Francis Ysidro Edgeworth

Francis Ysidro Edgeworth

Born: 1845. Died: 1926.

Biography

Francis 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). Alfred 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 neo-classical 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 Joseph 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 neo-classical 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 neo-classicism 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 neo-classicals 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, Gerard Debreu, Robert Aumann, Werner Hildenbrand and other mathematical economists.

Major Books of Francis Ysidro Edgeworth

- A Levy on Capital for the Discharge of the Debt, 1919
- Answers to Questions by Local Taxation Commission, 1899, Reprint of Royal Commission for Local Taxation
- The Cost of War and ways of reducing it suggested by economic theory, 1915
- Currency and Finance in Time of War, 1918
- Entries: "Average", "Census", "Cournot", "Curves", "Demand Curves", Difficulty of Attainment", "Distance in Time", "Error", 1894, in Palgrave, editor, Dictionary of Political Economy, Vol. 1.
- Entries: "Gossen", "Index Numbers", "Intrinsic Value", "Jenkin", "Jennings", "Least Squares" and "Mathematical Method", 1896, in Palgrave, editor, Dictionary of Political Economy, Vol. 2
- Entries: "Pareto", "Pareto's Law", "Probability", "Supply Curve" and "Utility", 1899, in Palgrave, editor, Dictionary of Political Economy, Vol. III
- Four Reports by the committee investigating best method of ascertaining and measuring variations in the monetary standard, 1887, Reports of the BAAS Parts 1 & 3; Part 2
- The Law of Error, 1902, Encyclopedia Britannica
- The Law of Error, 1905, Transactions of Cambridge Society
- Mathematical Psychics: An essay on the application of mathematics to the moral sciences, 1881
- Metretike, or the method of measuring probability and utility, 1887
- New and Old Methods of Ethics, 1877
- On the Relations of Political Economy to War, 1915
- Papers Relating to Political Economy, 3 volumes, 1925
- Preface, 1904, in J.R. MacDonald, editor, Women in the Printing Trades
- Probability and Expectation, 1911, Encyclopedia Britannica

Major Articles of Francis Ysidro Edgeworth

- 1879, The Hedonical Calculus, Mind
- 1882, Mr. Leslie Stephen on Utilitarianism, Mind
- 1883, The Law of Error, Phil Mag
- 1883, The Method of Least Squares, Phil Mag
- 1883, On the Method of Ascertaining a Change in the Value of Gold, JRSS
- 1883, The Physical Basis of Probability, Phil Mag
- 1884, A Priori Probabilities, Phil Mag
- 1884, Chance and Law, Hermathena
- 1884, On the Reduction of Observations, Phil Mag
- 1884, The Philosophy of Chance, Mind
- 1884, The Rationale of Exchange, JRSS
- 1885, Methods of Statistics, Jubilee Volume of RSS
- 1885, On Methods of Ascertaining Variations in the Rate of Births, Deaths and Marriages, JRSS
- 1886, The Law of Error and the Elimination of Chance, Phil Mag
- 1886, Problems in Probabilities, Phil Mag
- 1886, Progressive Means, JRSS
- 1887, The Choice of Means, Phil Mag
- 1887, The Empirical Proof of the Law of Error, Phil Mag
- 1887, Four Reports by the committee investigating best method of ascertaining and measuring variations in the monetary standard, Reports of the BAAS Parts 1 & 3; Part 2
- 1887, The Law of Error, Nature
- 1887, On Discordant Observations, Phil Mag
- 1887, The Method of Measuring Probability and Utility, Mind
- 1888, Mathematical Theory of Banking, JRSS
- 1888, New Methods of Measuring Variation in General Prices, JRSS
- 1888, The Statistics of Examinations, JRSS
- 1888, The Value of Authority Tested by Experiment, Mind
- 1889, Appreciation of Gold, QJE
- 1889, Economic Science and Statistics, Nature
- 1889, The Mathematical Theory of Political Economy: Review of Walras's Elements, Nature
- 1889, Points at which Mathematical Reasoning is Applicable to Political Economy, Nature
- 1889, On the Application of Mathematics to Political Economy: Address of the President of Section F of the British Association for the Advancement of Science, JRSS
- 1890, The Element of Chance in Competitive Examinations, Parts I & II, JRSS
- 1891, An Introductory Lecture on Political Economy, EJ
- 1891, Ancora a proposito della teoria del baratto, GdE
- 1891, La Théorie mathématique de l'offre et de la demande et le côut de production, Revue d'Economie Politique
- 1891, Osservazioni sulla teoria matematica dell' economica politica, GdE (trans. 'On the Determinateness of Economic Equilibrium')
- 1892, Correlated Averages, Phil Mag
- 1892, The Law of Error and Correlated Averages, Phil Mag
- 1892, Recent Attempts to Evaluate the Amount of Coin Circulating in a Country, EJ
- 1893, Statistical Correlation Between Social Phenomena, JRSS
- 1894, Asymmetric Correlation between Social Phenomenon, JRSS
- 1894, The Asymmetrical Probability Curve (Abstract), Proceedings of Royal Society
- 1894, The Measurement of Utility by Money, EJ
- 1894, One More Word on the Ultimate Standard of Value, EJ
- 1894, Recent Writings on Index Numbers, EJ
- 1894, Theory of International Values: Parts I, II and III, EJ
- 1895, The Stationary State in Japan, EJ
- 1895, Thoughts on Monetary Reform, EJ
- 1896, A Defense of Index-Numbers, EJ
- 1896, The Asymmetrical Probability Curve, Phil Mag
- 1896, The Compound law of Error, Phil Mag
- 1896, Statistics on Unprogressive Communities, JRSS
- 1897, La teoria pura del monopolio, GdE, (trans.'The Pure Theory of Monopoly')
- 1897, 1898, Miscellaneous Applications of the Calculus of Probabilities, Parts I, II and III, JRSS
- 1897, The Pure Theory of Taxation: Parts I, II and III, EJ
- 1898, 1899, 1900 On the Representation of Statistics by Mathematical Formulae, Parts I , II, III & IV, supplementary
- 1899, On a Point in the Theory of International Trade, EJ
- 1900, The Incidence of Urban Rates, Parts I, II and III, EJ
- 1900, Defence of Mr. Harrison's Calculation of the Rupee Circulation, EJ
- 1900, Review of Smart's Taxation of Land-Values, EJ
- 1901, Disputed Points in the Theory of International Trade, EJ
- 1902, Methods of Representing Statistics of Wages and Other Groups Not Fulfilling the Normal Law of Error, with A.L. Bowley, JRSS
- 1904, The Theory of Distribution, QJE
- 1906, The Generalised Law of Error, or Law of Great Numbers, JRSS
- 1906, Recent Schemes for Rating Urban Land Values, EJ
- 1907, 1908, Appreciations of Mathematical Theories, Parts I, II, III and IV, EJ
- 1907, On the Representation of Statistical Frequency by a Series, JRSS
- 1907, Statistical Observations on Wasps and Bees, Biometrika
- 1908, On the Probable Errors of Frequency Constants, I, II & III, JRSS
- 1910, Applications of Probabilities to Economics, Part I & Part II, EJ
- 1910, The Subjective Element in the First Principles of Taxation, QJE
- 1911, 1912, 1913, Contributions to the Theory of Railway Rates, Part I, II, Part III and Part IV, EJ
- 1911, Monopoly and Differential Prices, EJ
- 1913, A Variant Proof of the Distribution of Velocities in a Molecular Chaos, Phil Mag
- 1913, On the Use of the Theory of Probabilities in Statistics Relating to Society, JRSS
- 1914, On the Use of Analytical Geometry to Represent Certain Kinds of Statistics, Parts I, Ib, II, III & IV, JRSS
- 1915, Economists on War: Review of Sombart, etc., EJ
- 1915, Recent Contributions to Mathematical Economics, I & II, EJ
- 1916, British Incomes and Property, EJ
- 1916, 1917, On the Mathematical Representation of Statistical Data, Parts I, II, III, IV and V, JRSS
- 1916, Review of Pigou's Economy and Finance of War, EJ
- 1917, After-War Problems: Review of Dawson at al., EJ
- 1917, Some German Economic Writings about the War, EJ
- 1918, An Astronomer on the Law of Error, Phil Mag
- 1918, The Doctrine of Index-Numbers According to Prof. Wesley Mitchell, EJ
- 1918, On the Value of a Mean as Calculated from a Sample, EJ
- 1919, Methods of Graduating Taxes on Income and Capital, EJ
- 1919, Psychical Research and Statistical Method, JRSS
- 1920, Entomological Statistics, Metron
- 1920, Mathematical Formulae and the Royal Commission on Income Tax, EJ
- 1920, 1922, On the Application of Probabilities to the Movement of Gas Molecules, Part I & II, Phil Mag
- 1921, 1922, Molecular Statistics, Part I & Part II, JRSS
- 1921, On the Genesis of the Law of Error, Phil Mag
- 1922, Equal Pay to Men and Women for Equal Work, EJ
- 1922, The Mathematical Economics of Professor Amoroso, EJ
- 1922, The Philosophy of Chance, Mind
- 1923, Index Numbers According to Mr. Walsh, EJ
- 1923, Mr. Correa Walsh on the Calculation of Index Numbers, JRSS
- 1923, Statistics of Examinations, JRSS
- 1923, Women's Wages in Relation to Economic Welfare, EJ
- 1924, Untried Methods of Representing Frequency, JRSS
- 1925, The Element of Probability in Index-Numbers, JRSS
- 1925, The Plurality of Index-Numbers, EJ
- 1925, The Revised Doctrine of Marginal Social Product, EJ
- 1926, Mr Rhode's Curve and the Method of Adjustment, JRSS

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