Background
Edgeworth was born on February 8, 1845, in Edgeworthstown, Longford, Ireland. Richard Lovell Edgeworth was his grandfather, and Maria Edgeworth his aunt. His father was Francis Beaufort Edgeworth who "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.
Education
As a student at Trinity College, Dublin, and Balliol College, Oxford, Edgeworth studied ancient and modern languages. 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.
Career
On the basis of his publications in economics and mathematical statistics in the 1880s, he was appointed to a chair in economics at King's College London in 1888, and in 1891 was appointed Drummond Professor of Political Economy at Oxford University. Also in 1891, he was appointed the founding editor of The Economic Journal. He continued to be the editor or joint-editor until his death 35 years later. The Economic Journal remains one of the leading scholarly publications in economics today.
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. In statistics, Edgeworth is most prominently remembered by having his name on the Edgeworth series.
Contributions to economics. 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".
Edgeworth's conjecture. 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), the 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'.
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. 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).
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. This gave rise to the Bertrand-Edgeworth Model of oligopoly.
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 World War I was original, they were a bit too theoretical and did not achieve the practical influence he had hoped.
Edgeworth's limit theorem. Edgeworth's limit theorem relates to the equilibrium of supply and demand in a free market. See Edgeworth's limit theorem. 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 a definition for the reader.