Francis Ysidro Edgeworth FBA (8 February 1845 – 13 February 1926) was an AngloIrish philosopher and political economist who made significant contributions to the methods of statistics during the 1880s. From 1891 onward, he was appointed the founding editor of The Economic Journal.
Francis Ysidro Edgeworth  

Born  8 February 1845 Edgeworthstown, County Longford, Ireland 
Died  13 February 1926 (aged 81) Oxford, Oxfordshire, England 
Alma mater  Trinity College Dublin Balliol College, Oxford 
Awards  Guy Medal (Gold, 1907) 
Scientific career  
Fields  Philosophy, political economist 
Signature  
Edgeworth was born in Edgeworthstown, County Longford, Ireland. He did not attend school, but was educated by private tutors at the Edgeworthstown estate until he reached the age to enter university. His father, Francis Beaufort Edgeworth, was descended from French Huguenots and "was a restless philosophy student at Cambridge on his way to Germany when he decided to elope with a teenage Catalan refugee Rosa Florentina Eroles 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)...."^{[1]} Richard Lovell Edgeworth was his grandfather, and the writer, Maria Edgeworth, was his aunt.
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.^{[2]}
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 jointeditor until his death 35 years later.^{[3]}
Edgeworth was a highly influential figure in the development of neoclassical 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.
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. 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:^{[4]}
Edgeworth's close friend, William Stanley Jevons, said of Mathematical Psychics:^{[5]}
The Royal Statistical Society awarded him the Guy Medal 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.
In Mathematical Psychics (1881), his most famous and original 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) as the gametheoretic concept of "the core".^{[6]}
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 maximising 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 generalised utility function, U (x, y, z, ...), and drew the first 'indifference curve'.^{[6]}
He was the first one to use offer curves and community indifference curves to illustrate its main propositions, including the "optimal tariff".
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 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.
Edgeworth criticised the marginal productivity theory in several articles (1904, 1911), and tried to refine the neoclassical 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 relates to 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 definition for the reader.^{[7]}
His name was actually Ysidro Francis Edgeworth, but his family and friends called him Francis or Frank, and when he started publishing in 1876 he transposed his Christian names.
Bertrand competition is a model of competition used in economics, named after Joseph Louis François Bertrand (1822–1900). It describes interactions among firms (sellers) that set prices and their customers (buyers) that choose quantities at the prices set. The model was formulated in 1883 by Bertrand in a review of Antoine Augustin Cournot's book Recherches sur les Principes Mathématiques de la Théorie des Richesses (1838) in which Cournot had put forward the Cournot model. Cournot argued that when firms choose quantities, the equilibrium outcome involves firms pricing above marginal cost and hence the competitive price. In his review, Bertrand argued that if firms chose prices rather than quantities, then the competitive outcome would occur with price equal to marginal cost. The model was not formalized by Bertrand: however, the idea was developed into a mathematical model by Francis Ysidro Edgeworth in 1889.The model rests on very specific assumptions. There are at least two firms producing a homogeneous (undifferentiated) product and cannot cooperate in any way. Firms compete by setting prices simultaneously and consumers want to buy everything from a firm with a lower price (since the product is homogeneous and there are no consumer search costs). If two firms charge the same price, consumers' demand is split evenly between them. It is simplest to concentrate on the case of duopoly where there are just two firms, although the results hold for any number of firms greater than one.
A crucial assumption about the technology is that both firms have the same constant unit cost of production, so that marginal and average costs are the same and equal to the competitive price. This means that as long as the price it sets is above unit cost, the firm is willing to supply any amount that is demanded (it earns profit on each unit sold). If price is equal to unit cost, then it is indifferent to how much it sells, since it earns no profit. Obviously, the firm will never want to set a price below unit cost, but if it did it would not want to sell anything since it would lose money on each unit sold. In summary, Bertrand competition is often characterized as harsh, cutthroat competition between firms, driving prices down to marginal cost through a series of price undercutting.
Charles Francis KearyCharles Francis Keary (1848–1917) was born in StokeonTrent, England, and he became a scholar and historian. In his later work as a novelist he also influenced the modernist writer James Joyce. The late nineteenth century English novelist George Gissing read four of Keary's works including three novels in the first thirtyone days of 1896. He found Keary's novel Herbert Vanlennert, "a long, conscientious, uninspired book".Charles was born to a Galway Irish family which had settled in the industrial Midlands borough of StokeonTrent. He was the son of William Keary, who in 1874 would become the first mayor of StokeonTrent.
The young Charles was schooled at Marlborough College and then took his degree at Trinity College, Cambridge. He became fascinated by Scandinavian history and primitive mythology, then a promising new academic field, and wrote a number of scholarly books on such topics. His book The Vikings in Western Christendom (1890) stood as a standard work for many decades. He also became expert on Norway and the Norwegians, and knew many poets and writers there.
Keary worked from 1872 to 1887 at the Department of Coins at The British Museum in London, where he wrote and published A Catalogue Of English Coins In The British Museum: AngloSaxon Series (1887) with Herbert Appold Grueber, and contributed scholarly articles on coins to numismatic journals. Keary was awarded the Medal of the Royal Numismatic Society in 1894. During his time at the British Museum he was the best friend of Francis Ysidro Edgeworth, the AngloIrish philosopher.
Keary then turned from coins and history to writing ambitious literary novels, influenced by the Russian novelists of the time. These works were rather unusual, using a lack of conventional structure in an attempt to suggest the chaos of reality, allied to close observation and a dispassionate approach to character. His novel Herbert Vanlennart (1896) was based on his tour of India, which he had also written up in the short travel book India: Impressions (1903). His later novel Bloomsbury (1905) drew on his experience of moving amid the "curious neurotic intellectualism" (The Spectator review, 8 April 1905) of London literary circles in the Bloomsbury of the late 1880s and early 1890s. At that time, under the pseudonym H. Ogram Matuce, he had published a radically impressionistic prose work titled The Wanderer: From the papers of the late H. Ogram Matuce (1888). In a Spectator review (4 September 1909, of his later novel The Mount) the reviewer remembered that: "For some of us the publication of Mr. C. F. Keary's The Wanderer over twenty years ago was an event".
Keary tried the thenfashionable form of verse drama, with "The Brothers: a Fairy Masque" (1902) and "Rigel: a Mystery" (1904), and moved with more success into philosophy with his The Pursuit of Reason (Cambridge University Press, 1910). After his untimely death, from a heart attack, one further book appeared: The Posthumous Poems of C. F. Keary (1923). But the unfortunate timing of his death, coming amid the full clamour of World War One, hastened his rapid slide into almost total obscurity.
His collection of short works with weird and horrific elements, Twixt Dog and Wolf (1901), is known to have influenced James Joyce's novel Dubliners (1905) – as evidenced in a letter from Joyce dated 24 September 1905 (Letters of James Joyce, Vol. 2, p. 111). Twixt Dog and Wolf was described by fantasy historian Douglas A. Anderson as containing "literary weird fiction of a high order." Keary also wrote the libretto for the opera Koanga (1904) by the composer Frederick Delius, with whom he had detailed discussions. But the collaboration was short and fraught, and it led to no further work with Delius. (See: John White, "The Literary Sources of the Delius Operas", Delius Society Journal, Summer 2004, pp. 16–18).
Keary's sister was the Staffordshire folklorist and folksong collector Miss Alice Annie Keary, close friend of the major folklorist Charlotte Sophia Burne. Keary himself travelled in Europe and dabbled there in folksong collecting, publishing articles such as "Roumanian Peasants and their Songs".
Edgeworth's limit theoremEdgeworth's limit theorem is an economic theorem created by Francis Ysidro Edgeworth that examines a range of possible outcomes which may result from free market exchange or barter between groups of people. It shows that while the precise location of the final settlement (the ultimate division of goods) between the parties is indeterminate, there is a range of potential outcomes which shrinks as the number of traders increases.
Edgeworth (surname)Edgeworth is an English toponymic surname. It probably derives from Edgeworth in Gloucestershire, but the name is long established in Ireland, where it is claimed that the family settled in County Longford in 1583.Notable people with the surname include:
Richard Lovell Edgeworth (1744–1817), AngloIrish scientist, inventor, writer and educator, father of Maria Edgeworth and Michael Pakenham Edgeworth
His son Michael Pakenham Edgeworth (1812–1881), botanist
His daughter Maria Edgeworth (1767–1849), novelist
His grandson Francis Ysidro Edgeworth (1845–1926), statistician and economist
Henry Essex Edgeworth (1745–1807), Irish Catholic priest and confessor of Louis XVI
Kenneth Edgeworth (1880–1972), Irish astronomer, economist and engineerFictional characters:
Miles Edgeworth, character from the Ace Attorney video game series
Edgeworth Professor of EconomicsThe Edgeworth Professor of Economics at the University of Oxford is named in honour of Francis Ysidro Edgeworth, the Drummond Professor of Political Economy from 1891–1922.
Edgeworth boxIn economics, an Edgeworth box, named after Francis Ysidro Edgeworth, is a way of representing various distributions of resources. Edgeworth made his presentation in his book Mathematical Psychics: An Essay on the Application of Mathematics to the Moral Sciences, 1881.
Edgeworth's original twoaxis depiction was developed into the now familiar box diagram by Pareto in his 1906 book "Manual of Political Economy" and was popularized in a later exposition by Bowley. The modern version of the diagram is commonly referred to as the Edgeworth–Bowley box.The Edgeworth box is used frequently in general equilibrium theory. It can aid in representing the competitive equilibrium of a simple system or a range of such outcomes that satisfy economic efficiency. It can also show the difficulty of moving to an efficient outcome in the presence of bilateral monopoly. In the latter case, it serves as a precursor to the bargaining problem of game theory that allows a unique numerical solution.
Edgeworth conjectureIn economics, the Edgeworth conjecture is the idea, named after Francis Ysidro Edgeworth, that the core of an economy shrinks to the set of Walrasian equilibria as the number of agents increases to infinity.
The core of an economy is a concept from cooperative game theory defined as the set of feasible allocations in an economy that cannot be improved upon by subset of the set of the economy's consumers (a coalition). For general equilibrium economies typically the core is nonempty (there is at least one feasible allocation) but also "large" in the sense that there may be a continuum of feasible allocations that satisfy the requirements. The conjecture basically states that if the number of agents is also "large" then the only allocations in the core are precisely what a competitive market would produce. As such, the conjecture is seen as providing some gametheoretic foundations for the usual assumption in general equilibrium theory of price taking agents. In particular, it means that in a "large" economy people act as if they were price takers, even though theoretically they have all the power to set prices and renegotiate their trades. Hence, the fictitious Walrasian auctioneer of general equilibrium, while strictly speaking completely unrealistic, can be seen as a "shortcut" to getting the right answer.
Edgeworth himself did not quite prove this result—hence the term conjecture rather than theorem—although he did provide most of the necessary intuition and went some way towards it. In the 1960s formal proofs were presented under different assumptions by Debreu and Scarf (1963) as well as Aumann (1964). Both of these results however showed that the conditions sufficient for this result to hold were a bit more stringent than Edgeworth anticipated. Debreu and Scarf considered the case of a "replica economy" where there is a finite number of agent types and the agents added to the economy to make it "large" are of the same type and in the same proportion as those already in it. Aumann's result relied on an existence of a continuum of agents.
These proofs of the Edgeworth conjecture are seen as providing some qualified support for the idea that a large economy functions approximately as a price taking competitive economy of general equilibrium theory, even though agents have the power to set prices.
Edgeworth seriesThe Gram–Charlier A series (named in honor of Jørgen Pedersen Gram and Carl Charlier), and the Edgeworth series (named in honor of Francis Ysidro Edgeworth) are series that approximate a probability distribution in terms of its cumulants. The series are the same; but, the arrangement of terms (and thus the accuracy of truncating the series) differ. The key idea of these expansions is to write the characteristic function of the distribution whose probability density function f is to be approximated in terms of the characteristic function of a distribution with known and suitable properties, and to recover f through the inverse Fourier transform.
EdgeworthstownEdgeworthstown or Mostrim (Irish: Meathas Troim, meaning "frontier of the elder tree") is a small town in County Longford, Ireland. The town is in the east of the county, near the border with County Westmeath. Nearby towns are Longford 12 km to the west, Mullingar 26 km to the east, Athlone 40 km to the south and Cavan 42 km to the north.
Fisher informationIn mathematical statistics, the Fisher information (sometimes simply called information) is a way of measuring the amount of information that an observable random variable X carries about an unknown parameter θ of a distribution that models X. Formally, it is the variance of the score, or the expected value of the observed information. In Bayesian statistics, the asymptotic distribution of the posterior mode depends on the Fisher information and not on the prior (according to the Bernstein–von Mises theorem, which was anticipated by Laplace for exponential families). The role of the Fisher information in the asymptotic theory of maximumlikelihood estimation was emphasized by the statistician Ronald Fisher (following some initial results by Francis Ysidro Edgeworth). The Fisher information is also used in the calculation of the Jeffreys prior, which is used in Bayesian statistics.
The Fisherinformation matrix is used to calculate the covariance matrices associated with maximumlikelihood estimates. It can also be used in the formulation of test statistics, such as the Wald test.
Statistical systems of a scientific nature (physical, biological, etc.) whose likelihood functions obey shift invariance have been shown to obey maximum Fisher information. The level of the maximum depends upon the nature of the system constraints.
Frances Anne EdgeworthFrances Anne Edgeworth (née Beaufort) (1769–1865), known as Fanny, was an Irish botanical artist and memoirist. She was the stepmother and confidant of the author Maria Edgeworth.
Frank YatesFrank Yates FRS (12 May 1902 – 17 June 1994) was one of the pioneers of 20th century statistics.
Hector LeakHector Leak CBE (23 July 1887  5 April 1976) was a British statistician. He was appointed a CBE in 1942. He was also the president of the Royal Statistical Society during a short period in 1941. Awarded the silver Guy Medal in 1940.
HedonimetryHedonimetry is the study of happiness as a measurable economic asset. The first major work in the field was an 1881 publication of Mathematical Psychics by the famous statistician and economist Francis Ysidro Edgeworth, who hypothesized a way of measuring happiness in units. In recent times, it has been applied to many areas, including consumer behavior and health care.
HedonometerA hedonometer or hedonimeter is a device used to gauge happiness or pleasure. Conceived of at least as early as 1880, the term was used in 1881 by the economist Francis Ysidro Edgeworth to describe "an ideally perfect instrument, a psychophysical machine, continually registering the height of pleasure experienced by an individual."More recently, it has been used to refer to a tool developed by Peter Dodds and Chris Danforth to gauge the valence of various corpora, including historical State of the Union addresses, song lyrics, and online tweets and blogs. A version of the tool is available at hedonometer.org, which they call a sort of "Dow Jones Index of Happiness", and hope will be used by government officials in conjunction with other metrics as a gauge of the population's wellbeing.
Henry William MacrostyHenry William Macrosty (1865 – 19 January 1941) was President of the Royal Statistical Society between 1940–41.Macrosty was active in the Fabian Society for many years, writing a proposed bill creating an eighthour working day in 1893, "The Revival of Agriculture: a proposed policy for Great Britain" in 1905, and several other tracts for the society. From 1895 until 1906, he served on the society's executive.
OrganyàOrganyà is a municipality in the comarca of the Alt Urgell in Catalonia. It is situated on the right bank of the Segre river below the Trespons gorge, and is served by the C14 road between Ponts and La Seu d'Urgell. There is a monument to the Homilies d'Organyà, a 12th or 13th century collection of sermons which is the oldest literary text in the Catalan language to survive in its entirety, discovered in the town in 1904.
Organyà is the birthplace of Rosa Florentina Eroles (18151864), the mother of Francis Ysidro Edgeworth. [1]
The municipality surrounds an exclave of Cabó.
Patrick CraigiePatrick George Craigie (29 May 1843 – 10 January 1930) was a British agricultural statistician. He was born in Perth and educated at Edinburgh and Cambridge Universities. Craigie headed the Statistical, Intelligence, and Educational Branch of the Board of Agriculture from 1890 until his retirement in 1906 and was prominent in the Royal Statistical Society, serving as its President from 1902–1904. In 1908 he was awarded the Society's highest honour, the Guy Medal in Gold, recognising his "extraordinary services to statistical science in connection with the development of agricultural statistics." From 1861 to 1882 Craigie served in the Royal Perth Militia: his military rank served as a title and so in later years he was generally referred to as Major Craigie.
Valerie IshamValerie Susan Isham (born 1947) is a British applied probabilist and President of the Royal Statistical Society 2011–12.
Isham's research interests in include point processes, spatial processes, spatiotemporal processes and population processes. She went to Imperial College London (B.Sc., Ph.D.) where she was a student of a prominent statistician David Cox. She has been a professor of probability and statistics at University College London since 1992. She was the president of the Royal Statistical Society for 2011–2012. She was awarded its Guy Medal in Bronze in 1990.
 
 

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