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The net product in the Formule du Tableau Economique: Lessons from a formalism


It is well known since Phillips (1955) that the Formule du Tableau Economique can be translated into an input–output table. Phillips's translation is however far from faithful. We propose a more accurate translation that attempts to take seriously all the features of Quesnay's formalism, by considering in particular its clear, although tacit, distinction between current and capital accounts. This formalism is first approached as an autonomous object of analysis, and then serves as the basis for discussing the imputation of the net product, by considering successively three candidates to that imputation (other than the productive class): the class of landowners, the sterile class and nature.

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Fig. 1


  1. See Dos Santos Ferreira (1990, 2002), Steenge and van den Berg (2001, 2016), van den Berg (2006), Dos Santos Ferreira and Ege (2013).

  2. See Dupuy et al. (2020) for a recent assessment of the Tableau as an anticipation of national accounting.

  3. See Gehrke and Kurz (1995).

  4. Two conceptions of the Tableau Economique, one corresponding to the zigzag version of 1758–9, the other to the Formule of 1766–8, are confronted by Herlitz (1996).

  5. At the same time, the highly abstract nature of the Tableau Economique, together with the closed character of physiocratic theory, may have played the role of a barrier to entry and consequently been an obstacle to its diffusion (see Argemi, Cardoso and Lluch 1995).

  6. An exactly equivalent translation of the Tableau as a directed graph was proposed by Gilibert (1987, Fig. 1).

  7. Charles (2003) also insists on the visual rhetoric of the Tableau and stresses the fact that “the history of the Tableau as an image cannot be equated with that of Quesnay’s abstract economic model” (pp.549–550). He further comments that “the style of formalization he eventually selected was primarily visual and not mathematical” (p.543). Although this remark may apply to the successive versions of the zigzag, we believe that the final formalism displayed by the Formule is much more than an image and can be fully transcribed into the algebraic Leontief formalism.

  8. Steenge and van den Berg (2007) propose a transcription of the Tableau Economique into an input–output model doing “more justice to Quesnay’s intentions” by allowing “for a specification of differing productive capacities of sectors and for disequilibrium approaches” (op. cit., p.332). We do not try to cover in this paper the disequilibrium trajectories considered by Quesnay and we are in general critical of the idea of attributing to specific sectors of an integrated system an inherent capacity to generate a net product. In any case, the transcription we propose here means to be literal to begin with, independently of Quesnay’s intentions.

  9. The “dynamic” multiplier results from the expansion of the static (Keynesian) multiplier (1 – c)−1 in the power series 1 + c + c2 + c3 + …, where the propensity to consume c is iteratively applied to the (unit) income. The expansion of the Leontief inverse (I A)−1 in the Neumann series I + A + A2 + A3 + , with A as the Leontief matrix of (unit) productive consumptions, generalises the preceding result. A similar expansion can be found in the Grand Tableau of the Philosophie Rurale (Mirabeau and Quesnay 1763), where half of the revenue of each of the two production sectors is iteratively spent in purchases to the other sector, represented by dotted lines drawing a double zigzag. In all these three series expansions, the “dates” do not succeed in real time and can only be used as a heuristic device. The pseudo-dynamics of the zigzag are fully abandoned in the Formule in favour of a stationary equilibrium approach. Some of the Observations which conclude the Formule evoke deviations from this stationary equilibrium but do not engage in dynamics proper.

  10. Steenge and van den Berg (2007, p. 341) transcribe the Tableau Economique into a 2 × 2 Leontief matrix A, opening up the model. They thus step aside from Phillips in the same terms as we do. By contrast, they keep positive the diagonal entry of the productive class, without further discussion.

  11. “On the right [read “on the left”], at the top, is the sum of the advances of the productive class, which were spent in the preceding year, in order to give rise to the harvest of the present year. Below this sum is a line which separates it from the column of the sums that this class receives” (Quesnay 1766 [1768, p. 62]).

  12. The interest on the primitive advances does however not appear as one of the items above the horizontal line of the productive class column, together with the annual advances. By contrast, the advances of the sterile class, at the upper end of the oblique line originating in the productive class, do appear as such an item. This discrepancy thus appears as an anomaly.

  13. The reader will find in van den Berg (2006) a detailed introduction to the life and work of Achille Nicolas Isnard (1748–1803). Also, for a discussion of Isnard’s criticism of physiocracy along the same lines as those of our own analysis, see Steenge and van den Berg (2001). More specifically, for a parallel discussion of Isnard’s example highlighted in this paper, see van den Berg (2002).

  14. Isnard applies the notation N to what he calls the mass of “richesses foncières”, the equivalent of Quesnay’s “avances primitives” or “fonds de richesses d’exploitation.”.


  • Argemi L, Cardoso J-L, Lluch E. (1995) Postface. La diffusion internationale de la Physiocratie: quelques problèmes ouverts. In: Delmas B, Demals T, Steiner P. (eds), La diffusion internationale de la physiocratie (XVIIIe-XIXe). Presses Universitaires de Grenoble, Grenoble, pp 473–480

  • Barna T (1975) Quesnay’s Tableau in Modern Guise. Econ J 85:485–496

    Article  Google Scholar 

  • Cartelier J (1976) Surproduit et Reproduction. La Formation de l’Economie Politique Classique. Presses Universitaires et François Maspéro, Grenoble

    Google Scholar 

  • Cartelier J (1991) L'économie politique de François Quesnay ou l'Utopie du Royaume agricole. In: Quesnay F, Physiocratie, Flammarion, Paris, pp 9–64

  • Charles L (2003) The visual history of the Tableau Économique. Eur J Hist Econ Thought 10:527–550

    Article  Google Scholar 

  • Dos Santos Ferreira R (1990) De Petty à Sraffa, ou le triomphe de l’Arithmétique Politique. In: Arena R, Ravix JL (eds) Sraffa trente ans après. Presses Universitaires de France, Paris, pp 77–97

    Google Scholar 

  • Dos Santos Ferreira R (2002) Aristotle’s analysis of bilateral exchange: An early formal approach to the bargaining problem. Eur J Hist Econ Thought 9:568–590

    Article  Google Scholar 

  • Dos Santos Ferreira R, Ege R (2013) General equilibrium as competitive equilibrium: The significance of Walras’ achievement from a Cournotian viewpoint. Eur J Hist Econ Thought 20:625–645

    Article  Google Scholar 

  • Dupuy R, Le Masne P, Roman P (2020) From the accounts of Philosophie Rurale to the phyisiocratic Tableau: François Quesnay as a precursor of national accounting. J Hist Econ Thought 42:457–481

    Article  Google Scholar 

  • Gehrke C, Kurz HD (1995) Karl Marx on Physiocracy. Eur J Hist Econ Thought 2:53–90

    Article  Google Scholar 

  • Georgescu-Roegen N (1971) The Entropy Law and the Economic Process. Harvard University Press, Cambridge

    Book  Google Scholar 

  • Gilibert G (1987) Circular flow. In: Eatwell J, Milgate M, Newman P (eds) The New Palgrave: A Dictionary of Economics, vol 1. Macmillan, London, pp 424–426

    Google Scholar 

  • Herlitz L (1996) From spending and reproduction to circuit flow and equilibrium: the two conceptions of Tableau économique. Eur J Hist Econ Thought 3:1–20

    Article  Google Scholar 

  • Isnard AN (1781) Traité des Richesses. François Grasset, Lausanne

    Google Scholar 

  • Leontief W (1951) The Structure of American Economy 1919–1939: An Empirical Application of Equilibrium Analysis, 2nd edn. Oxford University Press, England

    Google Scholar 

  • Maital S (1972) The Tableau Economique as a Simple Leontief Model: An Amendment. Q J Econ 86:504–507

    Article  Google Scholar 

  • Malthus TR (1820) Principles of Political Economy, 2nd edn. W. Pickering, London, p 1836

  • Marx K (1862) Theorien über den Mehrwert. In: Marx K, Engels F (eds) Erster Teil (Band 26). Dietz Verlag, Berlin, p 1965

    Google Scholar 

  • Marx K (1893) Das Kapital: Kritik der politischen Ökonomie. In: Engels F (ed) Buch II: Der Zirkulationsprozess des Kapitals. Dietz Verlag, Berlin, p 1963

    Google Scholar 

  • Meek RL (1960) The Interpretation of the “Tableau Economique.” Economica 27:322–347

    Article  Google Scholar 

  • Mirabeau VR de, Quesnay F (1763) Philosophie rurale, ou Économie générale et politique de l’agriculture. Les Libraires Associés, Amsterdam

  • Petty W (1662) A Treatise of Taxes and Contributions. N Brooks, London

  • Phillips A (1955) The Tableau Économique as a Simple Leontief Model. Q J Econ 69:137–144

    Article  Google Scholar 

  • Quesnay F (1757) Impôts. In: Salleron L (ed) François Quesnay et la Physiocratie (Tome II Textes annotés par). INED 1958, Paris, pp 579–617

  • Quesnay F (1766) Analyse de la formule arithmétique du Tableau Economique de la distribution des dépenses annuelles d’une Nation agricole (Journal de l’Agriculture du Commerce et des Finances Juin 1766 11–41). In: du Pont de Nemours PS (ed) Physiocratie, ou Constitution naturelle du gouvernement le plus avantageux au genre humain. Leyde 1768, Netherlands, pp 45–98

  • Quesnay F (1767) Maximes générales du Gouvernement économique d'un Royaume agricole. In: du Pont de Nemours PS (ed) Physiocratie, ou Constitution naturelle du gouvernement le plus avantageux au genre humain. Leyde 1768, Netherlands, pp 105–172

  • Samuelson PA (1982) Quesnay’s “Tableau Economique” as a Theorist would Formulate it Today. In: Bradley I, Howard M (eds) Classical and Marxian Political Economy. Essays in Honour of Ronald L. Meek. MacMillan, London, pp 45–78

    Chapter  Google Scholar 

  • Sraffa P (1960) Production of Commodities by means of Commodities: Prelude to a Critique of Economic Theory. Cambridge University Press, England

    Google Scholar 

  • Steenge AE (2000) The Rents Problem in the Tableau Economique: Revisiting the Phillips Model. Econ Syst Res 12:181–197

    Article  Google Scholar 

  • Steenge AE, van den Berg R (2001) Generalising the Tableau Économique: Isnard’s Système des Richesses. Int J Appl Econ Econ 9:121–146

    Google Scholar 

  • Steenge AE, van den Berg R (2007) Transcribing the Tableau Économique: Input-Output Analysis à la Quesnay. J Hist Econ Thought 29(3):331–358

    Article  Google Scholar 

  • Steenge AE, van den Berg R (2016) Tableaux and Systèmes: Early French contributions to linear production models. Cah D’économie Politique Papers Polit Econ 71:11–30

    Google Scholar 

  • Tsuru S (1942) On Reproduction Schemes. In: Sweezy PM (ed) The Theory of Capitalist Development: Principles of Marxian Political Economy. Monthly Review Press, New York

    Google Scholar 

  • Turgot ARJ (1766) Réflexions sur la Formation et la Distribution des Richesses. In: du Pont de Nemours PS (ed) Éphémérides du citoyen ou Bibliothèque raisonnée des sciences morales et politiques. McMaster University, Hamilton, 1769–1770

  • Vaggi G (1987) Quesnay, François. In: Eatwell J, Milgate M, Newman P (eds) The New Palgrave: A Dictionary of Economics, vol 4. Macmillan, London, pp 22–29

    Google Scholar 

  • van den Berg R (2002) Contemporary responses to the Tableau Economique. In: Boehm S, Gehrke C, Kurz HD, Sturn R (eds) Is There Progress in Economics? Knowledge, Truth and the History of Economic Thought. Edward Elgar, Cheltenham

    Google Scholar 

  • van den Berg R (2006) At the Origins of Mathematical Economics: The Economics of A.N. Isnard (1748–1803). Routledge, London

    Google Scholar 

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Correspondence to Rodolphe Dos Santos Ferreira.

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An early, close, version of this paper was presented at the annual Conference of the European Society for the History of Economic Thought in Graz (24-27 February 2000) and had then and during the following couple of years a limited circulation. The present version went through several improvements, some of them suggested by the detailed comments of two anonymous referees to whom the authors are quite grateful.

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Dos Santos Ferreira, R., Ege, R. The net product in the Formule du Tableau Economique: Lessons from a formalism. Port Econ J (2022).

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  • Quesnay
  • Tableau Economique
  • Net product
  • Formalism
  • Input–output analysis

JEL Classification

  • B11
  • B16
  • D57