fulgurafrango (blog)
The British economist Alfred Marshall (1842-1924) is frequently credited with the supply-and-demand diagram, so much so that the familiar graph of equilibrium in the market for a single good is called the “Marshallian cross” (the other famous “cross”, of course, being the “Keynesian cross” of macroeconomics).
Here as in many cases, however, Stigler’s Law of Eponymy[1] holds, which states that no scientific discovery is named after its real discoverer. And the truth is, Marshall was not the first to draw that famous diagram.
1.
The honour instead belongs to Antoine-Augustin Cournot (1801-1877), now better known for the duopoly equilibrium he analysed, that was later found to coincide with John Nash’s concept of non-cooperative equilibrium. The first diagram containing demand and supply curves on an x–y plane is to be found in Cournot’s book published in 1838, Recherches sur les principes mathematiques de la theorie de la richesse. The actual graph can be found in the Appendix section of Cournot’s book, where all the diagrams he used are collected. (In the English translation, Researches in the mathematical principles of the theory of wealth; Macmillan 1892, the text is on p. 92 and the diagram (Figure 6) can also be found in the Appendix in the very last pages of the volume.)
In any case, Cournot’s actual diagram is reproduced below.
Here, MN is the demand curve and PQ is the supply curve (always remembering that Cournot measured price p on the horizontal and quantity y on the vertical). The problem Cournot investigates is what would happen to price p if a tax equal to VS′ were to be imposed on the good. He then depicts this as a shift of the supply curve from PQ to P′Q′, which then clearly raises price from 0T to 0T′. This gives the result Cournot wanted to show: that imposing a specific tax on a good will (a) raise its price, but (b) that “the rise in price will be less than the increase in the cost”, i.e., TT′ will be less than VS′.
It is notable (and curious), however, that Cournot made no further use of this comparative-static diagram in his work beyond the specific problem he posed, which was to show how the post-tax equilibrium price would increase by less than the amount of the tax. The other point to note about Cournot’s work is that he attached no particular welfare significance to these curves. In particular, he was not among the marginal-utility theorists who associated the demand curve with welfare significance at the individual level. He simply regarded the downward sloping curve as an aggregate market phenomenon, where a higher price drives away some buyers.
Cournot’s influence on Marshall is direct and is something the latter acknwledged. Rather than the better-known figures of the 1870s “marginalist revolution” (especially Walras and Jevons), Marshall in the Preface to the first edition of his Principles [para. 10] credits “the guidance of Cournot, and in a less degree of von Thünen” for his appreciation of marginal analysis and mathematical reasoning in general.
2.
Only three years after Cournot’s work appeared, however, the German Karl Heinrich Rau (1782-1870) drew supply-and-demand curves that explicitly described market-adjustment, or what might be termed the stability of equilibrium. In this sense Rau went beyond Cournot’s achievement. In the fourth (1841) edition of his Grundsätze der Volkswirtschaftslehre (Principles of political economy), Rau includes this diagram in the appendix:
Here (aside from the noting that Rau measures quantity on the horizontal and price on the vertical axis), the curves hg and fi are possible shapes of the demand curve, while ek and ed are possible shapes of supply curves. Rau writes (as quoted in Chipman [2014:174]):
“The line AB indicates the various prices of a particular good. The perpendicular lines ab, a′l, a′m, a″m, etc., express the amount of the demand that obtains at a particular price, or asked price [Preisforderung].
“If one connects the endpoints of these perpendiculars by a line h b l m g, this may be called the demand line….The demand line may also be curved, as is f b o n p i, and there are a number of conceivable curves in this case. If one assumes that the supply is fixed, this would then be represented by the lines ac, a″m, and a″″p and e c m p d is thus the supply line. If, at a higher price the supply increases, its respective amounts may then be indicated by the curve e c l n k.”
Rau asks us to imagine that at a price of 10 florins (fl.), demand would be ab and the supply ac. “The sellers take advantage of this situation and hold out for more, whereupon a portion of the buyers withdraw in the amount discernible through the approach of hg towards AB. If the asked price has reached 24, at which point the demand line meets the supply line at m, then exactly the demand still remaining can be satisfied, and thus the price will be established at roughly this amount, in which case the rectangle A m″ a e then also indicates the entire expenditure.”
This is as complete a description of equilibrium adjustment as one can find — and well before the Jevons-Walras marginalist revolution in 1870-1871. Just as Cournot essentially carried out an exercise in comparative statics, Rau established the stability properties of the demand-and-supply diagram.
As pointed out by Humphrey [2010: 31], however, the diagrams of Rau and Cournot carried no welfare implications because the demand curves in their case were not based on marginal utility but were understood as “empirical sales schedules” based on individual buyers or sellers joining or leaving the market as price varies [2].
Rau credited as his inspiration another Frenchman N.-F. Canard — who used algebra but no graphs to depict equilibrium — but there is no evidence Rau was acquainted with the work of Cournot (Canard’s rival) until he cited Cournot in a later (1847) edition of his book. Theocaris [1993: 154] surmises that Rau came to the idea of demand and supply curves independently of Cournot. As for Rau’s possible influence on him, Marshall appears to acknowledge it at least partially: “I saw Rau’s work before I saw Jenkin’s paper in the Recess Studies published in 1870; but even before that I had learnt from Cournot and von Thünen” (as cited in Theocaris [1993: 155]).
Welfare propositions had to await the association of demand curves with marginal utility, and the first to accomplish that was the Frenchman Jules Dupuit (1804-1866) who in 1844 wrote on the benefits (utility) from public works. Dupuit explicitly (but inaccurately) identified the marginal utility function with the demand curve and derived such concepts later associated with Marshall as consumer’s surplus and deadweight losses [Humphrey 2010:32]. Dupuit notably preceded Gossen [1857], Jevons [1871], and Walras [1874] in expounding the idea of diminishing marginal utility, although these others (but especially Walras) certainly contributed more than that principle. Dupuit, moreover, did not explicitly consider supply curves in his analysis.
3.
Another author preceding Marshall was Fleeming Jenkin (1833-1885), professor of engineering at Edinburgh, who apparently also worked largely independently. Jenkin’s contribution to the supply-demand apparatus appeared much later (“The graphical representation of the laws of supply and demand” [1870]) in an article dealing with trade union issues. It is remarkable for its explanation and use of many concepts subsequently associated with Marshall, including producer’s and consumer’s surplus, elasticity, and short- and long-run period-analysis. The parallelism with Marshall’s work is perhaps unsurprising, since both Jenkin and Marshall drew heavily from J.S. Mill[3] for inspiration.
Jenkin’s diagram is shown below (reproduced from Theokaris [1993: 89]).
(*”whole supply” denotes maximum feasible supply.)
This diagram from 1870 merely illustrates the algebraic solution Jenkin already provided in 1868, so that he is able to state: “In a given market, at a given time, the market price of the commodity will be that at which the supply and demand curves cut. This price is the price at which supply and demand are equal.” Like Cournot and unlike Marshall, Jenkin measured price on the abscissa and quantity on the ordinate. (On this axis issue, see an earlier blog.) In this later work (1871-1873), Jenkin used the same graphs to illustrate the concept of consumer’s and producer’s surplus.
Marshall’s famous and still-familiar synthesis of these developments finally appeared as Figure 39 in his Principles (first edition, 1890) and is buried in Footnote 86 of his Appendix H.
By this time, give or take five decades after Cournot and Rau and a few decades since Jenkin and the marginal-utility revolution (about which Marshall was always ambivalent), Marshall was more or less on sure footing when he finally assembled these disparate attempts and put the entire apparatus to work in a virtuoso performance, treating issues of equilibrium, stability, comparative statics, utility, welfare, and time in a single sweep.
Ultimately, as noted by Humphrey [2010], the story of the demand-and-supply diagram is one of “multiple independent discoveries” in the sense of Merton. Unlike other known “multiples”, however, notable here is the great gap in time between initial inventions and final statement, as well as the weak uptake and cross-fertilisation among the early writers. Language barriers (French, German, and English), disciplinal boundaries (mathematically trained engineers versus literary moral philosophers), and differing research agendas undoubtedly played a big role in keeping these inventions relatively obscure. Jevons, for example, never drew or used a supply-demand graph; Walras’s general equilibrium approach leads to completely different demand- and supply functions more akin to the reciprocal demand-and-supply curves Marshall used to analyse international trade.[4]
While certainly not that of an inventor, Marshall’s genius lay in transcending boundaries and systematising otherwise disparate contributions. Absent that service, it is doubtful whether that famous diagram would have occupied the prominent place it does in economic theory and pedagogy.♦
References
Chipman, J. [2014] German utility theory: analysis and translations. Routledge.
Cournot, A.A. [1892] Researches in the mathematical principles of the theory of wealth; Macmillan.
Creedy, J. [1999] “The rise and fall of Walras’s demand and supply curves”, Manchester School 67(2):192-202.
Humphrey, T. [2010] “Marshallian cross diagrams”, in: M. Blaug and P. Lloyd eds. Famous figures and diagrams in economics. Edward Elgar.29-37.
Marshall, A. [1921] Principles of economics. Eighth edition. Macmillan
Theocharis, R. [1993] The development of mathematical economics. Macmillan Press.
Footnotes
[1] Stephen Stigler, the statistician, is the son of George Stigler, the economist.
[2] Such curves may be simply understood as the sum of individual discrete-choice demand functions, e.g., where an individual’s demand for a product is Di (p) = 1 for p ≤ ri , and Di (p) = 0 for all other p, where ri is person i‘s reservation price. Diminishing marginal utility does not need to make an appearance here.
[3] In particular, Jenkin defined demand and supply functions, respectively, as D = f(A + 1/x) and S = F(B + x), where x is price. These not only described the respective negative and positive relationships with price but also included the shift parameters A and B to allow for comparative statics. Shifts in demand and supply were already described verbally by Mill in his Principles of political economy [1848].
[4] On this, see Creedy [1999].
