Francis Ysidro Edgeworth

Francis Y. Edgeworth

Francis Ysidro Edgeworth (February 8, 1845 – February 13, 1926) was an Irish polymath, a highly influential figure in the development of neo-classical economics. He was the first to apply certain mathematical techniques to individual decision making in economics. He expanded utility theory, introducing terms like indifference curve and Edgeworth box, and coined the famous Edgeworth conjecture.

Life

Francis Edgeworth was born in Edgeworthstown, Ireland, into a large and wealthy landowning family. His aunt was the famous novelist Maria Edgeworth, who wrote the Castle Rackrent. He was educated by private tutors until 1862, when he went on to study classics and languages at Trinity College, Dublin. In 1867 he enrolled to University of Oxford, where he obtained his degree in 1869 in Literae Humaniores. His degree was awarded in 1873.

In 1870s, Edgeworth moved to Hempstead, near London. He lived on the private income, and continued to study. He finished law school, and in 1877 was called to the bar by the Inner Temple. He also studied mathematics and statistics on his own. It is probably that he became interested in economy through his Hempstead neighbor, William Stanley Jevons.

Edgeworth published his first book, New and Old Methods of Ethics in 1877, followed by several minor papers. He made money by lecturing on a wide variety of topics, from Greek language and English theatre, to logic and mathematics. He tried several times to secure a more prestigious position at a university, but without success.

In 1881 he published his most famous book, Mathematical Psychics, in which he introduced several new concepts, like "Edgeworth's conjecture" and the "indifference curve". In it he demonstrated the high degree of originality, matched only by the difficulty of reading it. The book initially received a lukewarm welcome, but has influenced Alfred Marshall in writing his own Principles in 1890.

Edgeworth turned his interest to statistics and probability theory, writing in 1885 his Metretike. With this work he finally received academic recognition, and was elected President of Section F of the British Association for the Advancement of Science in 1889. In 1892 he published a series of papers on correlation coefficients.

In 1888 he was elected the Tooke Chair in Economic Sciences and Statistics and King's College, London, and in 1891 the Drummond Professor and Fellow of All-Soul's College in Oxford. He held the later position until his retirement.

In 1891 Edgeworth became the editor of the Economic Journal, the main publication of the British Economic Association, the position he served until 1911, when he was succeeded by John Maynard Keynes. He again became editor of it in 1919, when Kaynes became too busy with other duties, and stayed on it until his death.

In 1897, he published a survey of taxation, where he introduced his famous "taxation paradox", and in early 1900s he focused on the critic of the marginal productivity theory. He wrote the article on probability in the 1911 edition of the Encyclopædia Britannica, and served as the President of the Royal Statistical Society from 1912 to 1914. During the World War I he wrote on war finances.

Edgeworth became the sole heir of his family wealth in 1911, after his four older brothers previously died. He never married, although he attempted to court Beatrice Potter, the famous Fabian Socialist. Edgeworth died in 1926 in Oxfordshire, England

Work

Edgeworth’s published his Mathematical Psychics: An Essay on the Application of Mathematics to the Moral Sciences in 1881, which became his most famous and original book. In it he elaborated on the Economical Calculus and the Utilitarian Calculus, and presented his theory of economics. He attempted to apply mathematical principles on various social phenomena, including a capacity for happiness and a capacity for work. He concluded that women have less capacity for pleasure, and less capacity for work than men. In his Methods of Statistics (1885) he made an exposition of the application of significance tests for the comparison of means.

In Mathematical Psychics he also criticized William Stanley 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 as the game-theoretic concept of "the core".

Edgeworth's conjecture

Edgeworth argued that as the number of subjects in an economy increases, the degree of indeterminacy is reduced. In the case of perfect competition, where there is an infinite number of subjects, the contract becomes identical to the 'equilibrium' of economists. However, the perfect competition is almost impossible to meet in the real world. He said:

"Equilibrium is attained when the existing contracts can neither be varied without recontract with the consent of the existing parties, nor by recontract within the field of competition. The advantage of this general method is that it is applicable to the particular case of imperfect competition where the conceptions of demand and supply at a price are no longer appropriate." (Mathematical Psychics, p.31)

The only way of resolving indeterminacy of contract thus is to appeal to the utilitarian principle of maximizing the sum of the utilities of traders over the range of final settlements. Edgeworth introduced into economics the generalized utility function, U(x, y, z, ...), and the "indifference curve".

Edgeworth Box

Edgeworth Box is a way of representing various distributions of economic resources. It is a rectangular diagram with Subject A's Origin on one corner, and Subject B's origin on the opposite corner. The width of the box is the total amount of one good, and the height is the total amount of the other good. Thus, every possible division of the goods between the two people can be represented as a point in the box. If we draw among points in the Edgeworth's Box, we get indifference curves, representing combinations of the goods that are of equal value for both Subject A and Subject B. Edgeworth's original two axis depiction was developed into the now familiar box diagram by Pareto in 1906.

Edgeworth limit theorem

Edgeworth used a variant of what is now known as the Edgeworth box (with quantities traded, rather than quantities possessed, on the relevant axes) to analyse trade between groups of traders of various sizes. In general he found that 'Contract without competition is indeterminate, contract with perfect competition is perfectly determinate, [and] contract with more or less perfect competition is less or more indeterminate.'

International trade

He was the first one to use offer curves and community indifference curves to illustrate its main propositions, including the "optimum tariff".

Taxation paradox

Taxation of a good may actually result in a decrease in price.

He 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). The economists of his time disregarded Edgeworth’s taxation paradox as a “mistake”, but more than thirty years later, Harold Hotelling (1932) rigorously proved that Edgeworth had been right.

Monopoly pricing

In 1897, in an article on monopoly pricing, Edgeworth 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. At the same time, Edgeworth showed how price competition between two firms with capacity constraints and/or rising marginal cost curves resulted in indeterminacy.

Marginal productivity theory

Edgeworth criticized the marginal productivity theory in several articles (1904, 1911), and tried to refine the neo-classical theory of distribution on a more solid basis. Although his work in questions of war finance during the World War I was original, they were a bit too theoretical and did not achieve the practical influence he had hoped.

Legacy

Though Edgeworth's ideas were original and in depth, his manner of expression was not understandable to most of his contemporaries. Being well trained in languages and the classics, his words were long, intricate and erudite, not to mention the numerous obscure classical and literary references accompanying them.

Edgeworth was often regarded as “Marshall's man", referring to his support of Alfred Marshall. It was Edgeworth who greatly contributed toward the establishment of the Marshallian Neoclassical hegemony and the decline of any alternative approach.

Edgeworth himself never managed to attract any significant number of followers, thus never forming a school of thought. He was nevertheless respected by Arthur Bowley and W.E. Johnson in Britain, and Irving Fisher, Knut Wicksell and Vilfredo Pareto in United States. Pareto’s followers Harold Hotelling and Abba Lerner revived the interest in Edgeworth again in 1930s. In 1960s and 1970s, as the interest in mathematical economy flourished, Edgeworth’s works again became the center of academic curiosity. A group of mathematical economists, led by Herbert Scarf, Werner Hildenbrand, Martin Shubik, Gérard Debreu, and Robert Aumann, formed an "Edgeworthian" school of thought.

Publications

• Edgeworth, Francis Y. 1877. New and Old Methods of Ethics, or "Physical ethics" and "Methods of ethics". Oxford: J. Parker.
• Edgeworth, Francis Y. 1879. The Hedonical Calculus. Mind, 4(15), 394-408.
• Edgeworth, Francis Y. 1904. The Theory of Distribution. The Quarterly Journal of Economics, 2.
• Edgeworth, Francis Y. 1884. The Rationale of Exchange. Journal of Royal Statistical Society, 47, 165-6.
• Edgeworth, Francis Y. 1887. Metretike, or the method of measuring probability and utility. The Temple Co
• Edgeworth, Francis Y. 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.
• Edgeworth, Francis Y. 1894. The asymmetrical probability curve. Harrison and Sons.
• Edgeworth, Francis Y. 1894. Theory of International Values: Parts I, II and III. Economic Journal
• Edgeworth, Francis Y. 1915. On the Relations of Political Economy to War. London: Oxford University Press, H. Milford.
• Edgeworth, Francis Y. 1918. Currency and Finance in Time of War. London: Oxford University Press, H. Milford
• Edgeworth, Francis Y. 1925. Papers Relating to Political Economy (3 Vols.). Macmillan
• Edgeworth, Francis Y. 1981 (original published in 1881). Mathematical Psychics: An essay on the application of mathematics to the moral sciences. Augustus M Kelley Pubs. ISBN 0678003084

References

ISBN links support NWE through referral fees

• Blaug, Mark. 1992. Alfred Marshall and Francis Edgeworth. Edward Elgar Pub. ISBN 185278492X
• Edgeworth, Maria. 2006 (original published in 1800). Castle Rackrent. 1st World Library. ISBN 1421803712
• Fitzpatrick, P. J. 1960. Leading British statisticians of the nineteenth century. Journal of the American Statistical Association 55, 38-70.
• Friel, Charles M. Biographies of Statisticians: Francis Edgeworth. Sam Houston State University. Retrieved on February 22, 2007, <http://www.shsu.edu/~icc_cmf/bio/edgeworth.html>
• Gilles, Robert P. 2005. Economic exchange and social organization: the Edgeworthian foundations of general equilibrium theory. Springer. ISBN 0792342003
• Keynes, John Maynard. 1926. Francis Ysidro Edgeworth, 1845-1926: A memoir. London: Royal Economic Society.
• Kendall, M.G. 1968. Francis Ysidro Edgeworth, 1845-1926. Biometrika, 55, 269-275.
• NewSchool.edu. Francis Ysidro Edgeworth. Retrieved on February 22, 2007, <http://cepa.newschool.edu/het/profiles/edgew.htm>
• Spiegel, Henry W. 1991. The Growth of Economic Thought. Ed. Durham & London. Duke University Press.

External links

• A Chronology of Game Theory – On the history of Game Theory, by Paul Walker
• Biography – Short biography
• Francis Y. Edgeworth – Biography
• Francis Ysidro Edgeworth – Biography and resources on Edgeworth
• Game Theory – On the game theory in economics
• John J. O'Connor and Edmund F. Robertson. Francis Ysidro Edgeworth at the MacTutor archive
• New School: Francis Ysidro Edgeworth – Extended biography with a list of his works
• Work and life of F.Y Edgeworth – On Edgeworth’s life and work

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