Transcribing the Tableau Économique: Input-Output Analysis À La Quesnay

Click to increase image sizeClick to decrease image size

Acknowledgments

In addition we would like to thank two anonymous referees for their valuable remarks on an earlier version.

Notes

Earlier versions of this paper were presented at the 6th Annual Conference of the European Society for the History of Economic Thought, University of Crete, Rethymno, Crete, Greece, March 14–17, 2002, and at the “UK History of Economic Thought Annual Conference 2004,” Kingston University, September 1–3, 2004. We are indebted to the participants at both conferences for discussions and comments.

¹The earliest zigzag may have been produced at the end of 1758, but will have been disseminated among a very select group of people only. The first Tableau known to a larger public was the so-called “third edition” of 1759. The last use by Quesnay of the formule version of the Tableau was in the article “[Second] Problème Economique” published in Physiocratie in 1767. For full accounts of the publishing history of the Tableaux see Weulersse (1910, I, pp. 61–71), Meek (1962, pp. 265–72), and Kuczynski and Meek (1972).

²The reason why, according to Herlitz, the zigzag could—and the Formula could no longer—demonstrate dynamic effects was that the zigzag was an “open economic system” in the sense that expenditure continually leaks from the system through exchanges with “other systems, including the foreign one” (Herlitz 1996, p.15). The final Formule version, by contrast, depicted a “closed economy” with a complete circular flow and no need for the “emergency expedient” of foreign exchange (Herlitz 1996, p. 16).

³He has reiterated this view recently: “There are […] still ways in which some sectors of a modern economy generate larger surpluses (such as tax revenue) than others, and a consideration of the strategic role in development of the high-surplus-creating sectors in the manner of the great classical economists is still illuminating” (Eltis 2000b: introduction xliv).

⁴Within the closed model landlords' consumption is in effect conceived as a technique with fixed proportions. See Dorfman et al. (1958) or Pasinetti (1977) for an exposition of the closed Leontief model.

⁵Maital (1972) and Korte (1972) first presented modeling exercises along these lines. Later discussions include Samuelson (1986).

⁶Phillips's units were in milliards of livres, thereby following the Formula. Another, equally unsubstantial difference in our reproduction of Phillips's transcription is that the classes of artisans and landlords have swapped places.

⁷However, Quesnay did use this final version to examine the effects of two other kinds of “disturbances”: the imposition of indirect taxes and a decline in agricultural prices. See “First Economic Problem” and “Second Economic Problem” respectively. This by itself demonstrates that it is not quite right to consider the Formula version as a device that was solely designed to illustrate the ideal, equilibrium state.

⁸Eltis, who in his earlier work on Quesnay concentrated on the original Zigzag, has in recent years emphasized the importance of the lesser known Précis version which made its appearance in the Philosophie Rurale. See Eltis (1996, 2000). This version is indeed interesting in the context of the modern controversy about Quesnay's model. Since the Précis resembles the Formula quite closely, it allows for a more easy comparison between the existing I-O interpretations and dynamic interpretations like that of Eltis.

⁹x_β is the right-hand Perron-Frobenius eigenvector of matrix M_β.

¹⁰For a more extended discussion of Forbonnais's critique of the Tableau (and that of other contemporaries of Quesnay), see Van den Berg (2002).

¹¹The earliest editions of the zigzag show balance; only in Ami des Hommes is a disequilibrium zigzag presented. The same is true for the Précis. Again the Formule is first presented in balanced form (1766) and then used in the analysis of disturbances (“First” and “Second Economic Problem” 1767).

¹²Cf. Eltis (2000b, pp. 7–8).

¹³See van den Berg (2000, p. 198, n.4 and 5).

¹⁴In this context it is important to note that the term grande culture does not only stand for modern agricultural technology, but also for modern contractual relations in agriculture. The following definition is given in the Encyclopédie:

Farmer [Fermier] … one who cultivates land owned by someone else, and who reaps the fruits on fixed conditions; that is what distinguishes the farmer from the sharecropper [métayer]: what the farmer gives to the proprietor, be it in money or in kind, is independent of the variability of the harvests. The sharecropper [on the other hand] shares the harvest itself, whether it is good or bad, in a certain proportion (Le Roy, “Fermier,” Encyclopédie, Vol. 6, p. 527).

¹⁵Some lack of clarity exists about the precise function of the manufactures purchased by the farmers: are they strictly capital goods that replace the ten percent of fixed capital (avances primitives) that is written off annually? Are they mainly consumption goods? Or are they a combination of the two? It seems fair to say that Quesnay is ambiguous on this point. Modern commentators differ about the interpretation of these “interest goods.” According to Meek (1962, p. 279, n.5) the manufactures purchased by the farmers are solely products required for their personal maintenance (clothing, etc.). The products required for the upkeep and replacement of the capital stock, on the other hand, are purchased within the agricultural sector. This interpretation has been criticized by Vaggi (1987, p. 48) who argues that at least some machinery used in agriculture must be understood to be purchased from the artisan class. For our purposes it suffices to say that if at least some part of x₂₁ represents manufactures for the personal consumption of farmers and their subordinates, then it is easy to envisage a deviation due to changes in consumption patterns.

¹⁶See also section V (second subsection) where these Quenaysian sub-models are discussed in more detail.

¹⁷Also, the amounts exchanged are related to relative sizes of the population in each class.

¹⁸We believe the use of fixed coefficients in production to distort all versions of the Tableau économique. The Formula version does in this respect not really differ from the zigzag and the Précis. Admittedly, Quesnay and Mirabeau only demonstrate the effects of an increase in luxury consumption with the aid of the latter two versions. However, in our opinion the reason for this is not that the Formula was unsuited to this demonstration due to (implicit) fixed coefficients.

¹⁹“Les moeurs se suivent & se repompent par réflet dans toutes les classes; l'enchaînement moral étant par-tout le même que l'enchaînement physique. Cette révolution d'un sixieme sera la même chez l'Artisan & chez le Cultivateur.”

²⁰For a discussion of the relation between Cantillon's ideas and the uniform shift assumed in the Tableaux depicting luxe de décoration see Gehrke (2000, pp. 2–3).

²¹Below we show that the assumption of a uniform shift is not essential for validating Quesnay's conclusions. That is to say, the direction of the shift has to be imitated by all classes but not to the same extent or percentage.

²²This is the opinion of Pressman (1994, pp. 127–28) who states: “The principle—that surpluses arise exclusively in the agricultural sector—shows up in all non-input-output reconstructions of the Tableau. But how can a surplus be shown in an input-output table where by definition inputs must equal outputs for each industry? […] Quesnay was able to represent agricultural surpluses since he did not consider ‘rental services’ as an input.”

²³See for the use of Perron-Frobenius eigenvalues for this purpose Kurz and Salvadori (1995).

²⁴Note that artisans do not pay rents.

²⁵We observe that the precise size of the shift (here equal to a fraction θ of the first row) is not important to generate the desired effect. Only the direction of the shift and the response of the system are relevant (cf. note 21).

²⁶See Eltis (1996, 2000a).

²⁷In the physiocratic literature, landleases of seven or nine years are discussed. The duration of two years which, according to our interpretation, is implied in Quesnay's statement may again have been chosen for its convenience in the subsequent calculations.

²⁸Quesnay and Mirabeau give an eloquent defense of this point of view on p. 311 of the Philosophie rurale (see the last paragraph of the passage in the appendix).

²⁹We have the coefficients matrix of section IV with β = 0.4 and corresponding intensities vector.

³⁰Quesnay's calculations stop after two years. Therefore this third shortfall does not occur in the original example.

³¹One may distinguish a number of arguments used in the physiocratic literature to support the doctrine. Especially unconvincing is the distinction between the productive sector as the one creating or multiplying wealth, as opposed to the sterile sectors which are said to merely change forms or add wealth (see, for example, Quesnay 1766b, pp. 205–207). Other unconvincing arguments are appeals to the primacy of agriculture and its presumed self-sufficiency.

³²To be precise, Quesnay and Mirabeau use the terms vrais (and véritables) revenus versus faux revenus, while Mercier contrasts revenus réels with revenus factices & simulés. Mirabeau (1763, pp. 106) gives as examples of “false” net incomes: “security payments, fees, [industrial] profits, pensions, house rents etc.” (les gages, les émolumens, profits, pensions, loyers de maisons, &c.).

³³Just like the fact that the profitability of agriculture is harmed does not immediately alter the conviction that it is fundamentally the productive core of the economy.

³⁴Here the a_ij stand for the intermediate input coefficients. Note that Leontief used a transposed form of notation.

³⁵Next to Leontief (1936, 1937, 1941) and Stone and Brown (1962), also Deming and Stephan (1940) usually are credited with the origin of the method.

³⁶A simple error is made here; 1840 − 0.5 × 294 = 1693, not 1703.