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Abstract
A newly recovered manuscript contains Turgot’s calculations of the harmful effects of indirect taxes in comparison to the imposition of a direct tax on the freely disposable incomes of landowners. It shows an unexpected side of Turgot, who was thought to have been reluctant to apply mathematics to economic reasoning. His assumptions and mathematical method are explained and compared to Quesnay’s notion of repompement and Du Pont’s Courbes politiques.
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Acknowledgments
We thank the two anonymous referees for their suggestions and Frédéric Moyer for his assistance in attempting to date manuscripts.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Notes
1 Unless indicated otherwise, translations are our own.
2 There does not seem to exist any subsequent commentary on, or investigation of, Schelle’s remarks. Neither is there any earlier mention of Turgot’s calculations. Crucially, Du Pont’s edition of Turgot’s OEuvres (1808–1811), which before Schelle was the principal source for students of Turgot’s work, lacks any reference to them. Whether Du Pont did in fact know Turgot’s calculations is an issue considered in section 4 below.
3 The sale of the family archive of the Turgots was completed in February 2015. See the official press release: http://www.culture.gouv.fr/Presse/Archives-Presse/Archives-Communiques-de-presse-2012-2018/Annee-2015/Acquisition-par-l-Etat-des-manuscrits-Turgot. With their entry into the Archives Nationales in March 2015 the collection that Schelle and others called the Lantheuil archive has been renamed Fonds Turgot.
4 The reason to emphasise the fact that this manuscript is ‘still present’ is that regrettably Turgot’s papers have not, as the government’s press release would have it, ‘reached us practically intact’ (see previous note). A significant number of other writings that Schelle did transcribe for his edition of Turgot’s Works from originals in the Lantheuil archive have since gone missing. For some instances see below notes 12, 21, 52 and 60.
5 Schelle (ii, 308–310); AN 745AP/42, dossier 11, images 2–7. The watermark and countermark are the same as what is found in the paper on which ‘Appréciation’ was written (AN 745AP/42, dossier 11, images 11–14). In addition, superimposition of the papers on a light box shows that the stretches on the paper are identical. This makes it highly likely that the paper used for both drafts was produced at the same place and time. We are grateful to Frédéric Moyer for providing us with this detailed information.
6 This Plan, of which the manuscript version is lost, was presumably intended as advice to the controller-general Bertin (1719–1792) who was dismissed in December 1763; hence its dating to that year (see Du Pont iv, 203; Schelle ii, 293–294; Groenewegen Citation1977, xxi–xxiii).
7 In volumes 2 and 3 of the collected works Schelle included a range of Turgot’s official missives and letters about the implementation and assessment of various taxes in the Limousin. Still others remain unedited in the Archives Départementales of Haute-Vienne in Limoges (see Kiener and Peyronnet Citation1979, 325).
8 These are the two works that are specifically mentioned in Turgot’s Plan (see Schelle ii, 305).
9 Here Turgot was not very clear which of these components of cost corresponded to the ‘opportunity cost’ of capital. This notion would be developed more distinctly in his later writings where he argued that the necessary return on capital employed in agricultural production would establish ‘a kind of equilibrium’ with those of alternative allocations of a same sum. While that notion does not figure prominently in the physiocratic literature (although it occurs in some places), Turgot’s more ambiguous formulation in the passage quoted above is not unlike, for example, the discussion in Philosophie rurale (ch. ix, 189–190) about ‘l’intérêt du capital des avances’.
10 The idealised portrayal of the determination of the terms of land leases under the pressure of competitive bidding by commercial farmers was common amongst physiocratic authors in their more theoretical writings (see van den Berg Citation2000, 198 n.5), even while they recognized that the reality was different in large parts of rural France. In the Reflections too Turgot insisted that ‘[….] when competition among [the farmers] is very keen [fort animée], they give [the proprietor] the whole of this surplus, since the proprietor will let his land only to the man who offers the highest rent’ (Groenewegen Citation1977, 72; Schelle ii, 571). He developed this point in greater detail in the sixth letter on the grain trade of November 1770 (see Schelle iii, 305–306).
11 See Schelle (ii, 430–433) for the text of Turgot’s announcement of the prize competition of the Royal Agricultural Society of Limousin. Further details about the essay competition are provided by Decroix (2006, 97–99) and Orain (Citation2008, 60–62).
12 Letter dated 7 September 1766; translation in Groenewegen (Citation1992, 14, emphasis added). The original reads: ‘pour engager à travailler sur l’appréciation des effets de l’impôt indirect, évaluation encore incertaine pour moy quant à la quotité, que pour faire traiter la question générale, sur laquelle j’ay une conviction entière’. It should be noted that the copy of this letter which at one time was present in the Lantheuil collection, and of which Schelle (ii, 500–503) published a transcript, is now missing from the Fonds Turgot. Fortunately, the original is preserved in the National Library of Scotland (MS23157 no. 85).
13 Admittedly, as was suggested by one of the referees, the use of the same phrase in the two documents does not preclude the possibility that Turgot meant something less precise when using the term appréciation in his letter to Hume, since it may refer to various kinds of evaluations of the effects of indirect taxes, either of an empirical or theoretical nature.
14 For the first point see above n.5; for the second point see note 39. There is also no evidence that Turgot made his calculations in direct response to submissions to the prize competition. For what it is worth, the paper on which Turgot wrote his reports about the submissions of Saint-Péravy (AN745AP/40 dossier 2, images 124–133) and Graslin (ibid., images 134–139) differs from that of the Appréciation.
15 Translation Groenewegen (Citation1992, 24). This letter is dated 8 March 1768. The original reads: ‘car c’est une matiere que j’ay a coeur et que je crois susceptible de demonstration’ (National Library of Scotland MS23157 no. 88). The sole publication of this letter appears to have been in Hill Burton (Citation1846, 162–163).
16 Charles and Théré argue that ‘[c]learly, Turgot did not share Quesnay’s epistemology. For him, neither sensory evidence nor calculations were needed to create a set of economic principles.’ They suggest that Turgot would have been opposed to Quesnay’s entire quantitative approach to economic analysis. A more measured position is that of Larrère (Citation1992, 17–22) who argues that Turgot rejected some of the overly general assumptions on which Quesnay and his followers based their calculations such as constant returns on advances in agriculture. This is indeed very clear from Turgot’s criticism of Saint-Péravy’s calculations (see note 30 and van den Berg Citation2000). But such criticism did not imply a general rejection of the application of calculations to economic questions.
17 In the Fonds Turgot the set of calculation is immediately preceded by another unfinished draft that develops similar principles, entitled Effets de l’impôt indirect (AN 745AP/42, dossier 11, images 8–10). The latter draft Schelle did include in his edition of Turgot’s collected works (see Schelle, ii, 310–312). It should be noted that the paper on which this draft was written, differs from that used for the preceding and subsequent drafts (see note 5 above). This may mean that it is of a somewhat different date. Schelle (ii, 310), without the benefit of a material comparison, suggested the possibility that this draft was written ‘after 1763’. We simply cannot be sure.
18 For a recent introduction to the complexities of the fiscal regulations of the ancien régime see Chanel (Citation2016). Turgot did of course have an extensive practical experience with these complexities.
19 He called this possibility of different levels of competition in different industries an ‘external circumstance’ [circonstance étrangère] implying that the normal or ‘natural’ situation was one of ‘full competition’. About the conception of full competition in physiocratic writings see van den Berg (Citation2004).
20 Hume made this argument in a letter he probably wrote in late September 1766. Léon Say (1888, 53–55) first published in the original English the part of the letter containing this argument -though not the preceding account of Hume’s ongoing troubles with Rousseau. It was published in full in Greig (1932, 88–95). The original is in the Fonds Turgot (AN 745AP/41, dossier 2, images 108–110).
21 ‘le rapport de l’offre et de la demande’. Turgot to Hume, 25 March 1767; translation Groenewegen (Citation1992, 18). The copy of this letter on which Schelle (ii, 658–665) based his transcript is absent from the Fonds Turgot. The original of Turgot’s letter is still present in the National Library of Scotland (MS23157 no. 86).
22 ‘the fundamental price […] for a commodity is what the thing costs to the workman. In the case of the workman’s wage [le salaire de l’ouvrier], the fundamental price is the cost of his subsistence. It is impossible to tax the wage earner without increasing the price of his subsistence, since to his former expenditure that of the tax must be added. The fundamental price of labour is therefore raised. Now, although the fundamental price is not the immediate basis of the current value, it is, however, a minimum below which it cannot fall. For if a merchant loses on his wares, he ceases to sell or manufacture; if a workman cannot live by his labour, he becomes a beggar or a migrant. This is not all: the workman must have a certain profit, to meet contingencies and raise a family. In a nation where commerce and industry are free and active, competition settles this profit at the lowest possible rate’ (Groenewegen Citation1992, 18; Schelle ii, 663).
23 For Turgot’s discussions of the differences between these two systems see especially Schelle (ii, 305–306 and v, 517–518). He neatly summed up the essential difference as follows: ‘Under the first system it is the rate of the contribution of each proprietor in relation to the sum total of his revenue that is certain and determined by law, and the sum that the State draws to support public expenditure is uncertain. By contrast, under the second system the sum demanded by the State is certain and the rate at which each proprietor contributes out of his revenue is uncertain’ (ibid. v, 518). See Delmas (Citation2009, 82–83) for a brief general overview of the attitudes of French advocates of fiscal reform in the 18th century towards le système des impôts de quotité versus le système des impôts de répartition.
24 Translation Groenewegen (Citation1992, 17; emphases added). As pointed out in n.21, the draft version of the letter on which Schelle based his transcript is now missing. There are some minor differences in wording between Schelle’s transcript and the sent letter in the National Library of Scotland.
25 The idea that counting the incomes of artisans would be a double emploi is typical for the physiocratic demarcation of the boundaries of ‘national income’, according to which only agriculture contributed. This does of course imply the view that non-agricultural activities were ‘non-value-adding’. Elsewhere Turgot’s position on this issue is complicated due his insistence on the regular existence of profit in manufacturing and trade. In the Reflections he appears to have wanted to reconcile the idea that only agriculture was capable of generating a surplus over costs of production with the idea that some of this surplus was distributed as incomes earned outside agriculture. For discussions see Faccarello (Citation1990) and van den Berg (Citation2010, 50–51).
26 For instance, his reason for choosing the sum of 2100 million for the total product may simply have been that it neatly divides by three. It does not correspond precisely with any of the figures Quesnay chose in his Tableaux for réproduction totale. The most that can be said is that in some of the early zig-zags based on annual advances of 600, the total reproduction is calculated at a somewhat comparable magnitude of 2705 (see Quesnay Citation2005, 446).
27 Turgot owned a copy of Cantillon’s Essai (see Tsuda Citation1974, 494) and in a letter written in 1771 referred to this work in a positive manner (Schelle iii, 500). There is some evidence that he already read Cantillon in the 1750s (I make this point in more detail in van den Berg Citation2019).
28 Quesnay had written this article in the late 1750s, probably 1757 or 1758, for inclusion in the Encyclopédie. After that work ran into problems with the censor, he had withheld it and it remained unpublished until 1908. The relevant passage reads: ‘the expenses which the husbandman [laboureur] incurs in order to cultivate land […] are about equal to two-thirds of the product of the harvest, [and] ought to be returned to the husbandman through the harvest itself in order to be expended anew in the cultivation of land. Thus two-thirds of the harvest forms no part of the profit [profit] which is yielded by this harvest. This kind of wealth, therefore, which is used in the cultivation of land, ought not to bear the burden of any taxes at all, for if any part of it is taken away from the cultivator the products of landed property will be correspondingly reduced’ (translation Meek Citation1962, 103; for the original French see Quesnay Citation2005, 218).
29 In fact, the only known copy of Impôts, preserved in the Archives Départementales of Haute-Vienne in Limoges, is the one once owned by Turgot.
30 The tax burden on the net product would increase from 3/7 to 1/2. One should not conclude from this that Turgot meant that all proprietors would pay the same increase in absolute terms. In his other writings, especially his Observations sur le mémoire de Saint-Péravy, he carefully developed the insight that different landed properties, both due to different natural fertilities of soils and due to investments to improve productivity of the land, yielded different amounts of rent. An increased level of tax on the net product was to be raised in proportion to the rents collected, those lands yielding little rent paying less in absolute terms.
31 ‘cette augmentation influe encore sur toutes les depenses et sur celles de l’impot. mais l’augmentation devient toujours de plus en plus petite [….] [une] serie decroissante’
32 This fraction, which he obtained by dividing 65,365,131 by 1.5 billion, is indeed very close to the precise result of 65,383,113/1.5 billion, which gives a fraction of 1/22.94 (see appendix 2A).
33 The number 34,782,608 is exactly 800 millions divided by 23 (ignoring the remainder, as he did throughout).
34 He took care to point out that this involved another ‘abstraction’, namely from the fact that it may take time for farmers to renew the terms of their leases after the effects of additional taxes were felt. Turgot pointed out that he assumed that the change in tax burden for farmers could be ‘considered anticipated, [hence] we suppose that the farmer could immediately pass on [renverser sur le champ] to the proprietor the effect of the indirect tax’ (cf. Turgot’s use of the term l’impôt anticipé, in accordance with physiocratic usage, in Schelle ii, 432). Here, presumably, Turgot did not want the time it would take for adjustments of lease contracts to complicate his main argument. On another occasion, however, he did not fail to provide a detailed explanation of the significance of lags in the adjustments of terms of lease contracts for the profitability of agricultural enterprises (see Schelle iii, 301–303). By similarly emphasising the temporary inflexibility in contractually agreed rent payments for the incidence of taxation in his Appréciation, he could have made more of the immediate financial burden that indirect taxes would place on cultivators. Arguments along these lines were developed, for example, by Le Mercier de la Rivière (Citation1767, 277–278) or Baudeau (Citation1768, 174–186).
35 This was ad hoc in the sense that earlier in the memo Turgot had not distinguished between avances annuelles (the means of production used up within one agricultural cycle) and the avances primitives (the means of production lasting more than one cycle). One would have thought that some of the 800 million spent by farmers on commodities produced by blacksmiths, wheel wrights, barrel makers etc. would be classed as avances primitives and therefore the increase in prices of such goods would already have been included in the 4.4% increase. Perhaps one should therefore say that adding another 10% was something of an afterthought. This percentage was often used in the physiocratic literature to account for the costs of avances primitives, and it was sometimes estimated as a percentage of avances annuelles (see e.g., Quesnay Citation2005, 469).
36 Here he made a small error: taking 38,260, 868 away from 400,000,000 gives 361,739,132. Therefore Turgot was out by 200.
37 In effect Turgot conceived land payments as ‘unearned incomes’. That is to say, they were not payments for the delivery of a service, of which the price were to be raised when its ‘cost of production’ increased. The same conception of rent in physiocratic theory more widely, and in the Tableaux specifically, posed problems for later ‘translations’ of the physiocratic depiction of the economic process into modern input-output terms. For a discussion of this point see Steenge and van den Berg (Citation2007, 340).
38 Turgot did not state his reason for using 1/24 instead of 1/23 (or 1/30 instead of 1/29 in his alternative calculation). Presumably he intended it as a correction for the fact that he was now calculating a reduction in a sum, rather than an increase.
39 The (non-digitised) sixth page of the document remained empty. This suggests that Turgot stopped rather than that his continuation has gone missing. In the absence of further textual evidence it is vain to speculate whether Turgot meant to continue or revisit this particular piece of analysis.
40 In the alternative calculation the numbers are 51,482,811 (the total sum of indirect taxes, see above p. 8) minus 42,666,698 (the sum of three deductions arrived at using the same logic as in the original calculations). This gave a remainder [Reste] of 8,816,112.
41 Thanks to his social status and the intervention of powerful contacts on his behalf, Mirabeau’s incarceration, in comfortable surroundings of the chateau de Vincennes, only lasted two weeks, followed by an exile to his private estate for a mere two months. Nevertheless, the episode warned him and other économistes not to challenge the fiscal policies of the government and the interests of the financiers too openly.
42 Letter dated 20 February 1766 (Schelle ii, 504–515). The identity of physiocratic author of the specific Mémoire sur l’impôt anticipé on which Turgot was here commenting (ibid. 514) is not certain. For a discussion see Quesnay (Citation2005, 1299–1300). In the official call for the prize competition Turgot made the same point that ‘in some [physiocratic] writings’ the costs of indirect taxes had been estimated to be ‘double of what is paid if the State had demanded the proprietors directly the same sum as the public Treasury draws from indirect taxation’ (Schelle ii, 433).
43 This assumption is found already, for example, in the Tableau that purported to analyse the detrimental effects of taxation in the sixth part of Mirabeau’s l’Ami des hommes (1760): ‘The Tableau demonstrates the destructive effects of Taxes surcharged and absorbed by the charges of collectors and collection [frais de régie & de perception]. It is constructed on the basis of 400 million of net product, or of total revenue; & two hundred million of Taxes, with a surcharge of [another] two hundred million for costs of collection’ (Quesnay Citation2005, 511). Even though this doubling was here no more than an assumption, whether or not informed by some ‘empirical’ estimation, Mirabeau would write about it as if it was the result of a rigorous demonstration (see his letter of November 1762, cited by Weulersse Citation1910, ii, 356 n.3)
44 See e.g., Schelle (ii, 648; iv, 515) for the idea that once indirect taxes become too high, people are prepared to assume the risks involved with frauds and the smuggling of contraband; or about the high costs involved with collecting indirect taxes (Schelle iv, 515).
45 This paper cannot deal with the physiocratic discussions of the theory of taxation as a whole. Delmas (Citation2009) is a useful recent attempt to give an impression of this large topic. Delacroix (2006) provides the larger French context of fiscal thought during the Ancien Régime. As indicated, apart from Mirabeau’s Théorie de l’impôt and Philosophie rurale, Quesnay’s articles Impôts probably exercised most influence on Turgot’s conceptions in the Appréciation. Quesnay’s Second problème économique, first published in Physiocratie (1767–1768), discussed below, was his most extensive later attempt to trace the effects of indirect taxes. Other more notable physiocratic discussions of the theory of taxation in connection to Turgot’s views are Le Mercier de la Rivière (Citation1767, ch. xxvii to xxxiv), Baudeau (Citation1768), and Le Trosne (Citation1770, 1779). The latter massive work developed in much greater detail ideas that were similar to the Mémoire sur les municipalités (see below).
46 Hishiyama (Citation1960, 3–4) showed that the mechanism of the dynamic Tableaux can be written as a diminishing series. Eltis (Citation1975) adopted the same formalisation. For a discussion of the modern reception of the dynamic Tableaux in relation to Input-Output transcriptions of the Tableaux see Steenge and van den Berg (Citation2007, 332–336). Arguably, the only other significant instance in the same period of the application of a diminishing series to an economic problem is the analysis in Auxiron (1766) of the rebalancing of the sizes of the agricultural and artisan sectors after a ‘disturbance’ (a doubling of the population in an economy facing diminishing returns in agriculture). This takes the form of an oscillating series that is quite different from what is implied in either Turgot’s Appréciation or Quesnay’s Tableaux (see van den Berg and Dhesi Citation2004).
47 Instead, the displacement took the familiar form of a relative shift in landowners’ expenditures towards the ‘sterile class’. Thus in the sixth part of l’Ami des Hommes the Tableau that purported to show the ‘dépredations relativement à l’impôt’ showed a shift from the ideal spending pattern of half of the rent incomes on each class to ¼ to the ‘productive’ class and ¾ to the ‘sterile’ class (Quesnay Citation2005, 510–511).
48 While Quesnay did not use the term in his Essai physique sur l’oeconomie animale (1747), Buffon and Daubenton in their Histoire naturelle (1766, i, 123) described the production of semen as a repompement continuel in the animal body. Tissot (OEuvres 1770, viii, 636) explained the build up to an epileptic fit as a repompement of fluids in the body. In the Encyclopédie the same term was used in several medical entries: ‘Impureté’ (vol. 8, 636) stated that some physicians justified the bleeding of patients to avoid the repompement of impurities in the blood; ‘Inflamatoires, maladies’ (vol.8, 727) noted that inflammations involved a repompement dangereux in the blood; also see ‘Lait, maladie de’ (vol. 9, 211) and ‘Métastase’ (vol. 10, 441).
49 Before he became Quesnay’s follower Mirabeau (Citation1756, 101) had already compared the need for government to make money circulate throughout the state to the action of the heart, which continually pumps and pushes [repompe & repousse] blood. In Théorie de l’impôt (1760, 171) he used the word somewhat differently to indicate the surcharges of tax collectors: ‘But always the activities of contractors, which do not yield the treasury more than 115 million in tax revenues, surcharges [repompe-t-elle] at least 60 million on the 200 [million] of taxes expended in the Kingdom’. These uses differ from the use of the noun repompement in the passage quoted from Philosophie rurale (the term is also used on page 266 of the same work) where it seems to denote the ‘inflationary’ effect of indirect taxes. Later Quesnay used repompement in his ‘General Maxims’ (Meek Citation1962, 262; Quesnay Citation2005, 596). Also see n.51 below.
50 Interestingly, in his editor’s introduction to Quesnay’s ‘Second problème économique’ in Physiocracy, Du Pont made a link between the Doctor’s attempt to analyze the different effects of direct and indirect taxes and Turgot’s effort to stimulate work on this issue. It was, Du Pont wrote, ‘a truly interesting question for the happiness of nations, which currently occupies a large number of learned men, in England […] and in France, where the Royal Society of Agriculture of Limoges has made it the subject of one of its prize competitions’ (Quesnay Citation2005, 619).
51 The 73 million was composed of 1/11th of ‘direct taxes of 300 millions’, 1/11th of ‘the portion of the indirect taxes amounting to 250 millions which accrues to the sovereign’ and 1/11th of ‘250 millions of costs entailed by the indirect taxes’ (Meek Citation1962, 197; cf. Quesnay Citation2005, 630). Apparently, Quesnay took only these components into account, and not the expenditures of the ‘productive class’ or those of the proprietors, because the former alone related to taxation. Beyond that Quesnay’s reasoning is hard to follow (cf. Pressman Citation1994, 102). A similar thing may be said of a later work that appears to calculate the size of repompement after the introduction of an indirect tax. In Loix naturelles de l’agriculture et de l’ordre social, Butré argues: ‘The public revenue is no more than an illusory mass, because of the repompement undergone by the indirect tax, which absorbs a quarter of it. Such is the effect of this disastrous collection, it surcharges all expenditures, alters all exchange values, and gives them a false appearance that is but a pure illusion, through the false prices that it gives to consumption goods’ (Butré 1781, 167). How exactly Butré arrived at the fraction of one quarter is not clear. On page 166 he stated that in his example the indirect tax was 280 million and the costs of collection 120 million; this 400 million is a quarter of the total expenditures of ‘nearly 1600 million’. But how this relates to the estimate of a repompement of one quarter is hard to say. About Butré’s quantitative contributions see Sabbagh (Citation2017) and Charles and Théré (Citation2016). Judging by a couple of denigrating remarks in his letters to Du Pont, Turgot did not have a high opinion of Butré (Schelle ii, 520–521; iii, 15).
52 This writing was another unfinished manuscript, composed in 1777 after his dismissal and intended for the instruction of Benjamin Franklin at the time of the American Revolution. As Albertone (Citation2014, 112–118) explains, even though Franklin was an enthusiastic partisan of the economic principles of the physiocrats, he ended up rejecting the impôt unique for practical reasons. Unfortunately, these materials as transcribed by Schelle (v, 510–519) from the Lantheuil archive are missing from the Fonds Turgot. Another copy is found, however, in AN AP154/II/155. I thank one of the reviewers for this reference.
53 The mémoire he read on that occasion is apparently lost (for details see Spiegel Citation1955, iv, n.6). Du Pont’s letter was only published in 1892 by Carl Knies, though without the intriguing diagram that represents his decreasing series. Not until 1955 did Du Pont’s numerical analysis receive much attention, when Spiegel published an English translation of the letter and included the diagram. Subsequently, Theocharis (Citation1961) added it to the expanding collection of ‘early contributions’ to mathematical economics that had started to be compiled since the late 19th century. Also see Maclain (Citation1977, 132–135). Recently, Charles and Théré (Citation2016, 318, n.25) have found that the diagram, as published by Spiegel, can no longer be located in the Margrave of Baden family archive. Instead they have discovered an early draft of the diagram, reproduced in Excerpt 3 of their article.
54 Enlisting the assistance of mathematicians would be ‘a good idea […] to gain, through their support, secured by their own labor, the support of a large number of persons with whom their opinion carry weight’ (Spiegel Citation1955, p. 16). It was for this reason, he noted, that he had sent a copy of his mémoire to Daniel Bernoulli. The latter’s response is not known. In this connection one should also note the one surviving letter of a correspondence between Du Pont and Isnard (Eleutherian Mills Historical Library W2-27). In this letter, dated 28 December 1773, ‘Du Pont discusses the principles of differential calculus in a manner that Isnard, who at the time was teaching this subject, would have recognised as rather inept’ (van den Berg Citation2006, 12). There is no mention in the letter of the application of mathematics to economic theory. Therefore the possible connection with Courbes politiques is limited to the fact that both writings show Du Pont’s interest in this period with phenomena of incremental quantitative change. For a more general discussion of Isnard’s mathematical contributions in comparison to Du Pont and Butré see Charles and Théré (Citation2016, 318–320).
55 For example ‘the baker must include among the cost of his subsistence, which determines his wage, his own and his family’s consumption of meat. The increase in the price of this [meat] must further raise the price of his bread’ (SpiegelCitation1955, 3). In reality, he explained to his young correspondent, there were of course not just two professions but ‘over one hundred’, such as ‘wool merchants, drapers, tailors, tanners, shoemakers’ etc. which were ‘all mutually interrelated’ (ibid. 4).
56 One would perhaps expect a fall in prices once taxes were removed, also because, as we just saw, at the beginning of his letter Du Pont described the increases in prices subsequent to the introduction of indirect taxes. Later on he argued, however, that the taxes produced a margin between producer prices ‘at first hand’ and consumer prices. The removal of the taxes would give rise to a reduction of consumer prices at the same time as allowing a rise in producer prices. Higher prices for farmers would allow them to extend production to less fertile lands (see Spiegel Citation1955, 7–8) giving rise to larger agricultural output and higher rent payments which ‘would give the owners of land an opportunity for diffusing wages amongst artisans and for stimulating activities which would supply the latter with the means to acquire goods and to multiply their satisfactions’ (ibid. 9). The discussion on these pages is reminiscent of Turgot’s discussion of differential returns in agriculture in his report on the prize essay of Saint-Péravy of 1767, but which admittedly had not been addressed in the Appréciation; cf. above n.30.
57 This work was started in 1771 as a series of letters between Turgot and Condorcet. Not only did Du Pont present a version of this work at Mirabeau’s Tuesday dinners but he also sent a copy to the Margrave of Baden (see Knies Citation1892, 233ff; Schelle i, 4; iv, 3; iii, 513–539; AN745AP/41 dossier 2, images 64–68). Of course, a more famous example of a work that Turgot entrusted to Du Pont was the manuscript of the Réflexions, which was subsequently published in the Ephémérides du citoyen.
58 A somewhat different question is whether Du Pont got to read Turgot’s Appréciation eventually. This is likely. Certainly from just after his friend’s death in March 1781 Du Pont had access to his private papers, acting as his literary executor, and claiming in a letter to Malesherbes of April 1781 that ‘only I have had all his manuscripts’ (cited in Schelle 1888, 213, n.1). He kept possession of various manuscripts until at long last he produced Turgot’s OEuvres in 1808–1811, in the mean time even carrying some of them across the Atlantic and back (see Saricks Citation1965, 314–315). Given his authorship of Courbes politiques one would think that Du Pont should at least have been interested in Turgot’s calculations. Maclain (Citation1977, 135) has suggested that Du Pont did not return to his one mathematical contribution after 1774, but this is contradicted by the fact that as late as 1796 he presented a version of Des Courbes politiques to the Class of Moral and Political Sciences of the French National Institute (see La Décade philosophique, littéraire et politique, issue 28 June 1796, 141; also see Staum (Citation1996, 293, n.9) who has a reference to the Archives de l’Institut, Académie des Sciences morales et politiques document A3, Procès-verbaux of the presentations to the class of 12 floréal year IV (1 May 1796).
59 In correspondence from the mid-1760s onwards Turgot regularly commented on Du Pont’s publications and his editorial activities. The latter also sometimes sent him drafts of his writings for comment. But the only indication that he may also have sent Turgot a draft of his Courbes politiques comes in a letter dated 14 March 1774 (which would be about the right time) which Turgot starts with: ‘I have received, my dear Du Pont, your little sheet together with your manuscript about prices’ (‘J’ai reçu, mon cher Du Pont, votre petit billet avec votre manuscript sur les prix.’ Schelle iii, 661). Unfortunately this is all Turgot says about that document.
60 For example, this is probably true for his fascinating but unfinished draft of ‘Value and Money’. This point is made in more detail in van den Berg (Citation2014). Unfortunately, this manuscript is another example of the many pieces that are now missing from the Fonds Turgot.
61 Turgot’s mathematical writings are now accessible (AN745AP/39 dossier 3). Like Du Pont, he may have wanted to interest more capable mathematicians in his economic studies. In the period 1765–1766 he tried to employ the mathematician Jean-Étienne Montucla (1725–1799) after introducing him to Philosophie rurale (see Schelle ii, 440, 515). But this employment, which followed Montucla’s trip to Guyana to work under Turgot’s brother, Étienne François, seems to have been of short duration (see letter of 15 May 1764 [745AP/34 doss.2 im.73]). A letter of 16 July 1768 (AN745AP/41 doss.2, im.202-3) suggests some on-going contacts at a later date. From the early 1770s Turgot developed a friendship with Condorcet with whom on some occasions he discussed mathematical topics. There is, however, no evidence of him having asked Condorcet’s advice in applying mathematics to the theory of taxation. After Turgot’s death, however, Condorcet would discuss the former’s views of taxation in his Vie de Monsieur Turgot. On that occasion he attempted to illustrate these views by means of a long mathematical footnote (see Condorcet and de Caritat Citation1786, 178–184). However, this exposition appears to have no relation with Turgot’s calculations.
62 Significantly, it was Du Pont who under Turgot’s instructions drafted this proposal for the fundamental reform of the administrative apparatus. For the collaboration of the two men on this ambitious document and its subsequent fate see Schelle (iv, 568–574). For a more general assessment see Skornicki (Citation2011, chapter 4).
63 The deleted number is obtained by dividing 350 by 30. The number replacing it, however, appears to be the result of dividing 350m by 300. Since this does not follow from Turgot’s reasoning, it appears to be a basic error. It is carried into the next terms and explains most of the divergence between the original calculations and their replacements.
64 11,666,666/1500m
65 1,166,666/1500m
66 361,666,666/129
67 There appears to be a calculation error here: 351,166,666/1285 = 273,281 and not 233,592. The latter number could be obtained by dividing the government expenditure number by approximately 1503, but that number does not follow from Turgot reasoning.
68 2,803,617/1500m
69 Note that this number is obtained by 273,281/1,500m. Therefore, even though Turgot wrote down the number 233,592 just above, he must in fact have calculated the correct number 273,281 ; see note 67.
70 50m + 11,666,666 + 2,803,617
71 50m + 1,166,666 + 233,592
72 Here Turgot makes an error that leads to an underestimation of over 2000, since 364,470,283/535 = 681,253.
73 351,400,258/5488
74 679,196/1500m
75 64,030/1500m
76 Here Turgot appears to divide 351,464,288 by 23420 rather than by 23426.
77 165,375/1500m
78 Here Turgot writes down the wrong answer since 15,007/1,500,000,000 = 1/99,953. But see next note.
79 This result is obtained from the calculation 351,479,295/99,953. This denominator makes sense given the previous step, although there Turgot wrote down the wrong denominator ; see previous note.
80 50m +11,666,666 +2,803,617 +679,196 +165,375 +40,277 +10,000
81 50m +1,166,666 +233,592 +64,030 +15,007 +3,516
82 27,586,206 + 2,758,620 + 12,321,872