Abstract
Karl Heinrich Rau (1792–1870), a highly influential German Professor of Political Economy at the University of Heidelberg,1 had already published in his Grundsätze der Volkswirthschaftslehre in 1826 some elementary mathematical formulas. This part of his contribution has already been dealt with by me in Early Developments. But Rau had also by 1821 given2 an equation of exchange formula as well as functional relations and curves linking number (and size) of forms with their costs and their gross and net product.
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Notes and References
Karl Heinrich Rau was born at Erlangen and spent most of his life at Heidelberg, where he was a professor of political economy. He was also for a time a member of parliament and was the founder of the Archiv der politischen Oekonomie und Polizeiwissenschaft. On Rau, see; J. K. Ingram, ‘Rau, Karl Heinrich’, Palgrave’s Dictionary of Political Economy, vol. iii, London, 1899, pp. 264–5;
K. Pribram, ‘Rau, Karl Heinrich’, Encyclopaedia of the Social Sciences, vol. xiii, 1934, p. 122;
A. Forstmann, Volkswirtschatliches Theorie des Geldes, vol. 1, Berlin, 1943, p. 192;
G. Homberg, ‘Die Vertreter der mathematischen Nationalökonomie im deutschsprächigen Raum vor dem Erscheinen des Cournotschen Werkes (1838)’, unpublished thesis, Albert-Ludwigs-Universität, Freiburg im Breisgau, 1971, pp. 93–107;
K. H. Hennings, Karl Heinrich Rau and the Graphic Representation of Supply and Demand (Discussion Paper), Fachbereich Wirtschaftswissenschaften, Universität Hannover, Reihe C, Nr. 35, 1979;
E. Schneider, Einführung in die Wirtschaftstheorie, part IV, Tübingen: Mohr, 1970, p. 131;
Y-N. Shieh, ‘K. H. Rau and the Economic Law of Market Areas’, Journal of Regional Science, vol. 25, 1985, pp. 191–9;
E. W. Streissler, The Influence of German Economics on the Work of Menger and Marshall’, in B. J. Caldwell (ed.), Carl Menger and his Legacy in Economics, Durham and London: Duke Univ. Press, 1990, pp. 31–68;
W. Roscher, Geschichte der National-Oekonomik in Deutschland, München: R. Oldenbourg, 1874, pp. 847–54; Theocharis, 1983, p. 116.
K. H. Rau, Ansichten der Volkswirthschaft mit besonderer Beziehung auf Deutschland, Leipzig: Göschen, 1821, pp. 96–8, 156–9, 182–6 and Fig. 7.
K. H. Rau, Grundsätze der Volkswirthschaftslehre, fourth edition, Heidelberg: C. F. Winter, 1841(a);
Communication of M. Quetelet: ‘Extraits de deux lettres, qui lui ont été adressées par M. le professeur Rau de Heidelberg’, in ‘Économie Politique’, Bulletins de l’Académie Royale des Sciences et Belles-Lettres de Bruxelles, vol. VIII, 2nd part, Bruxelles: M. Hayez, 1841(b), pp. 148–51 and fol. opp. p. 152. A translation of the first extract, with a preface, is included in Baumol and Goldfeld, 1968, pp. 181–3.
For the correspondence Rau-Quetelet, see L. Wellens-De Donder, ‘Inventaire de la correspondance d’Adolphe Quetelet’, in Académie Royale de Belgique, Classe des Sciences, Mémoires, vol. XXXVII (2), Bruxelles, 1966, p. 120.
H. F. von Storch, Cours d’Économie Politique, 6 vols, St. Pétersburg, 1815;
German translation, with appendices, by Rau: Handbuch der Nationalwirthschaftslehre, mit Zusätzen von Rau, 3 vols, Hamburg, 1819–20. The appendices were also published separately in 1820.
Rau, Grundsätze der Volkswirthschaftslehre, third edition, Heidelberg, 1837, p. 7; Rau, 1841(a), p. 7.
N.-F. Canard, Principes d’Économie Politique, Paris, 1801. Apart from the original French edition, Rau cites the German translations of this work in 1806 and 1824. Rau, 1841(a), p. 45. On Canard, see Theocharis, 1983, pp. 67–76.
Rau, 1837, p. 7n., and also pp. 41, 43–4. Also Rau, 1841(a), p. 7n. and also pp. 43, 45–6. On all these, see Theocharis, 1983, pp. 67–76, 104–11, 102–4, 111–12 and 76–7. Rau’s relevant passage on precursors in mathematical economics is quoted verbatim by C. J. Garnier, Traité d’Économie Politique, fourth edition, Paris: Garnier-Guillaumin, 1860, p. 618.
K. H. Rau, Grunsätze der Volkswirthschaftslehre, fifth edition, Heidelberg: C. F. Winter: 1847, p. 10n.
The reference is to A. Scialoja, I principii della Economia Sociale esposte in ordino ideologico, 1840. On this author, see Theocharis, 1983, p. 78.
On this, see Cournot, 1960 (1897), p. 53; H. von Mangoldt, Grundriss der Volkswirthschaftslehre, Stuttgart: Engelhorn, 1863, p. 47; Marshall, 1936, p. 96n.
See the first edition of Marshall’s Principles, 1890, p. 135, where Rau’s Grundsätze is cited; also see A. Marshall, Principles of Economics, ninth (variorum) edition, vol. II, London: Macmillan, 1961, p. 782.
Rau, 1841(b), pp. 148–9 and fig. I, opp. p. 152. See also Baumol and Goldfeld, 1968, pp. 181–3; Y-N. Shieh, ‘K. H. Rau and the Economic Law of Market Areas’, Journal of Regional Science, vol. 25, 1985, pp. 191–9.
Rau, 1841(b), p. 149. A similar topic had already been tackled by the French mathematician Gaspard Monge in 1781, who had examined the problem of minimisation of the cost of transport from a given area of origin to a given destination, when the loads to be transported have necessarily to pass through one of two given points, such as two bridges. Monge’s solution showed that it would pay loads originating from a portion of the area of origin to travel through the one point and loads from another portion of the area of origin to travel through the second point, the demarcation of the two portions of the area of origin being determined by two hyperbolas, whose foci would be the two fixed points. G. Monge, ‘Mémoire sur la théorie des déblais et des remblais’, 1781, in Histoire de l’Académie Royale des Sciences, Année MDCCLXXI. Avec les Mémoires de Mathématique et de Physique pour la même Année, Paris: Imprimerie Royale, 1784, pp. 34–8, 666–704 and Plates 18 & 19.
On this see F. Etner, Histoire du calcul économique en France, Paris: Economica, 1987, pp. 65–6, who considers that Monge’s studies mark ‘the birth of operational research’ and also reproduces one of Monge’s diagrams.
Rau, 1841(b), p. 149. On this aspect, see R. G. D. Allen, Mathematical Analysis for Economists, London: Macmillan, 1949, pp. 80–2,
who ascribes the solution of the problem to E. Schneider, in his ‘Bemerkungen zu einer Theorie der Raumwirtschaft’, Econometrica, vol. III, 1935, pp. 79–105.
F. A. Fetter, ‘The Economic Law of Market Areas’, The Quarterly Journal of Economics, vol. 38, 1924, pp. 520–9.
C. F. W. Launhardt, Mathematische Begründung der Volkswirtschaftslehre, Leipzig: Teubner, 1885. I refer to the Scientia Verlag Aalen, Darmstadt, edition, 1963, pp. 157–9. See, also, by the same author, ‘Die Bestimmung des zweckmässigsten Standortes einer gewerblichen Anlage’, Zeitschrift des Vereines Deutscher Ingenieure, vol. XXVI, 1882, pp. 105–16. On Launhardt, see Schneider, 1935, pp. 86–9.
Schneider, 1935, pp. 86–9; also by the same, Price and Equilibrium, sixth edn, N. York: Macmillan, 1962, pp. 62–70; C. D. Hyson and W. P. Hyson, ‘The Economic Law of Market Areas’, The Quarterly Journal of Economics, vol. 64, 1950, pp. 319–27.
E. Cheysson, ‘La statistique géométrique; ses applications industrielles et commerciales’, Le Génie Civil, vol. X, 1887, pp. 206–10 and 224–8.
On Cheysson, see R. F. Hébert, ‘A Note on the Historical Development of the Economic Law of Market Areas’, The Quarterly Journal of Economics, vol. 86, 1972, pp. 563–71.
K. H. Rau, Grundsätze der Volkswirthschaftslehre, eighth edn, vol. I, Leipzig und Heidelberg: Winter, 1868, pp. 216 and 370–1.
P. Kaufmann, Untersuchungen im Gebiete der politischen Oekonomie, betreffend Adam Smith’s und seiner Schule staatswirthschaftliche Grundsätze, Bonn: A. Marcus, 1829, pp. 8–9, 14–16.
J. Lang, Grundlinien der politischen Arithmetik, Charkow, 1811, pp. 117–19; see also Theocharis, 1983, pp. 109–11.
F. Lutz, ‘Uber die Umlaufsgeschwindigkeit des Geldes’, Jahrbücher für Nationalökonomie und Statistik, vol. 144, 1936 p. 387.
Rau’s formula had also been previously cited by K. F. Maier, Goldwanderungen, Jena, 1935, p. 9.
A. W. Marget, The Theory of Prices: A Re-examination of the Central Problems of Monetary Theory, London: P. S. King, 1938, pp. 10–11. For a later formulation of the equation of exchange by A.-E. Cherbuliez, see later in this book.
H. von Mangoldt, ‘Mangoldt’s Grundriss der Volkswirthschaftslehre’, Göttingische Gelehrte Anzeigen, 1863, pp. 2041–55. See also K. H. Hennings, ‘The Transition from Classical to Neoclassical Economic Theory: Hans von Mangoldt’, Kyklos, vol. 33, 1980, p. 670n.
W. Roscher, Geschichte der National-Oekonomik in Deutschland, München: Oldenbourg, 1874, p. 850.
Fisher, 1960 [1897], p. 176. Some mathematics is also found in: K. H. Rau, Malthus und Say über die Ursachen der jetzigen Handelsstockung, Hamburg, 1821, pp. 210–12 and 236–40; by the same ‘Ueber den kleinsten Umfang eines Bauerngutes’, Zeitschrift für die gesamte Staatswissenschaft, vol. 12, 1858, pp. 213–59 (see pp. 226–34).
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© 1993 Reghinos D. Theocharis
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Theocharis, R.D. (1993). Karl Heinrich Rau on Curves and Market Areas. In: The Development of Mathematical Economics. Palgrave Macmillan, London. https://doi.org/10.1007/978-1-349-12992-8_4
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