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Space, Railways, and Market Structures1 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 economics- 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”, “competition 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 Mathematical Economics. Owner of special talent for analytical geometry, Sánchez de Bustamante worked out various issues of economic analysis, appropriate for arigorous study of railway transportation (value, 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.
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