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Francis Ysidro Edgeworth (né Ysidro Francis Edgeworth, February 8, 1845 – February 13, 1926) was an Irish polymath who studied at Trinity College, Dublin before obtaining a scholarship to Balliol College, Oxford where he subsequently became a professor. A deep thinker, his contributions were far ahead of his time.

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 large. The high degree of originality demonstrated in his most important book on economics, Mathematical Psychics, was matched only by the difficulty of reading it. He frequently referenced literary sources and interspersed the writing with passages in a number of languages, including Latin, French and Ancient Greek.

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.
While Jevons noted:

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.
He was the editor of the Economic Journal from its creation in 1891 and was succeeded in this role by John Maynard Keynes in 1926.

As a self-taught mathematical statistician he is remembered by the eponymous Edgeworth series. He wrote the article on Probability in the 1911 edition of the Encyclopædia Britannica. In 1928 A. L. Bowley published a book F. Y. Edgeworth’s Contributions to Mathematical Statistics.

The Royal Statistical Society awarded him the Guy Medal in 1907, and he later (1912-14) served as President of the Society.

He was also a barrister, and held the Tooke chair of Economic Science at King’s College, London and later the Drummond Chair of Political Economy at Oxford.

In Mathematical Psychics (1881), his most famous and original book, 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".

As 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), 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 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’.

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).

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.

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.

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.