Rationalising the supply-and-demand cross, 1838–1890

Abstract

This study takes its bearings from the proposition that the supply-and-demand apparatus of what came to be called the “Marshallian cross” is an unsatisfactory representation of actual supply and demand forces, which are better characterised in the manner of the classical economists. From that point of departure it then enquires into how that representation nevertheless arose in the period from 1838 to 1890, notwithstanding its lack of robustness as economic theory – via consideration of the economics of five key contributors prior to Marshall. The investigation confirms that there is no plausible basis for a general presumption in favour of the conventional rising supply function – other than the marginal productivity theory of factor pricing, which is itself unsatisfactory.

Keywords:

• A.-A. Cournot
• F. Jenkin
• H.K.E. von Mangoldt
• rising supply-price
• K.H. Rau

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1 See Cournot (1838; Figure 6 in the set of diagrams accompanying the book, with 101–104), Cournot (1897, 90–92), and Humphrey (2010, 29–32) – the latter also indicating the contributions to SAD geometry, prior to Marshall (1879), of Karl Heinrich Rau, Jules Dupuit, Hans von Mangoldt and Fleeming Jenkin.

2 RSP must properly be understood in real terms. But when a change initiated in one industry changes multiple prices, whether supply-price rises or falls with output can turn, arbitrarily, upon mere choice of numeraire.

3 In all the above, “curve” and “function” have been used interchangeably. But there is an asymmetry between the supply and demand sides – between the former expressed in observable, measurable phenomena, and the latter partly derivative from unobservable supposed phenomena. Supply-price equations are functions in a more substantial sense than demand curves or functions ever could be.

4 But inappropriately identifying demand so understood with “sales”; i.e., demand actually realized. He explicitly allows as an exception, what later come to be called snob effects (Cournot 1897, 46).

5 The costs explicitly mentioned in Cournot’s example are “materials and labour”, “the value of the raw materials, the wages or profits of the agents who cooperate in making and marketing it, and the interest on the capital necessary”. Later, transport costs in particular are detailed as: “the price of necessaries and the wages of the agents by whom the transportation is mechanically carried on, … insurance premiums, and the profits of the merchant, who ought to obtain in his business the interest on the capital employed and a proper return for his industry” (Cournot 1897, 57–58, 117; see also 128, 157–158).

6 Dupuit claims this notion of utility is shared by Adam Smith (87). But it is clear that for Smith use-value is heterogeneous, purposive and objective – the use-value of a hat is for covering the head, the use-value of a chair is for sitting, and so on – essentially the same as Aristotle’s conception (Aspromourgos 2009, 119–125). Indeed, the quotation from J.R. McCulloch (1828) that Dupuit appeals to as justification for his interpretation of Smith indicates precisely this: “the capacity of bread, for example, to appease hunger, or of water to quench thirst”. (Dupuit’s accusation that the Physiocrats equated utility with cost of production (90n) is equally unfounded.) Dupuit provides no citation whatsoever for his McCulloch quotation; but the editors of the translation indicate its location in McCulloch’s edition of Smith (1776). They cite the 1853 edition (which of course, Dupuit could not have used); but the relevant text is already in the first, 1828 edition (vol. 4, 83–84).

7 For an interpretation of Dupuit’s economics as a whole, and in its larger intellectual context, see Mosca (1998).

8 There is, however, a brief comment on falling unit cost in relation to differences in unit cost across different producers of the same commodity (40–41); and the issue is further raised in relation to multiple equilibria (50–51).

9 For an overview of Mangoldt’s economics as a whole, although with a tendency to overgenerous interpretation, see Hennings (1980), which also shows that in some respects Mangoldt’s economics is a hybrid of classical elements and incipient marginalist theory – and on Mangoldt and joint production in particular, see Kurz (1986, 155–156).

10 Jenkin (1887c [1868], 15–19) also provides an exposition of SAD, without diagrams, but including an algebraic formulation of the functions. There is a further, slight algebraic formulation in Jenkin (1887a [1871–2], 107–108), but interestingly, Jenkin puts the algebra aside: “There is, however, little or no advantage in adopting this algebraic form, because we cannot suppose that in any instance φ(x) or φ₁(x) [the SAD functions] will be any tolerably simple function”. Commenting on William Stanley Jevons, Jenkin observes: “utility, as he defines it, admits of no practical measurement” (109–110).

11 There is no reference to physical returns, except for one sentence (p. 92), accompanied by a diagram (Figure 13 at p. 91), which is a peculiar attempt at characterizing increasing returns to scale – by a supply curve for low outputs levels and a different, lower supply curve for high output levels, but both curves rising with output. There is also no discussion of firm versus industry (a comment also applicable to Mangoldt).

12 For the background and context for this work, see Whitaker (1975, vol. 1, 57–66, vol. 2, 3–7, 111–117, 181–186), Groenewegen (1995, 153–179). All our page references are to the “Domestic Values” text, which is separately paginated from the “Foreign Trade” text. Humphrey (2010, 30) cites “The Pure Theory of Foreign Trade, … fig. 22a” for Marshall’s SAD diagram, but this is actually the second of four diagrams in which Marshall maps the demand curve against a continuously positively-sloped supply curve; and all of these figures are connected with the “Domestic Values” text, not the “Foreign Trade” text.

13 This is in contrast to the diagrams of Cournot, Dupuit and Jenkin, but in agreement with those of Rau and Mangoldt. If either of the latter influenced Marshall in this respect, it was Rau (Streissler 1990, 57; Groenewegen 1995, 153–154; Rau 1847, 578–580). As Groenewegen indicates, Rau (1847) is the edition possessed by Marshall. From the 1841 4th edition forward, Rau’s book included an appendix presenting a SAD-cross diagram (Hennings 1979, 9; the appendix is translated in Hennings 1979, 16–17, and in Chipman 2014, 174–175). Rau supposes both supply as a fixed quantity and the possibility of supply as a positive function of price – the latter, with only very slight rationalization. In the book appendix he simply conjectures “[i]f supply increases with higher prices …”, the only further comment on the issue being: “[i]f on the other hand [i.e., not fixed supply] the expectation of a higher price were to increase supply, …” (Hennings 1979, 16–17). In a separate document of 1841 he merely comments: “There are commodities whose production can easily be increased in a very short time. If then the price rises, the supply will increase” (also translated in Hennings 1979, 13–15, and in Chipman 2014, 134–136). Hennings (1979, 5–6) makes a convincing case for Rau’s probably having been unaware of Cournot’s SAD diagram of three years earlier. The relevant Hennings text, previously unpublished, is reproduced in the Appendix below.

14 Groenewegen (1995, 140) notes: “By 1879 … the essentials of his system were complete”. The 1879 analysis is also prefigured in an unpublished Marshall essay, including SAD diagrams, probably written at the beginning of the 1870s (Whitaker 1975, vol. 1, 119–159; acutely analysed in Bharadwaj 1978) – and forms of the SAD apparatus are to be found as well in other pre-1890 Marshall writings published by Whitaker.

15 For a fuller treatment of these factors, and contrasted with the classical conception of SAD, see Aspromourgos (2019, sections 4–5).

16 I am indebted for this information to the University Library of the University of Michigan at Ann Arbor where Rau’s library is kept as the Parsons Collection. [Rau’s library was gifted to the University of Michigan Library by Philo Parsons in 1870, a part of what became a larger ‘Parsons Collection’.]

17 I am indebted to the University Library in Heidelberg for this information.

18 See Rau (1826, §10) in all editions from 1841 on, and before 1876.

19 This is overlooked by Schneider (1960: 382), who maintains that Rau knew Cournot’s work because he quoted the Recherches.

20 This is unlikely, however. Quetelet probably knew of Cournot, as Cournot had translated into French the Treatise on Astronomy by his close friend J.F.W. (Sir Frederick) Herschel (see Cournot 1835). Cournot’s Traité de la Théorie des Fonctions (1841) was in Quetelet’s possession, but (at least according to the published list) Cournot’s Recherches was not. See Bluff (1881). I owe this information to Mme L. Wellens-de Donder [Attachée Scientifique, Centre Nationale d’Histoire des Sciences, Bibliothèque Nationale, Brussels – earlier acknowledged by Hennings for ‘valuable information’].

21 [Rau edited the Archiv der politischen Ökonomie und Polizeiwissenschaft, 1835–1853. In 1853 it was amalgamated with the Zeitschrift für die gesammte Staatswissenschaft, of which Rau was a co-editor until 1869.]