholar
  67. 144a.
    I have not been able to consult another work included in both the above bibliographies by S. van Houten, Verhandeling over de Waarde, 1859.Google Scholar
  68. 145.
    H. D. Macleod, The Theory and Practice of Banking, vol. i, London: Longman, Brown, Green & Longmans, 1855, pp. 189–201; by the same, The Elements of Economics, London: Longman Green, vol. II, 1886, pp. 80–5.Google Scholar

Copyright information

© Reghinos D. Theocharis 1993

Authors and Affiliations

  • Reghinos D. Theocharis
    • 1
  1. 1.Athens University of Economics and BusinessAthensGreece

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