Abstract
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.
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Notes and References
J.-G. Courcelle-Seneuil, Traité théorique et pratique d’Économie Politique, Paris: Guillaumin, 1858; 2nd edn, Paris: Amyot, 1867.
J.-G. Courcelle-Seneuil, Traité théorique et pratique des opérations de Banque, fourth edition, Paris: Guillaumin, 1864, pp. 500–1, 510–11, 548–65.
E. Laspeyres, Wechselbeziehungen zwischen Volksvermehrung und Höhe des Arbeitslohns, Heidelberg: Akademische Verlagshandlung von J. C. B. Mohr, 1860.
H. D. Macleod, The Theory and Practice of Banking, vol. 1, London: Longman, Brown, Green & Longmans, 1855, pp. 189–97.
H. D. Macleod, The Elements of Political Economy, London: Longman etc., 1858;
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.
H. D. Macleod, A Dictionary of Political Economy: Biographical, Bibliographical, Historical, and Practical, vol. 1, London: Longman etc., 1863(b), pp. 573–81.
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.
H. D. Macleod, The Elements of Banking, London: Longmans etc., 1882, pp. 83–91.
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.
F. A. Hayek, ‘Macleod, Henry Dunning’, Encyclopaedia of the Social Sciences, vol. 10, 1933, p. 30.
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.
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’.
R. Jennings, Natural Elements of Political Economy, London: Longman, Brown, Green & Longman, 1855.
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.
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’.
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.
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.
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;
C. D. W. Goodwin, Canadian Economic Thought, Durham, NC: Duke University Press, 1961, pp. 75, 116–18;
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.
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.
G. Boccardo, ‘Aritmetica politica’, Dizionario etc., vol. 1, 1857, pp. 190–2.
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.
G. Boccardo, ‘Matematica applicata all’ Economia Politica’, Dizionario della Economia Politico, e del Commercio, 3rd edn, vol. 2, Torino, 1881, pp. 216–20.
L. Walras, ‘Éléments d’économie politique pure, Lausanne, 1874’.
W. S. Jevons, ‘The Theory of Political Economy, London, 1874’.
S. F. Lacroix, ‘Traité élémentaire du calcul des Probabilités, Parigi, 1833’.
G. Dufour, ‘Delle Imposte. Genova, 1861’.
E. Morpurgo, ‘La statistica e le scienze sociali. Firenze, 1872’.
A. Favaro, ‘Giornale degli Economisti. Padova, Agosto, 1875’.
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.
G. Boccardo (ed.), Biblioteca dell’ Economista, ser. 3, vol. II, Torino: Unione Tipogafico-editrice, 1878, pp. 1–1388.
G. Boccardo, ‘Lavori pubblici’, Dizionario etc., vol. 3, 1859, pp. 652–3.
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.
On Marx and mathematical economics, see: L. Smolinski, ‘Karl Marx and Mathematical Economics’, Journal of Political Economy, vol. 81, 1973, pp. 1189–1204;
J. Zeleny, The Logic of Marx, Oxford: Blackwell, 1980, pp. 89–102.
K. Marx, Mathematische Manuskripte, (ed. W. Endemann), Kronberg: Scriptor Verlag, 1974. On this, see also: Smolinski, 1973; Zeleny, 1980.
A.-E. Cherbuliez, Précis de la science économique et de ses principales applications, 2 vols, Paris: Guillaumin, 1862.
C. Le Lièvre, Le travail et le prêt a intérêt, Paris: Guillaumin, 1865, pp. 53–7.
A. W. Marget, The Theory of Prices: A Re-examination of the Central Problems of Monetary Theory, London: P. S. King, 1938, p. 10.
W. Roscher, Die Grundlagen der Nationalökonomie, Stuttgart und Tübingen: Cotta’scher Verlag, 1854, book II, ch. 3.
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.
É. Levasseur, La Question de l’Or, Paris: Guillaumin, 1858.
C. Jellicoe, ‘The Bank of England; its present Constitution and Operations’, Quarterly Journal of the Statistical Society, vol. XIX, London, 1856, pp. 272–83.
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.
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.
R. Price, Observations ... etc, 4th edn, London, 1783, vol. ii, pp. 32–7.
J. H. T. du Villard de Durand, Recherches sur les Rentes, les Emprunts et les Remboursements, Paris et Genève, 1787.
Excerpts are published in W. J. Baumol and S. M. Goldfeld, Precursors in Mathematical Economics: An Anthology, London, 1968, pp. 153–4.
F. Callet, Tables portatives de Logarithmes, Paris: Didot, 1783, pp. 32–40.
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.
D. Jones, On the Value of Annuities and Reversionary Payments, 2 vols, London: Baldwin & Cradock, 1843.
* 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.
* W. Farr, ‘The Income and Property Tax’, Quarterly Journal of the Statistical Society, vol. XVI, London, 1853, pp. 1–44, esp. pp. 19 seq.
* 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.
A. C. Courtois, Des opérations de Bourse, Paris: Guilaumin, 1855.
C. Le Touzé, Traité théorique et pratique du change, des arbitrages et des matières d’or et d’argent, Paris: Guilaumin, 1859.
A.-P. Violeine, Tables pour faciliter les calculs des probabilités sur la vie humaine tels que rentes viagères, assurances etc., Paris, Mallet Bachelier, 1859.
F. Thoman, Theory of Compound Interest and Annuities with Logarithmic Tables, London: John Weale, 1859.
E. Pereire, Tables de l’intérêt composé, des annuités et des rentes viagères, Paris, 1860.
* T. Wittstein, Mathematische Statistik und deren Anwendung auf Nationalökonomie und Versicherungs-Wissenschaft, Hannover: Hanhn’sche Hofbuchhandlung, 1867.
* 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.
H. Charlon, Théorie mathématique des opérations financières, Paris: Gauthier Villars, 1869.
* 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.
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.
I have not been able to consult another work included in both the above bibliographies by S. van Houten, Verhandeling over de Waarde, 1859.
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.
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Theocharis, R.D. (1993). Other Authors on Mathematical Economics. In: The Development of Mathematical Economics. Palgrave Macmillan, London. https://doi.org/10.1007/978-1-349-12992-8_11
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