Space, Railways, and Market Structures1

In Memory of Héctor Grupe

By Manuel Fernández López Institute of Economic Research (University of Buenos Aires), CONICET, and National Academy of Economic Sciences 1. Introduction The market demand for a good descends when its price increases. This is a plain fact, observable in the real world. However the same fact may mean different things for the seller, according to the number of other competitors operating in the market. When the number is high, and thus small the part of total production under control of an individual business, any seller may change its own supply without altering the market price. If he supplies more, this doesn't cause the market price to be diminished. Any individual supplier, at the market price, may throw on the market at the same price all the units supplied, whatever the quantity. Selling one unit more accrues to him an additional gross revenue (i.e. “marginal revenue”) equal to the price (or unit revenue). His profit is increased whenever the selling of one unit more causes a cost-increase which is less than the increase of gross revenue: that is, when marginal cost is less than the market price. On the contrary, when the share of the individual seller in the market supply is significant, an increase of his individual supply is perceived by the market as a greater supply, and thus the market price decreases. All the more when the seller is just one (a monopoly) for the whole market. In such a case, the market demand is also the monopolist's unit or average revenue. In such a case, a firm's larger supply leads to lesser unit and marginal revenue. Unit or average revenue is no longer coincident with marginal revenue: the former is an average of different revenues, while the latter is just the revenue produced by the last unit sold. Economic calculus leads to compare marginal cost (MC) and marginal revenue (MR). The latter outcome is due to Augustin Cournot, and is known since 1838. But ideas flow internationally, and the Irish scholar Dyonisius Lardner –termed as “fabulous figure” by Robertson (1951)– studied railway engineering at the renowned École des Ponts et Chaussées at Paris, at a time when Jules Dupuit -a forerunner of neoclassical - made research work of economic issues. In 1850 Lardner published Railway Economy, a treatise on the new art of transport, where Cournot's monopoly was translated as the supply of railway transportation, and the price as a transportation tariff. Since railway business is monopolistic by nature, a lower tariff increased the demand for transportation, and vice versa. Two economic chapters, 12 and 13, respectively, referred to railway costs and revenues, based on data from Belgian, state-owned railways, about which Lardner was an expert. Lardner went even further, and thirty years before Marshall's Principles, depicted in a diagram –the only one appearing in the work, so-called “Lardner's diagram”– the cost and gross revenue curves of transportation. The difference was the net profit, that was to be maximized. Lardner, implicitly, identified the firm's optimum with the equality between marginal cost and marginal revenue. It meant an introduction of the modern theory of the firm to English-speaking economists and a bridge to Cournot's work. Lardner was, as Schumpeter (1954) remarked –with Cournot and C. Ellet– one of the few who understood “the supply-and-demand mechanism” as well as “the monopolistic pricing”. According to Hutcheson (1955), Lardner anticipated an answer to “the growing problems, in the second half of the century, of the pricing policies of public utilities especially in transport, with their large fixed and comparatively small variable costs,

2 where the divergences between marginal and average cost and marginal and average revenue were so important and inescapable” (my italics). No more than two years later, J. B. Alberdi declared in his book Bases and starting points towards the political organization of the Argentine Republic (1852), the need of the “iron roads” to overcome the great distances of the country: “the railway and the electric telegraph, which mean the suppression of space, do this portent”, he wrote. Or alternatively, they meant a means of making productive the fertile and extensive fields of the humid pampas. This is undoubtedly one of the grounds on which the Argentine Constitution (1853) has allowed so wide a security to foreign capital. Alberdi's proposal, launched five years before the very first metre of railway was built, was not an utopia. The United Kingdom since 1846 had opened her foreign trade to raw materials from abroad, which soon influenced on Argentina, especially as an expansion of sheep breeding. But the big push did not come out before 1879, when the pampas were cleaned from hostile native tribes. Then railway building turned out to be an urgent need. Within the academic sphere, such a need was reflected in the opening during the eighties of a chair on Railways in the course of Engineering. The chair was occupied since 1888 by the engineer Alberto Schneidewind (1855-1934), who graduated in Germany and who introduced in the teaching his own translation of Launhardt's Theorie des Trassirens (Theory of Network Planning) –a true treatise on Location Theory- published at Buenos Aires in 1895. Schneidewind did not confine to a single source, and his lectures on Railways also included Lardner's ideas, and the fixing of the optimum size of a railway undertaking through marginal cost and revenue. As a master, Schneidewind had outstanding disciples. Two of them, engineer Carlos M. Ramallo (1873-1963) from Córdoba, and engineer Teodoro Sánchez de Bustamante (1892-1976) from Jujuy, performed high posts at the State Railways. At the Faculty of Economic Science they worked at the chair of Transports and Tariffs, which started to be taught in 1916. Ramallo's lecture program included Lardner's diagram in Part III of the subject, devoted to the “laws of demand and supply and transport-prices”, “ and monopoly” and “aspects of railway monopoly”. Inspired by Schneidewind's lectures, Sánchez de Bustamante –who would be an outstanding figure of Argentine science, including presidency of the Academy o of Sciences at Buenos Aires– published in 1919 Researches on . Owner of special talent for analytical geometry, Sánchez de Bustamante worked out various issues of economic analysis, appropriate for arigorous study of railway transportation (, utility, price, demand and supply, monopoly and competition, rent), performing on them both an analytic and a geometric treatment (he inserted 15 diagrams in 10 items). He studied Cournot's monopoly through a diagram which neither Cournot nor any other author did ever include in any publication: he depicted for the first time the marginal revenue curve under monopoly. Still in 1924 Sánchez de Bustamante published a study On a wrong construction of Lardner's diagram, where he amended the Italian treatise-writer Filippo Tajani. The issue of a decreasing demand curve under monopoly, and the divergence between average and income revenue, was elaborated by some economists in the late 1920's (Sraffa 1926, Harrod 1927).2 Elaborating Sraffa's idea that monopolistic rather than competitive traits dominate in economic life, and that each seller is, in some measure, a monopolist, the marginal income curve became a crucial tool in the analysis, especially in J. Robinson's Theory of imperfect competition (1933). This book would be recognized all over the world as a first rate contribution of the 20th century. In its equipment, the main tool was the marginal revenue curve: a Harrodian device, according to common opinión, but for us an instrument anticipated with precision and elegance in 1919 by Sánchez de Bustamante.

3

2. Marginal Revenue Curve: A negligible discovery?

Monopoly, while being a fact of real economic life, was since Cournot studied from the viewpoint of pure economics, wherein a few abstract (mathematical) notions or stylised behaviour were placed in the stead of myriads of empirical observations. That replacement, besides attracting many mathematicians -eager to till in a new field- furnished economics with exact tools that allowed a more perfect formal analysis of economic issues. The success of some piece of analysis, therefore, turned out to be based on the good shot to insert an issue into a chapter of mathematics. Simple monopoly analysis is counted among the earliest issues, to be settled in the above way: monopolistic behaviour could be stylised as a problem of maximising the value of certain function, “qui lui donnera le plus grand profit possible” (Cournot 1838, § 26); “in such a way as to afford him the greatest possible total net revenue” (Marshall 1962: V, xiv, §2). “the net gain of the monopolist should be a maximum” (Edgeworth 1925:112). Monopolistic behaviour, then, became reduced to little more than an elementary exercise in differential calculus. Thus no reason was arised for suspecting that highly renowned members of the mathematical school were not able to draw every significant consequence from such a simple problem. Was it so? The fathers of Monopoly Analysis (Cournot, Marshall, Edgeworth), notwithstanding their mathematical background and having authored the notions of “elasticity of demand”, “graphic method”, “Monopoly Revenue”, etc. did not unfold every formal property from their creature. My assertions are, first, that the marginal revenue curve was unknown to those precursors. Second, that this tool was not a minor one. And third, that the accepted list of their discoverers is not complete. If all three assertions (or rejections) are true, the following statements by distinguished economists should be disregarded:

“I take this opportunity to mention a point on which Mrs. Robinson lays great emphasis in her Foreword and indeed throughout her book, ‘the marginal revenue curve.’ She gives credit, for both the thing and the word, to several of her contemporaries, particularly to Mr. Harrod and Professors Yntema and Viner. It is quite natural that use of this convenient tool suggested itself at that time to many (including Chamberlin), especially to those who had previously struggled with the clumsier Marshallian total curves. We must not, however, forget that the tool was first used by Cournot, and no author of the 1920’s or 1930’s can have any objective claim to it” (Schumpeter 1954: 1152n. My italics). “That grown men argued seriously in 1930 about who had first used or named the curve that we now call ‘marginal revenue’ is a joke. Cournot had settled all that a century earlier in a completely modern manner” (Samuelson 1967. My italics).

3. Landmarks of the marginal revenue concept

In this section the milestones in the story of marginal revenue curve are reviewed. A succinct presentation of the canonical curves may serve as a term of comparison as well as an introduction to the subject.

A prototype

4

In the diagram, average revenue = A = p = φ(q), and marginal revenue = M = σ(q) = d[q φ(q)]/q = q φ’(q) + φ(q). Then M/A is = q φ’(q)/ φ(q) + 1 = –1/ε + 1, where ε ≡ – p/p’q. In elasticity terms, M = A(1 – 1/ε) = p(1 - 1/ε) (Yntema 1928: 697). Hence M = A – A /ε, and A – M = A /ε = p/ε (Harrod 1934: 447). A firm, operating in any market structure, maximises profits by setting its supply at the level in which marginal cost equals marginal revenue (M). The latter depends on the elasticity of demand, and this, in turn, upon the market regime. Under pure competition a firm, other things equal, may sell any output at the same market price: price coincides with M. But under less than pure competition a firm cannot sell a greater output unless it cuts price. In such a case, at any positive supply, M is lesser than average revenue (A). As in other economic concepts involving just two variables, M may be stated in symbols or shown graphically. In symbols, M is the derivative of p×q (price times quantity) with respect to q: (pq)’ = p’q + p; p’ ≡ dp/dq; p’ < 0.

Cournot

The concept of M was introduced by Cournot (1838 V:64) as ‘accroissement du produit brut’ or ‘increase of the gross receipts’.3 Cournot , however, set out an imperfect result from a very simple operation. If total revenue is p times D(p), that is p D(p), then marginal revenue is p dD/d p + D, or in differential terms: p dD + Dd p. Cournot chose the latter way, but, unbelievably, took only into account the first term, neglecting the second (D dp). In his words: ‘p dD est l’accroissement du produit brut’ (§ 29:64). ‘p dD is the increase of the gross receipts’ (Bacon’s translation: § 29:48) This was called “fallacious argument” by Shackle (1967:17), “where pdD, instead of pdD + Ddp, is wrongly called the ‘increase of gross receipts’ ...”. Besides that incompleteness, it is noteworthy that Cournot took derivatives with respect to price, not with respect to quantity. As regards to the graphic method, Cournot profusely4 inserted ‘figures’ in only four of the twelve chapters of Recherches, to wit:

Fig. 1 – (p, D) courbe (de la demande) (ch. IV) Fig. 2 – (D1, D2) reaction curves (duopoly) (ch. VII) Fig. 3 – (D1, D2) reaction curves (duopoly) (“) Fig. 4 – (X, Y) roots of y = – Fx/F’x (“) Fig. 5 – (X, Y) roots of y = - Fx/F’x (“) Fig. 6 – (p, y) cost-demand equations (ch. VIII) Fig. 7 – (p1, p2) producers’ interdependence (ch. IX) Fig. 8 – (p1, p2) producers’ interdependence (“) Fig. 9 – (p1, p2) producers’ interdependence (“) Fig. 10 – (p1, p2) producers’ interdependence (“)

In the above list, the first pair of variables stand for the x-axis and the y-axis, as they appear in Cournot’s diagrams; in the middle appears the name or description of the curve ; and the roman number indicates the chapter to which the diagram corresponds. Chapter V, ‘Du monopole’, where the concept of ‘increase of the gross receipts’ is introduced, was not benefited by diagrams. Among the remaining diagrams, where may we find the alleged ‘courbe de l’accroissement du produit brut’? Nowhere, of course. And where is the second term of p dD + Dd p? Nowhere either. Then the tool named ‘marginal revenue curve’ was not first used by Cournot. And Cournot had not

5 settled all that in a complete manner. But today we do have the curve at our disposal – although Cournot did not invent it– and on the other hand the formula is known in its complete development –although Cournot did not present it in a complete shape–. Then there is room for later authors to have an objective claim to originality.

Marshall

Marshall, as is known, declared himself to have worked ‘Under the guidance of Cournot’ (Preface to the Principles, 1890). The term corresponding to Cournot’s ‘p dD’ occurs -in Marshall’s Note XIV of the Mathematical Appendix to the Principles- as ‘β∆p’, where β is the quantity of the good (instead of price p) and ∆p is the differential of the demand price, where the corresponding derivative is taken with respect to quantity, viz:

“Now if p be the price per unit, which he receives for an amount β of villa accommodation, and therefore pβ the price which he receives for the whole amount β; and if we put for shortness ∆β in place of dβ/dx1δx1 , the increase of villa accommodation due to the additional element of labour δx1; then the net product we are seeking is not p∆β, but p∆β + β∆p; where ∆p is a negative quantity, and is the fall in demand price caused by the increase in the amount of villa accommodation offered by the builder”.5

Sraffa

Articles by Viner (1921) and Sraffa (1926) suggested to expand monopoly analysis to cover cases of descending demand for individual sources of production, whether or not the supply of some product consisted of one source or several.

Harrod

Roy F. Harrod caught during 1928 the bird of inspiration, but was unable to keep it within his hands. In The Life of J. M. Keynes (1951:159), with undisguised regret he recalled: ‘I submitted [to J. M. Keynes] a short article, setting out what I called “the increment of curve”.’ Keynes’ zeal, however, having made the publication of Harrod’s paper be delayed up to June 1930, blocked that his claim ‘to have “invented” this well-known tool of economics was without challenge’. Professor Walter Eltis, in his Palgrave’s article on ‘Harrod’, concisely stated that if the article had appeared in 1928 it would have produced Harrod’s claim for international priority.

Yntema

Theodore Yntema depicted marginal revenue as a decreasing straight line, without connecting it neither to the average revenue or demand curve involved, nor to the parabolic gross income curve implied. In 1928 he made known the curve in the Journal of Political Economy, thus becoming the first who published the curve in an English-speaking economic journal. Surprising as it may seem, T. Yntema did not take the stand of claiming originality on the MR curve at the time of a round table on ‘imperfect competition’ had taken place at the 46th Annual Meeting of the American Economic Association, presided by J.A. Schumpeter (Schumpeter 1934 a), where the rara avis was dissected by Yntema, Chamberlin, Jaffe, Morrison and Nichol.

6

Robinson

Joan Robinson first published her ‘marginal revenue curve’ in an article in the Economic Journal, on December 1932. But the MRC would not be a star born perfect. The diagram at page 548 -two pages after the curve is christened- where both average and marginal revenue curves are depicted, is flagrantly wrong, the horizontal distance of AR to the y-axis being more than thrice (instead of exactly twice) the horizontal distance of MR to the same axis.6 Let us make a few remarks on this flaw. Any article submitted to a major journal implies two efforts: that of the author, in order to present his results in the most perfect and unobjectionable way; and that of the editor, to scrutinize carefully and stop the publication of an imperfectly worked out paper. Was aware that his average-marginal curves were wrongly drawn, and purposefully submitted a mistaken diagram to the Economic Journal? It doesn’t seem likely: Joan Robinson was then a 29-year scholar, eager to excel in economics, and least of all would like to fall under the criticism of Pigou or any other. If Joan Robinson was unconcious of the mistaken diagram, wasn’t either the editor of the Economic Journal, precisely , who only four years before had rejected Harrod’s paper about the same curve? Not either the co-editor, D. H. MacGregor? Nor any among the distinguished members of the Royal Society Council, like Pigou or Bowley? The most natural interpretation is that none of those able British economists, on December 1932, knew with precision the formal properties of marginal revenue curve, as we know them at present time. This knowledge, may be added, reflects itself as a visual ability that allows to draw, at first sight, a marginal curve from an average one (as we, teachers of the History of Economics, do at the blackboard when explaining Ricardo’s theory of rent). Why in 1932 there was no such a visual ability? Simply because they lacked familiarity with the curve, for they had not seen such a curve ever before. In Theory of Imperfect Competition, Robinson wrote that the marginal revenue curve had a central place, and even that the book arose as an attempt to apply it to various problems. She referred to the discovery of the MR curve as ‘a race to the pole’, and quoted as co-discoverers: Mr. C. H. P.Gifford –her former professor– from Magdalene College, Mr. P. A. Sloan, from Clare College, Mr. R. F. Harrod, professor T. O. Yntema, from Chicago, Dr. E. Schneider, Dr. H. v. Stackelberg, and professor J. K. Mehta, ‘among many others who seem to have discovered it independently’. If not as the true discoverer, Robinson claimed priority for the statement of theorems relating marginal and average curves:

“Mr. Harrod set out in an analytical form some relations between marginal and average curves which I had discovered by geometry. At this Pole I can claim to have arrived by a route of my own” (Robinson 1933:vi).

The curve after Robinson

After 1933 many outstanding economists engaged in discussions and produced contributions related to the MRC. The following people, selected by M. Blaug as “Great Economists” –after or before Keynes– used the MRC in the papers indicated in parenthesis: Joseph Schumpeter (1934 a,b), Abba Lerner (1934), J. R. Hicks (1935), R.H.Coase (1935), Michał Kalecki (1937, 1940), Fritz Machlup (1937, 1947), Nicholas Kaldor (1938), Paul Douglas (1939), George Stigler (1939, 1940, 1947), Tibor Scitovsky (1941), Kenneth Boulding (1942, 1948), Oskar Lange (1943), Don Patinkin (1947), Sidney Weintraub (1949, 1955), James Buchanan (1952), F.H.Hahn (1959), Harold Demsetz (1959), William Baumol (1964), James Meade (1972, 1974), and Harvey Leibenstein (1973).

7

But other outstanding economists deserve also to be mentioned in this connection: R. F. Kahn (1937), Hans Singer (1937), Edgar Hoover (1937), Helen Makower (1938), Gerhard Tintner (1939, 1942, 1946), Paul Sweezy (1939), Benjamin Higgins (1939, 1940, 1942, 1949), Martin Bronfenbrenner (1940), M. W. Reder (1941), Gardner Ackley (1941), G.F.Shove (1942), Joseph Spengler (1946, 1950), J. de V. Graaf (1950), William Fellner (1951), Hans Brems (1952), G.C.Archibald (1955), Peter Newman (1960), Paolo Sylos-Labini (1967), Jagdish Bhagwati (1968), Edward Mishan (1968, 1971), Richard Schmalensee (1981), Robert Ekelund (1982), Assar Lindbeck (1994). The curve also gained the pages of books: Mehta (1932), Schneider (1932), Stackelberg (1934), Crum (1938), Boulding (1940), Stigler (1946), Samuelson (1948), Schneider (1949), Nordin-Salera (1951), Scitovsky (1952), Aubert (1952), Baumol and Chandler (1954), Lombardini (1955), Fellner (1960), Eastham (1962), Michel (1962), Shackle (1967), Chiang (1967), etc. The issues dealt with by means of MRC diversified as time elapsed, either on pure issues or on applied ones. Among the former, the results on simple monopoly served as basis to discriminating monopoly, bilateral monopoly, natural monopoly, , duopoly, and so on. Also specific issues in connection with MRC were developed: degree of monopoly, kinked demand curve, stability, indeterminacy, etc. On the side of , one issue is relevant for the present paper: railway economics. Besides the above references to Kalecki (1940), Scitovsky (1941), Higgins (1939), Spengler (1950), and Mishan (1968, 1971), the following papers dealt with railways through the MRC tool: Durbin (1936), Chamberlin (1937), Colberg (1941), Clemens (1941, 1951), Urquhart, Siegel and Leonard (1953), Wellisz (1963), Currie, Murphy and Schmitz (1971), and Engerman (1972). The above enumeration allow us to state that there is one story after 1932 and other story before that date. Therefore, the derogatory statements on the MRC must be disregarded.

4 A neglected contribution

The graphic of MR was neither Cournot’s creature nor Marshall’s, the main creators of that approach. It was introduced and developed, in every aspect and detail, by an Argentine scholar, the engineer Teodoro Sanchez de Bustamante (hereafter referred to for brevity as SB). SB wrote Researches on mathematical economics, a short book printed in 1919, with Preface dated on 4 December 1918. His motives and procedures were not alien, firstly, to his attendance to Prof. Schneidewind’s lectures on Railways at the Faculty of Engineering, University of Buenos Aires (UBA); secondly, the natural monopoly trait of the railway ; and thirdly, Cournot’s analysis of monopoly, that involved a decreasing demand curve.7 SB accomplished in 1918 a graphic display of Cournot’s monopoly (reproduced in Appendix), where he introduced the MR curve, under the name of ‘specific revenue’. He perceived that in the case of a descending demand curve for the goods supplied by a monopolist, it was not coincident with the ‘specific revenue curve’ (p.23) and that this in turn could be derived from the former for any volume of output. In such case ‘the values of p and q corresponding to the maximum’ of G (profit) would be determined through σ(q), as he named the curve of specific revenue,8 and not through ϕ(q), the demand curve. It’s possible that SB derived his Chapter 8 from a reading of Cournot’s Recherches. The following statement by SB,

8

“Both variables are linked by the law of demand : p = φ (q) and, therefore, in the study of the profits made by the monopolist and the buyers, it is indifferent to consider p or q as the independent variable.” (SB,§ 8, p. 20) may be imagined as paraphrasing Cournot’s passages: “Puisque D est lié à p para la relation D = F(p) ...” (Cournot V, § 27) “... Au lieu de poser, comme précédemment, D = F(p), il nous sera commode d’employer ici la notation inverse p = f(D)” (Cournot VII, § 43)

5 The marginal revenue curve as a multiple discovery

The approach of multiple discovering (Niehans 1995, De Marchi et alia 1995) is helpful for the case. There is no need to amend the accepted story, but just to add to it a fresh one, thus producing a richer story. In this respect, such an addition is not different to several accepted additions of another names to those traditionally known as discoverers,9 a trend which is likely to continue as long as the universe of co-operation among historians of economics goes on expanding on a pluralistic and international basis.

Imperfect communication

SB’s contribution seemingly passed unnoticed outside Argentina. His book was published in Spanish and its printing consisted probably in a few copies. Argentine scholars suffered very much the barrier of language. Researchers of SB’s time -such as Alexander E. Bunge- being aware of the limited acquaintance on Spanish language by colleagues around the world, when reaching some interesting result overcame the language barrier by translating their contributions into English or French, printing it privately, and then sending them to those somehow interested on them. SB’s case was clearly one of incommunicado.

Sameness

In the various mathematical definitions or graphic representations of marginal revenue, at least eight features may be discerned, each of them opening several choices: α) is it a derivative or a differential?; β) if any of them, with how many terms?; γ ) is the sign taken into account or not?; δ) which variable is independent, price or quantity?; ε) which source’s demand, that of the single firm or the industry?; ζ) the creature is labelled or not?; η) is it stated in mathematical or graphic terms, or both?; θ) is the marginal curve displayed alone or together with the average one?. SB’s statement, notwithstanding being the earliest, contained every issue as later accepted, and it was free from errors. It was the most rigorous and comprehensive in this story: besides the curve, SB offered a mathematical formulae as a derivative with two terms (Cournot 1838: 64, showed it as a differential, with only one term, viz. pdx; Marshall 1962:698 also defined MR as a differential, with two terms: p∆β + β∆p). SB considered a derivative, taken with respect to quantity (Cournot took his derivative with respect to price, a viewpoint shared by Chamberlin), and made explicit the negative sign of one of the terms (on behalf of p’ < 0, the negative slope of demand). Some authors (Cournot, Marshall, Note XIV) stated MR just through mathematical symbols, or others (Harrod, Chamberlin, Robinson) only through diagrams. SB also superposed in the same diagram both curves of MR and of AR (as would do Harrod, Chamberlin, and specially Robinson), being coincident at the origin, and from then on the abscissas of the MR and AR kept, for every ordinate, the relationship MR = ½ AR, later explained by Robinson (1933:II,3).

9

The only exception was SB’s christening of the curve (i.e. ‘specific revenue’), not coincident with Cournot’s accroissement du produit brut, or with the eventually accepted name, due to E. A. G. Robinson. But others’ were not either: Harrod called it ‘increment of aggregate demand curve’, Yntema ‘curve of gross marginal income’, Schneider ‘Grenzumsatzkurve’, and Chamberlin ‘addition to total income as any succesive unit is being sold’.10 The definition of ‘specific revenue’ offered by SB (‘infinitesimal increment of gross revenue perceived’) may well be thought as a description or expansion of Harrod’s name (‘increment of aggregate demand’). 11

α β γ δ ε ζ η θ Cournot 1838 f' 1 ● p F ~L m ● Marshall 1890 d 2 ● q ~L m ● Bustamante 1919 f' 2 (-) q F L m+g A+M Yntema 1928 f' 2 ● q F L g M Harrod 1930 ● ● ● I L g A+M Chamberlin 1933 ● ● ● F L g A+M Robinson 1933 ● ● ● F L m+g A+M Prototype f' 2 (-) q F L m+g A+M

6 Sánchez de Bustamante’s contributions to science

Let us say a few words about the context of discovery. At the faculties of Engineering during the last third of 19th century, it was currently used the language of differential calculus, the same which would be characteristic of the mathematical school of economics. It meant a bridge between Engineering and Economics, which some dared to cross; among others, the Professor of Roads, Railroads and Bridges, at the Polytechnic Institute of Hannover, Wilhelm Launhardt, author of a celebrated book on Walrasian economics, published in 1885. Teodoro Sánchez de Bustamante (1892-1976) studied Engineering at the University of Buenos Aires, where he was a student of Albert Schneidewind, Professor of Railroads, who followed Launhardt’s guiding lines, i.e. conjoining railroad engineering, spatial economics, and the mathematical treatment of economic issues. That professor worked also at the state section of the Argentine railroad network, organised at the time on a mixed base, one state-owned and a private one. The former in practice operated along similar lines as the German railroad policy, and found a theoretical support in Launhardt’s works, that showed as socially optimum the monopoly of railways by the State. As railroads were natural monopolies, there arose a contradiction between private profit maximisation and the maximum satisfaction of social wants. In Cournot’s book, chapter 5 on Monopoly, an answer was offered to the first criterion: to equate cost and revenue in the margin. The criterion stemming from Cournot’s analysis of monopoly could be compared to the competitive solution, wherein price was fixed at the non-profit minimum average cost level. The first criterion could be applied to privately-owned railroads, where profits were maximum, high fares, and capital invested and volume of services supplied sensibly inferior to those consistent with the ‘general ’. The second could be applied to state-owned railroads, with fares set at the level of minimum average cost, and greater capital invested and volume of services supplied. Political power was able to choose a fare equal to the competitive solution, even in the case of a (natural) monopoly, ir order to allow the service to a greater number of users, at a lower rate. The economic analysis of railroads, as a natural monopoly, led directly to the case of Cournot’s monopoly.

10

When he graduated with honours in 1916, the young Faculty of Economic Sciences of the University of Buenos Aires began to teach the subject ‘Transport and Tariffs’, a chair entrusted to C. M. Ramallo, also a former disciple of Schneidewind. Soon additional specialists were looked for, in order to achieve a more integrated chair. Among them was included Sánchez de Bustamante, author of Researches on Mathematical Economics, a book based on Schneidewind’s lectures, enriched by the reading of mathematical economists like Launhardt, Cournot, Osorio, Antonelli, and others. Once graduated, Sánchez de Bustamante worked on transportation. By the time he published his work on Mathematical Economics, he acted as engineer at the Ministry of Public Works of Argentina. He dated the Foreword of his book in 4 December 1918. Two years later, on 6 December 1920, on the occasion of a contest to fill teaching posts in the chair of Transports and Tariffs, Sánchez de Bustamante explained the meaning of his book and the subjects there developed. On 6 December 1920, SB reported:

Under the title of ‘Researches on mathematical economics’, the undersigned published, early in 1919, an original work on economic issues whose previous knowledge is indispensable for studying the principles and norms that have to rule every practical and scientific tariff system. Such a work was the outcome of a study of the subject, performed by the author, based on the knowledge acquired in the course on ‘Railways’ at the Faculty of Engineering – Consequence of that are the applications that, as examples, are shown in the pages of the cited work: railway monopoly, classifiers, maximum profits (p. 27); distance to market, influence on rent (p. 30); railway competition, effect on transportation price (p. 31); tariff formation, study on rent (p. 32), &c. [From SB’s unpublished personal file, Faculty of Economic Sciences, UBA]

The above statement slightly touches the issue of originality, but does not allude in particular to the ‘specific revenue curve’. This opens the possibility that SB has drawn it from Schneidewind’s lectures. However, the present author is inclined to think that the curve was an SB’s creation, in view of his insistence in explaining that the monopolist’s equilibrium should lay on the curve of specific revenue σ(q), and not on the demand curve φ(q). It is an opportune moment to remark SB’ talent for diagrammatical analysis. Besides the 1919 book, other contributions centered around graphical expressions of some economic or mathematical law, as ‘On a wrong depiction of Lardner’s diagram’ (1924), and ‘Geometrical and rigorous proof of the derivatives of sin x and cos x’ (1939). After his 1919 book, SB attained (1923) a teaching post in ‘Transport and tariffs’12 at UBA. For years his academic effort was concentrated on two fields: economics of transportation and mathematical analysis. In 1938 he became the head of the Institute of Transportation Economics at the Faculty of Economic Sciences, UBA, until 1945. In 1949 he was elected member of the National Academy of Sciences of Buenos Aires, and Emeritus Academician in 1973.

7 Conclusions

Seen as a case of multiple discovery, SB’s curve seems to have passed the test of sameness, and so the priority issue becomes obvious. Likewise insuperable barriers of communication explain the neglect of SB’s discovery. All that being taken into account, we think that Niehans' reference to marginal revenue curve as a multiple discovery, occurring at page 20, lines 24-5 of his 1995 paper, should be amended as follows: «MARGINAL REVENUE CURVE. T. Sanchez de Bustamante 1919. T. Yntema 1928. R. Harrod 1952 [1930, ch.3.»]

11

Appendix: Researches on mathematical economics (1919) § 8 Monopoly: Cournot´s equation

by TEODORO SÁNCHEZ DE BUSTAMANTE

From what has been said about demand we may infer that under a regime of monopoly there is no arbitrariness in the monopolist's fixing unit price at the level p in order to sell a given quantity q, and vice versa, that the quantity to be sold is not arbitrary when fixing the unit price. Both variables are linked by the law of demand: p = ϕ (q) and, therefore, in the study of the profits made by the monopolist and the buyers, it is indifferent to consider p or q as the independent variable. If q is the total quantity sold, and the unit price of selling-buying is unique and equal to the maximum borne by the demand, ϕ (q), the buyer's (or buyers') surplus utility is, as before:

∫ ϕ (q) dq – qϕ (q). And if: τ(q) Stands for the specific production cost or expenditure when q is the total quantity produced, then

∫ τ(q) dq Expresses total cost or expenditure, and

∫ τ(q) dq/q = ω (q) Expresses the average or unit cost. The difference G = q ϕ (q) – q ω (q) = q[ϕ (q) – ω (q)], whether positive or negative, expresses the profit or loss made by the monopolist. Graphically (as in Fig. 9), it is depicted by the area of rectangle EDHC. In order that the difference G be a maximum or minimum, it is necessary that dG/dq = ϕ (q) – ω (q) + q[dϕ/dq – dω/dq] = 0

And that this differential quotient change its sign when q takes vanishing values. The derivative -either with respect to q or p- of the difference G as function of the demand and unit production costs, equalled to 0, is Cournot's equation. The previous form: dG/dq = ϕ (q) – ω (q) + q[dϕ/dq – dω/dq] = 0 of Cournot's equation, provides a construct –useful when the functions and are analytically unknown- to determine graphically the values of p and q that maximise monopolist's profits. Through points D and C (fig. 9), in which the normal to the q-axis of abscissa q, cuts the curves ϕ(q) [demand] and ω(q) [average cost], let's draw the tangents DM and CN to these curves, and the parallels DE and CH to the referred axis; and through the intercepts E and H of these parallels with the p- axis, draw the parallels ES and HT to the tangents DM and CN, respectively. These parallels determine over the straight line DC, from the points D and C, the segments DS and CT, whose values are: DS = DE.tan α = - qdϕ/dq

12

CT = CH.tan β = qdω/dq

The addition: DS + CT = q[dϕ/dq – dω/dq]

Must be equal to: ϕ (q) – ω (q) = DC in the cases of maximum or minimum G [profits]. Then, in these cases, the parallels to the referred tangents must intercept on the normal to the q-axis at the abscissa q. But the construction done indicates that the point T is a point of the curve τ(q), defined by the equation:

q ∫0 τ(q) dq = qω(q), and that the point S is a point of the curve σ (q), defined by the equation:

q ∫0 σ (q) dq = qϕ (q), as is easily proved deriving these equations: τ (q) = ω (q) + q dω/ dq σ (q) = ϕ (q) + q dϕ/ dq and interpreting graphically. The magnitude τ(q), derivative with respect to q of the total expenditure done, shows, as has been seen, the specific expenditure, i.e. the quantity that times the infinitesimal increment of production dq gives the infinitesimal increment τ(q) dq of cost or total expenditure in production. The magnitude σ(q), the derivative with respect to q of the income or total revenue received by the monopolist, expresses the specific revenue, that is the quantity that multiplied by the infinitesimal increment dq of goods sold, gives the infinitesimal increment σ(q) dq of total revenue perceived. In consequence: to determine graphically the values of p and q corresponding to the maxima and minima of G [profits], from the curves of demand ϕ(q), and unit average cost ω(q), let's depict, through the usual procedure just seen, the curve of specific revenue σ(q), and that of specific cost τ(q). The ordinates of ϕ(q), passing through the intercepts of these curves, depict the unit average prices p, and the abscissas the corresponding quantities q. Being defined σ (q) as seen, there directly follows the preceding consequence, noting that:

G = ∫ σ (q) dq – ∫ τ(q) dq = ∫ [σ (q) dq – τ(q)] dq And that, when G is maximum or minimum: dG/dq = σ (q) – τ(q) = 0 Then σ (q) = τ(q) and the differential quotient changes its sign as q passes through its vanishing values. The surface bounded by the curves σ (q) and τ(q), and bounded by the p-axis, and by the normal to the q-axis whose abscissa shows the total quantity q sold and the unique unit price ϕ(q), represents the profit, positive or negative, earned by the monopolist, provided that the parts of this surface are added up algebraically, regarding as positive those above the curve and as negative the others. It is evident that these parts compensate exactly for the values of p determined by the intersection between ϕ(q) and ω(q). [Fig. 10]

13

List of publications of Teodoro Sánchez de Bustamante

ABBREVIATIONS: BA: Buenos Aires; FCE: Facultad de Ciencias Económicas (Faculty of Economic Sciences); RCE: Revista de Ciencias Económicas; UBA: University of Buenos Aires

α ) On ways of communication and transportation:

1922 La libertad de tarificar en la legislación ferroviaria argentina (Régimen de las leyes 2873 y 5315). Estudio técnico-económico (BA: Coni), 38 p. 1924 Sobre una equivocada construcción del diagrama de Lardner. Estudio de economía ferroviaria. RCE, Yr 11, No.36-37, July-August: 43-50. 1933 La vialidad en la República Argentina y su estado actual. Part 1. RCE, Yr 21, No. 148, November: 833-58. Part 2, RCE, Yr 21, No. 149, December: 951-76. Part 3, RCE, Yr 22, No. 150, January 1934: 35-68. Offprint: BA: FCE, 89 p. 1937 El camino a Bolivia por la Quebrada de Humahuaca; contribución a su estudio. Work presented to the Third National Congress of Highways. BA: Mercatali, 63 p. 1938 Orígenes y desarrollo de la vialidad en el mundo. BA: Porter Hnos. 15 p. 1938 Itinerarios y lugares de turismo en la Provincia de Jujuy. 1938 Algunos antecedentes y aspectos de los ferrocarriles argentinos. RCE, Yr 26, No. 207,October: 1003-16. 1939 La vialidad y los transportes por caminos en la Argentina. BA: FCE, 305 p. 1939 La coordinación de transportes de la ciudad de Buenos Aires; antecedentes y exposición del régimen creado por la Ley 12.311. RCE, Yr 27, No. 218, September: 811-39. 1940 Introducción al curso de economía y organización de los transportes. RCE, Yr 28, No. 226, May: 421-28. 1940 Los ferrocarriles argentinos de capital privado en los últimos once años (1928-1939). Posibilidad económico-financiera de su nacionalización. 1941 El Cuarto Congreso Sudamericano de Ferrocarriles, celebrado en Bogotá, en febrero de 1941. La Ingeniería, BA, March: 165-72. 1942 Los servicios públicos de teléfonos en la Argentina. BA: FCE, 310 p 1942 Constitución y contabilidad de reserves para renovaciones en las empresas de servicios públicos. RCE, Yr 30, No. 256, November: 1021-47. 1942 Régimen jurídico-económico de las telecomunicaciones. Servicio público de teléfonos. Información bibliográfica. RCE, Yr 30, No. 256, November: 1140-42. 1943 ¿Estatización o industria privada en materia de servicios públicos de transportes y comunicaciones? RCE, Yr 31, No. 267, October: 963-73. 1943 Orígenes y desarrollo de la vialidad argentina. Turismo. BA, September: 6-7. 1944 La radiodifusión en la Argentina. BA: UBA, FCE, Instituto de Economía de los Transportes. Publication No. 9, 5p. 1945 Corporación de transportes de la ciudad de Buenos Aires; algunos de sus problemas económicos. BA: Kraft, 133 p. 1953 La determinación del valor en la expropiación pública. RCE, Yr 41, No. 44, November-December: 453-8 1958 La vialidad patagónica. BA: Dirección Nacional de Vialidad. Technical publication, vol. 49, 75 p.

14

β) On mathematics:

1929 Sobre un erróneo desarrollo en serie de tang x. RCE, Yr 17, No.96, July: 552-54. 1930 Introducción al curso de Matemáticas. RCE, Yr 18, No.110, September: 902-12. 1939 Demostración geométrica, rigurosa, de las derivadas de sen x y cos x. RCE, Yr 27, No. 215, June: 501-4.

γ) On economics:

1919 Investigaciones de economía matemática [Researches on mathematical economics]. BA: Coni, 32 p. 1938 Expresión matemática de la tasa de interés. RCE, Yr 26, No.208, November: 1229-31. 1940 Costo y precio de los transportes ferroviarios en la Argentina. RCE, Yr 28, No, 222, January: 15-42.

δ) On public finance:

1926 Régimen financiero y contabilidad de las obras públicas nacionales. BA: Univ. Press, 26 p. 1937 Financiación de las carreteras. RCE, Yr 25, No. 193, August, 659-81. 1942 Constitución y contabilidad de reservas para renovaciones en las em- presas de servicios públicos. RCE, Yr 30, No. 256, November, 1021-47.

ε) Miscellanea:

1912 Hacia la sombra - A tale. Winner of the prize “La Prensa”. 1941 El infinito. Conference at the National College of Buenos Aires, 25 September, BA: Univ. Press, 30 p. 1943 Notas de un viaje al Pacífico. BA: C.J.Bianchi, 27 p. 1947 La propiedad. Limitaciones a la disposición jurídica según el régimen del Código Civil. BA: V. Abeledo, 121 p. 1950 La probabilidad y el destino. RCE, Yr 38, No. 24, July-Aug.,267-75. 1953 Reflexiones sobre el espacio y el tiempo. BA: D.Talabriz, 20 p.

References ABBREVIATIONS: AER: The American Economic Review EJ: The Economic Journal Em: Econometrica EJHET: The European Journal of the History of Economic Thought JPE: The Journal of Political Economy QJE: The Quarterly Journal of Economics RES: The Review of Economic Studies

Ackley, G. (1942).Spatial competition in a discontinuous market.QJE 56(2):212-30,Feb. Allen, R. G. D. (1938). Mathematical analysis for economists. London: Macmillan. Archibald, G. C. (1955). Inventory investment and the share of wages in manufacturing income. EJ 65(258):257-70, June. Aubert, J. (1949). La Courbe d’Offre. Paris: Presses Universitaires de France. Baumol, W. J. (1964). and welfare economics. AER 54(3):44- 52. Papers and Proceedings, May. Baumol, W. J., Chandler, L.V. (1954). Economic Processes and Policies. New York:

15

Harper & Brothers Publishers. Besomi, D. (1997). Roy Harrod and traditional theory. EJHET 1:92-115. Besomi, D. (1999). The Making of Harrod’s Dynamics. London: Macmillan Press. New York: St. Martin’s Press, 1:16-8, 7:172. Bhagwati, J. (1968). More on the equivalence of tariffs and quotas. AER 58(1):142-46, March. Boulding, K. E. (1942). Economic Analysis. New Yok: Harper & Brothers Publishers. Rev. Ed., 1948. Boulding, K. E. (1942).The theory of the firm in the last ten years. AER 32(4):791-802, December. Boulding, K. E. (1948). Samuelson’s Foundations: The role of mathematics in economics. JPE 56(3):187-99, June. Brems, H. (1952). A discontinuous cost function. AER 42(4):577-86, September. Bronfenbrenner, M. (1940). Applications of the discontinuous oligopoly demand curve. JPE 48(3):420-27, June. Buchanan,J.M.(1952).The theory of monopolistic quantity discounts.RES 20(3):199-208 Chamberlin,E.H.(1937).Monopolistic or imperfect competition? QJE 51(4):557-80, Aug. Chamberlin, E.H., ed. (1954). Monopoly and competition and their regulation. Papers and Proceedings of a Conference held by the International Economic Association. London: Macmillan & Co. Chamberlin, E. H. (1957). Towards a more general theory of value. New York: Oxford University Press. Chamberlin, E.H. (1962)[1933]. The Theory of Monopolistic Competition. A Re- Orientation of the Theory of Value. Cambridge, Massachusetts: Harvard University Press. 8th ed. Chiang, A. C. (1967). Fundamental methods of mathematical economics. New York: McGraw-Hill, Inc. Clemens, E. W. (1941). Price discrimination in decreasing cost industries. AER 31(4):794-802, December. Clemens, E. W. (1951). Price discrimination and the multiple-product firm. RES 19(1):1-11. Coase, R. H. (1935). The problem of duopoly reconsidered. RES 2(2):137-43, Feb. Colberg, M. R. (1941). Monopoly prices under joint costs: Fixed proportions. JPE 49(1):103-10. February. Cournot, A. (1938)[1838]. Recherches sur les Principes Mathématiques de la Théorie des Richesses. Paris: Hachette. Repr. Marcel Rivière, 1938. Crum, W. L. (1938). Rudimentary Mathematics for Economists and Statisticians. QJE 52:1-164. Supplement, May. Currie, J. M., Murphy, J. A., Schmitz, A. (1971). The concept of and its use in economic analysis. EJ 81(324):741-99, December. De Marchi, N., P. Mirowski, A. Roncaglia and J.Niehans (1995). Editorial: debate on Jürg Niehans, ‘Multiple discoveries in economic theory’. EJHET 2:275-98, Autumn. Demsetz, H. (1959). The nature of equilibrium in monopolistic competition. JPE 67(1):21-30, February. Douglas, P. H. (1939). The effect of wage increases upon employment. AER 29 (1):138-57. Supplement, Papers and Proceedings, March. Dunlop, J. T., Higgins, B. (1942). “Bargaining power” and market structures. JPE 50(1):1-26, February. Durbin, E. F. M. (1936). Economic calculus in a planned economy. EJ 46(184):676-90, December. Edgeworth, F. Y. (1925). Papers relating to Political Economy. London: Macmillan. Ekelund, R. B., Jr., Higgins, R. S. (1982). Capital fixity, innovations, and long-term contracting: An intertemporal economic theory of regulation.AER 72(1):32-46, March. Eltis, W. (1987). Harrod, Roy Forbes. In John Eatwell, Murray Milgate and Peter

16

Newman (eds.) The New Palgrave -A Dictionary of Economics. London: The Macmillan Press, II:595-600. Engerman, S. L. (1972). Some economic issues relating to railroad subsidies and the evaluation of land grants. The Journal of 32(2):443-63, June. Fellner, W. (1951). The influence of market structure on technological progress. QJE 65(4):556-77, November. Fellner, W. (1960). Emergence and content of modern economic analysis. New York: McGraw Hill Book Company, Inc. Fernández López, M. (2001). La ciencia económica argentina entre guerras (1918- 1939). Saber y tiempo, Buenos Aires 11,153-77. Graaff, J. de V. (1950). Income effects and the theory of the firm. RES 18(2):79-86. Hahn, F. H. (1959). The theory of selling costs. EJ 69(274):293-312, June. Harrod, R. F. (1930). Notes on supply. EJ 40(158):232-41. June. Reprinted in Economic Essays. London: Macmillan, 1952, 3:77-88. Harrod, R. F. (1931). The Law of Decreasing Costs. EJ 41(164):566-76. December. Harrod, R. F. (1933). A Further Note on Decreasing Costs. EJ 43(170):337-41. June. Harrod, R. F. (1963)[1951]. The Life of John Maynard Keynes. London: Macmillan. Reprinted 1963, New York: St Martin’s Press. Hicks, J. R. (1935). Annual survey of economic theory: the theory of monopoly. Em 3(1):1-20, January. Higgins, B. (1939). Elements of indeterminacy in the theory of non-. AER 29(3):468-79, September. Higgins, B. (1940). The incidence of sales taxes: A note on methodology. QJE 54(4) Part I:665-72, August. Higgins, B. (1949). The optimum wage rate. The Review of Economics and Statistics 31(2):130-39, May. Hoover, E.M., Jr. (1937). Spatial price discrimination. RES 4(3):182-91, June. Hutchison, T. W. (1955). Insularity and Cosmopolitanism in Economic Ideas, 1870- 1914. AER, Papers and Proceedings 45(2):1-16, May. Kahn, R. F. (1937). The problem of duopoly. EJ 47(185):1-20, March. Kaldor, N. (1938). Professor Chamberlin on monopolistic and imperfect competition. QJE 52(3):513-29, May. Kalecki, M. (1937). A theory of commodity, income, and capital taxation.EJ 47(187):444-50, September. Kalecki, M. (1940). The supply curve of an industry under imperfect competition. RES 7(2):91-112, February. Lange, O. (1943). A note on innovations. RES 25(1):19-25, February. Lardner, D. (1850). Railway Economy. A Treatise on the New Art of Transport. New York: Augustus M. Kelley, 1968. Leibenstein, H. (1973). Competition and X-efficiency: Reply. JPE 81(3):765-77, May- June. Lerner, A.P. (1934). The concept of monopoly and the measurement of monopoly power. RES 1(3):157-75, June. Lerner, A.P., Singer, H.W. (1937). Some notes on duopoly and spatial competition. JPE 45(2):145-86, April. Lindbeck, A., Snower, D. J. (1994). How are product demand changes transmitted to the labour market? EJ 104(423):386-98, March. Lombardini, S. (1953). Il Monopolio nella Teoria Economica. Milan: Società Editrice “Vita e Pensiero”. Machlup, F. (1937). Monopoly and competition: A classification of market positions. AER 27(3):445-51, September. Machlup, F. (1947). Rejoinder to an Antimarginalist. AER 37(1):148-54, March. Makower, H. (1938). Elasticity of demand and stabilisation. RES 6(1):25-32, October. Marshall, A. (1962)[1920]. Principles of Economics. London: Macmillan.

17

Meade, J. E. (1972). The theory of labour-managed firms and of profit sharing. EJ 82(325):402-28, March. Meade, J. E. (1974). labour-managed firms in conditions of imperfect competition. EJ 84(336):817-24, December. Mehta, J. K. (1932). The Elements of Economics. London: Routledge & Sons, Ltd. Michel, M. (1961). Stratégie du marché – théorie de la firme et vente sous marque. Paris: Presses Universitaires de France. Mishan, E. J. (1968). What is producer’s surplus? AER 58(5):1269-82, December. Mishan, E. J. (1971). The postwar literature on : An interpretative essay. Journal of Economic Literature 9(1):1-28, March. Newman, P. (1960). The erosion of Marshall’s theory of value. QJE 74(4):587-99, November. Niehans, J. (1995). Multiple discoveries in economic theory. EJHET 1:1-28, Spring. Nordin, J. A., Salera, V. (1950). Elementary Economics. New York: Prentice-Hall. Patinkin, D. (1947). Multiple-plant firms, cartels, and imperfect competition. QJE 61(2):173-205, February. Reder, M. W. (1941). Monopolistic competition and the stability conditions. RES 8(2):122-25, February. Robertson, R. M. (1951). Jevons and His Precursors. Em 19(3):229-49, July. Robinson, J. (1932). Imperfect competition and falling supply price. EJ 42(168):544-54. December. Robinson, J. (1964)[1933]. The Economics of Imperfect Competition. London: Macmillan. Samuelson, P.A. (1948). Economics – An introductory analysis. New York: McGraw-Hill Book Company, Inc. Samuelson, P.A. (1967). The Monopolistic Competition Revolution. In R. E. Kuenne (ed.) Monopolistic Competition Theory: Studies in Impact. Essays in Honor of Edward H. Chamberlin, New York: Wiley. Repr. Collected Scientific Papers of Paul A. Samuelson, III:18-51. Schmalensee, R. (1981). Economies of scale and barriers to entry. JPE 89(6)::1228- 38, December. Schneider, E. (1932). Reine Theorie monopolistischer Wirtschaftsformen. Tübingen: J. C. B. Mohr (Paul Siebeck). Schneider, E. (1949). Einführung in die Wirtschaftstheorie. Tübingen: J. C. B. Mohr Verlag (Paul Siebeck). Schumpeter, J. A.(1954). History of Economic Analysis. New York: Oxford U. Press. Schumpeter, J. A., Yntema, T.O., Chamberlin, E.H., Jaffe, W, Morrison, L.A., and Nichol, A.J. (1934a). Imperfect Competition. AER, 24(1):21-32. Supplement, Papers and Proceedings, March. Schumpeter, J. A., Nichol, A.J. (1934b). Robinson’s Economics of Imperfect Competition. JPE 42(2):249-59, April. Scitovsky, T. D. (1941). Prices under monopoly and competition. JPE 49(5):663-85, October. Scitovsky, T. D. (1952). Welfare and Competition: The Economics of a Fully Employed Society. London: Allen & Unwin. Shackle, G.L.S. (1967). The Years of High Theory: Invention and Tradition in Economic Thought, 1926-1939. Cambridge: At the University Press, chapter 4. Shove, G. F. (1942). The place of Marshall’s Principles in the development of economic theory. EJ 52(208):294-329, December. Spengler, J. J. (1946). Monopolistic competition and the use and price of urban land service. JPE 54(5):385-412, October. Spengler, J. J. (1950). Power blocs and the formation and content of economic decisions. AER 40(2):413-30. Papers and Proceedings, May. Stackelberg, H. v. (1934). Marktform und Gleichgewicht. Vienna and Berlin: Verlag

18

von Julius Springer. Stigler, G. J. (1939). Production and distribution in the short run. JPE 47(3):305-27, June. Stigler, G. J. (1939). Notes on the theory of duopoly. JPE 48(4):521-42, August. Stigler, G. J. (1946). The Theory of Price. New York: The Macmillan Company. Stigler, G. J. (1947). The kinky oligopoly demand curve and rigid prices. JPE 55(5):432-49, October. Sweezy, P. M. (1939). Demand under conditions of oligopoly. JPE 47(4):568-73, August. Sylos-Labini, P. (1967) Prices and wages: A theoretical and statistical interpretation of Italian experience. Journal of Industrial Economics 15(2):109-27, April. Tintner, G. (1939). The problem of bilateral monopoly: A note. JPE 47(2):263-70, April. Tintner, G. (1942). The theory of production under nonstatic conditions. JPE 50(5):645- 67, October. Tintner, G. (1946). Multiple regression for systems of equations. Em 14(1):5-36, January. Urquhart, M.C., Siegel, I.H., Leonard, W.N. Discussion (in Technology). AER 43(2):303-12. Papers and Proceedings. May. Viner, J. (1921). Price Policies: The Determination of Market Price. In L. C. Marshall (ed.), Business Administration, Chicago: University of Chicago Press), 343-7. Also in J. Viner (1958) The Long View and the Short: Studies in Economic Theory and Policy. Glencoe: Free Press. Weintraub, S. (1949). The theory of consumer monopsony. RES 17(3):168-78. Weintraub, S. (1955). Revised doctrines of competition. AER 45(2):463-79. Papers and Proceedings, May. Wellisz, S. H. (1963). Regulation of natural gas pipeline companies: An economic analysis. JPE 71(1):30-43, February. Yntema, T. O. (1928). The influence of dumping on monopoly price. JPE 36(6): 686-98. Notes

1 A previous version of this paper was presented at the VIIe colloque of the European Society for the History of Economic Thought, “L’agent économique: théorie et histoire”, Paris Carré des Sciences, 30 janvier – 1er février 2003 2 The Swiss researcher Daniele Besomi has let me know that “The thinking of some alert economists seem to have converged on this point in the late 1920's” (letter of March 28, 2001). 3 The translation of the French Cournot’s term produit as the English word ‘receipts’, is due to N.T.Bacon. 4 Cournot inserted more diagrams per word than Marshall in his Principles. This contradicts Keynes’ assertion that Marshall may be claimed as ‘the founder of modern diagrammatic economics’ (Keynes 1924, § IV). 5 Marshall (1962)[1920], Mathematical Appendix, Note XIV: 698-9. 6 I guess that comments on that mistake might be the source of Robinson’s (1933) chapter II, that allowed that author to draw a number of results from the MR and AR curves, and their mutual relationship through elasticity. 7 To Harrod (1952: vi), indeed, the theory of imperfect competition was a generalisation of Cournot’s monopoly to the case of imperfect competition. 8 Cf. Appendix. 9 Such as Gervaise besides Hume, Tinbergen in addition to Solow, Kantorovich in tune with Dantzig, and so on. 10 Chamberlin (1933:14). 11 To quote again Daniele Besomi (see footnote 2): “in those years discovery was, so to say, in the air. After Harrod published his article in 1930, he received a number of letters suggesting alternative names or pointing out that others were working at the same concept”. 12 The subject was so named as Clément Colson’s book Transports et tariffs (1890), although its professors had all been students of Schneidewind, a follower of Launhardt.