Francis Ysidro Edgeworth

Life

Ysidro Francis Edgeworth – the order of his forenames later reversed – was born in Edgeworthstown, County Longford, Ireland, the son of Francis Beaufort Edgeworth and his wife, Rosa Florentina, daughter of exiled Catalan general Antonio Eroles. Francis Beaufort Edgeworth, when "a restless philosophy student at Cambridge on his way to Germany", had met Rosa, a teenage Spanish refugee, on the steps of the British Museum, and they subsequently eloped. Francis Beaufort Edgeworth was the son of politician, writer, and inventor Richard Lovell Edgeworth (father also of the writer Maria Edgeworth), by his fourth wife, the botanical artist and memoirist Frances Anne, daughter of the Anglican clergyman and geographer Daniel Augustus Beaufort, of French Huguenot origin. The Edgeworth family, which settled in Ireland in the 1580s, was distinguished, descending from Francis Edgeworth, joint Clerk of the Crown and Hanaper in 1606, who inherited a fortune from his brother Edward Edgeworth, Bishop of Down and Connor. Richard Lovell Edgeworth was a descendant, through his mother, of the English judge Sir Salathiel Lovell.

The youngest of seven children, Edgeworth did not attend school, but was educated by private tutors at the Edgeworthstown estate until he reached the age to enter university.

As a student at Trinity College Dublin he studied classics getting a scholarship in 1863 and graduating in 1865. In 1867, he went to Oxford and was admitted to Balliol College, Oxford in 1868. At Oxford, Edgeworth studied ancient and modern languages. During his studies, he was influenced by Jeremy Bentham's writings.

A voracious autodidact, he studied mathematics and economics only after he had completed university. He qualified as a barrister in London in 1877 but did not practise.

On the basis of his publications in economics and mathematical statistics in the 1880s, Edgeworth was appointed to a chair in economics at King's College London in 1888, and in 1891, he was appointed Drummond Professor of Political Economy at Oxford University. In 1891, he was also appointed the founding editor of The Economic Journal. He continued as editor or joint-editor until his death 35 years later.

The Royal Statistical Society awarded him the Guy Medal in Gold in 1907. Edgeworth served as the president of the Royal Statistical Society, 1912–14. In 1928, Arthur Lyon Bowley published a book entitled and devoted to F. Y. Edgeworth's Contributions to Mathematical Statistics.

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Contributions to economics

Edgeworth was a highly influential figure in the development of neo-classical economics. He was the first to apply certain formal mathematical techniques to individual decision making in economics. He developed utility theory, introducing the indifference curve and the famous Edgeworth box, which is now familiar to undergraduate students of microeconomics. He is also known for the Edgeworth conjecture, which states that the core of an economy shrinks to the set of competitive equilibria as the number of agents in the economy gets larger. In statistics, Edgeworth is most prominently remembered by having his name on the Edgeworth series.

Though Edgeworth's economic ideas were original and in depth, his contemporaries frequently complained of his manner of expression for lack of clarity. He was prone to verbosity and coining obscure words without providing definition for the reader.

Mathematical Psychics (1881)

His most original and creative book on economics was Mathematical Psychics: An Essay on the Application of Mathematics to the Moral Sciences, published in 1881 at the beginning of his long career in the subject.

In the book, he criticised 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) to be the game-theoretic concept of "the core". The book contained the first instance of the indifference curve, as level sets of the generalised utility function, U(x, y, z, ...).

The book was notoriously difficult to read. He frequently referenced literary sources and interspersed the writing with passages in a number of languages, including Latin, French and Ancient Greek. The mathematics was similarly difficult, and a number of his creative applications of mathematics to economic or moral issues were judged as incomprehensible. However, one of the most influential economists of the time, Alfred Marshall, commented in his review of Mathematical Psychics:

This book shows clear signs of genius, and is a promise of great things to come... His readers may sometimes wish that he had kept his work by him a little longer till he had worked it out a little more fully, and obtained that simplicity which comes only through long labour. But taking it as what it claims to be, 'a tentative study', we can only admire its brilliancy, force, and originality.

Edgeworth's close friend, William Stanley Jevons, said of Mathematical Psychics:

Whatever else readers of this book may think about it, they would probably all agree that it is a very remarkable one.... There can be no doubt that in the style of his composition Mr. Edgeworth does not do justice to his matter. His style, if not obscure, is implicit, so that the reader is left to puzzle out every important sentence like an enigma.

Edgeworth's limit theorem

When the number of agents in an economy increases, the degree of indeterminacy is reduced. In the limit case of an infinite number of agents (perfect competition), the set of possible contract becomes fully determinate and identical to the 'equilibrium' of economists. The only way of resolving this indeterminacy of contract would be to appeal to the utilitarian principle of maximising the sum of the utilities of traders over the range of final settlements.

International trade

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

Taxation paradox

In what became known as the taxation paradox, Edgeworth found that the taxation of a good could result in a decrease in price. He used the example of pricing for rail passengers, where a tax on first-class tickets could result in lower prices for both first-class and regular class passengers.

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).

Monopoly pricing

In 1897, in an article on monopoly pricing, Edgeworth criticised 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. This gave rise to the Bertrand–Edgeworth model of oligopoly.

Marginal productivity theory

Edgeworth criticised 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 World War I was original, they were a bit too theoretical and did not achieve the practical influence he had hoped.