Francis Ysidro Edgeworth, 1845-1926.

Francis Beaufort Edgeworth was a restless philosophy student at Cambridge on his way to Germany when he decided to elope with a teenage Catalonian refugee he met on the steps of the British Museum. One of the outcomes of their marriage was Ysidro Francis Edgeworth (the name order was reversed later), who was destined to become one of the most brilliant and eccentric economists of the 19th Century.
Edgeworth was born in 1845 in Edgeworthstown, County Longford, Ireland into a large, well-connected and eccentric Anglo-Irish landowning family. The famous novelist Maria Edgeworth, of Castle Rackrent fame, was his (elderly) aunt. Although Edgeworth was the fifth son of a sixth son, all the other heirs eventually died, leaving him to inherit Edgeworthstown in 1911. A lifelong bachelor (for a brief period, he hopelessly attempted to court Beatrice Potter), the Edgeworth line died out with him.
Edgeworth was educated at Edgeworthstown by tutors until 1862, when he went on to study languages and the classics at Trinity College, Dublin. He proceeded in 1867 to Oxford (initially at Exeter, then Magdalen and then, finally, from 1868, Balliol College). He graduated in 1869 with a First in Literae Humaniores, but his degree was only awarded in 1873.
Around 1870, Edgeworth moved to Hempstead, in the environs of London. Very little is known about the next decade of his life. Edgeworth subsisted on private income. He must certainly have studied law, for in 1877, he was called to the bar by the Inner Temple. It is also presumed that he learnt mathematics and statistics on his own. It is likely that his interest in this topic was “inherited” from his father’s friend, William Rowan Hamilton, from his Oxford tutor, Benjamin Jowett, and from his close friendship with his Hempstead neighbor, William Stanley Jevons.
In his first book, New and Old Methods of Ethics (1877), Edgeworth combined his interests, applying mathematics — notably the calculus of variations and the method of Lagrangian multipliers — to problems of utilitarian philosophy. His main concern, following up on Sidgwick, was “exact utilitarianism”, defined loosely as the optimal allocation of resources that maximized happiness of a society. He argued that ultimately it falls upon the “capacity for pleasure” of people in a society. He recognized that, under uncertainty, “equal capacity” ought to be assumed. However, he then went on to argue that certain classes of people “obviously” have a greater capacity for pleasure than others (e.g. men more than women), and thus some amount of inequality is justifiable on utilitarian principles. He struck a Darwinist note when, in an attempt to sound optimistic, he argued that “capacities” would evolve over time in a manner that the egalitarian solution would become justifiable in the future. He resurrected his argument, and gave it a more frighteningly eugenicist tinge, in his 1879 paper.
Although qualified as a barrister, Edgeworth did not practice law but rather fell into the academic underground of Victorian Britain for the next decade. Edgeworth lectured on a wide variety of topics (Greek, English theatre, logic, moral sciences, etc.) in a wide variety of settings, from Bedford College for Women in London to Wren’s private training school for Indian civil servants. The pay was miserable and prestige non-existent. A hopelessly impractical and deferential man, his applications for more permanent and lucrative positions at established academic institutions met with heartbreakingly little success.
He was giving evening lectures on logic at King’s College, London when he published his most famous and original book, Mathematical Psychics (1881). In it, he criticized Jevons’s theory of barter exchange, showing that under a system of “recontracting” there will be, in fact, many solutions, an “indeterminacy of contract”. Edgeworth’s “range of final settlements” was later resurrected by Martin Shubik (1959) as the game-theoretic concept of “the core”. Edgeworth also articulated what eventually became known as “Edgeworth’s conjecture”, namely that as the number of agents in an economy increase, the degree of indeterminacy is reduced. He argued that in the limit case of an infinite number of agents (“perfect competition”), contract becomes fully determinate and identical to the “equilibrium” of economists. This proposition generated an enormous amount of interest during the 1960s and 1970s. However, as situations of “perfect competition” are not likely to be met in any society, Edgeworth had argued that the only way of resolving this indeterminacy of contract would be to appeal to the utilitarian principle of maximizing the sum of the utilities of traders over the range of final settlements. Incidentally, it was in this 1881 book that Edgeworth introduced into economics the generalized utility function, U(x, y, z, …), and drew the first “indifference curve”.
Edgeworth’s seminal work was given lukewarm reviews by W. Stanley Jevons (1881) and Alfred Marshall (1881). Edgeworth attempted to reach out again to economists and others by restating his theory in a series of journal publications (e.g. 1884, 1889, 1891). Marshall appropriated Edgeworth’s result in his own Principles (1890) textbook, but his distortion of the idea led to a brief controversial exchange of notes in the Giornale degli Economisti in 1891. Alas, it all to no avail. Marshall had successfully swept the entire matter under the rug, where it was to stay for much of the next eighty years.
Edgeworth’s interests were changing anyway. From 1883 onwards, Edgeworth began making his monumental contributions to probability theory and statistics. In his 1885 book Metretike, Edgeworth presented the application and interpretation of significance tests for the comparisions of means. In a series of 1892 papers, Edgeworth examined methods of estimating correlation coefficients. Among his many results was “Edgeworth’s Theorem” giving the correlation coefficients of the multi-dimensional normal distribution. For his efforts, he was elected President of Section F of the British Association for the Advancement of Science in 1889 and later served as president of the Royal Statistical Society (1912 to 1914).
In 1888, on the strength of testimonials from friends and luminaries such as Jevons and Marshall, Edgeworth finally attained his first professional appointment, to the Tooke Chair in Economic Sciences and Statistics and King’s College, London. But that was only a stepping stone. In 1891, he was elected Drummond Professor and Fellow of All-Soul’s College in Oxford, a much-craved position he would hold until retirement.
In 1891, he was also appointed the first editor of The Economic Journal, the main organ of the fledgling British Economic Association (what later became the Royal Economic Society). This was a task he performed with remarkable diligence until 1911, when the post was assumed by John Maynard Keynes. Edgeworth returned as joint editor in 1919, when Keynes had gotten too busy with other activities. Edgeworth continued actively in this role until his death in 1926.
His interest in economic theory picked up again around this time. In 1894, he published a survey of international trade theory in a series of articles in the Economic Journal. In it, he pioneered the use of offer curves and community indifference curves to illustrate its main propositions, including the “optimum tariff”. In that same year, he engaged Eugen von Böhm-Bawerk in a brief controversy over the opportunity cost doctrine.
In 1897, he published a lengthy survey of taxation. It was here that he articulated his famous “taxation paradox”, i.e. that taxation of a good may actually result in a decrease in price. His paradox was disbelieved by contemporaries, “a slip of Mr Edgeworth”, as E.R.A. Seligman put it. However, many years later, Harold Hotelling (1932) rigorously proved that Edgeworth had been correct. Edgeworth also set the utilitarian foundations for highly progressive taxation, arguing that the optimal distribution of taxes should be such that “the marginal disutility incurred by each taxpayer should be the same” (Edgeworth, 1897).
It was also in 1897 when Edgeworth produced his Giornale article on monopoly pricing, where he criticized Cournot’s exact solution to the duopoly problem with quantity adjustments as well as Bertrand’s “instantly competitive” result in a duopoly model with price adjustment. Instead, Edgeworth showed how price competition between two firms with capacity constraints and/or rising marginal cost curves resulted in indeterminacy. For a modern statement of the “Bertrand-Edgeworth” duopoly model, see Levitan and Shubik (1972).
As a critic of the marginal productivity theory, Edgeworth’s articles (1904, 1911) helped refine the Neoclassical theory of distribution on a sounder basis. During the First World War, Edgeworth became particularly interested in questions of war finance. His work in this, although highly original, were a bit too theoretical and did not achieve the practical influence he had hoped.
Finally, as editor of the Economic Journal, Edgeworth often took upon himself the role of reviewing new books in economics. He produced a prodigious amount of reviews, some of which have became classics on their own.
Edgeworth’s contributions to economics were stunning in their originality and depth. But he was notoriously poor at expressing his ideas in a way that was understandable to most of his contemporaries. Trained in languages and the classics, he habitually wrote (and spoke!) in long, intricate and erudite sentences, sprinkling them with numerous obscure classical and literary references. He was in the habit of inventing words (e.g. brachistopone = the “curve of minimal work”) without bothering to define them clearly for readers who could not spot the Greek roots.
If his prose was taxing to read, his use of mathematics was even more negligent of his readers’ abilities. Having taught himself mathematics, Edgeworth must have assumed everyone else had done so as well. He did not bother to provide preliminary explanations of the techniques he was using. Without warning, Edgeworth would glide breathlessly back and forth from his impenetrable prose to no less impenetrable mathematical notation and analysis.
A final point about his personality may be worth mentioning. Many have accused Edgeworth of being excessively “deferential” to authority. He certainly had many “heroes” upon whom he heaped high praise, such as Sidgwick, Jevons and Galton. But he was also quick to wrap his words in velvet when handling opponents such as J. S. Nicholson, Charles Bastable, E.R.A. Seligman and Alfred Marshall.
However, this “deferential” aspect of his character may be due to the simple fact that Edgeworth was not a fighter by nature. Perhaps the painful decades of professional insecurity contributed to this fear. Although he was involved in several critical controversies (as was inevitable for such an original thinker), he would usually withdraw at the first sign of resistance or petulance on the part of his intellectual opponent. His exit would usually be accompanied with a shower of flattery in the hope of avoiding any ill-feeling. And many of his opponents were remarkably vicious. Alfred Marshall, for instance, was a notoriously dirty scrapper and was not averse to intimidation in order to win a debate. If Edgeworth “exhalted [Marshall] to Achilles” (as Schumpeter (1954: p.831) described it), it might be partly because he wanted to avoid incurring his wrath.
Nevertheless, at Oxford and the Royal Economic Society, Edgeworth was largely regarded as “Marshall’s man” and, indeed, he often solicited Marshall’s opinion on many of his decisions. Whatever his motivations, it is true Edgeworth’s professional activities contributed directly to the ascendancy of the Marshallian Neoclassical hegemony and the decline of alternative approaches in Britain around the turn of the century. He blocked Oxford appointments to “undesirable” heterodox scholars such as John A. Hobson. For the Economic Journal, Edgeworth seemed to adopt the editorial policy of rejecting papers which strayed from Marshallian Neoclassicism in their analytical approach or threatened to strike up debates on method that might be uncomfortable to the Marshallian orthodoxy. The work of Lausanne School economists, like Barone, were routinely rejected, as were those of the English Historical school. In his own work and book reviews, Edgeworth defended the Marshallian position against the more radical Neoclassicals of the day.
Edgeworth himself never established a following and his work had little impact in Britain, with the possible exceptions of Arthur Bowley and W.E. Johnson. Across the water, Edgeworth’s work was respected by Irving Fisher, Knut Wicksell and Vilfredo Pareto, but most of his leads were not followed.
However, as the 20th Century progressed, Edgeworth’s stock grew as Marshall’s faded. In the 1930s, some of his contributions were picked up by Paretians such as Harold Hotelling, John Hicks and Abba Lerner. The 1960s and 1970s were characterized by the flowering of an “Edgeworthian” school, led by Martin Shubik, Herbert Scarf, Gérard Debreu, Robert Aumann, Werner Hildenbrand and other mathematical economists