Francis Ysidro Edgeworth
Encyclopedia
Francis Ysidro Edgeworth FBA (8 February 1845, Edgeworthstown
– 13 February 1926, Oxford
) was an Irish
philosopher and political economist who made significant contributions to the methods of statistics
during the 1880s. From 1891 onward he was the editor of a leading academic journal in economics
and his own writings in economics were influential.
, 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. 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 Catalonia
n refugee 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) ..."
As a student at Trinity College, Dublin
, and Balliol College, Oxford
, Edgeworth studied ancient and modern languages. A voracious autodidact, he studied mathematics or economics only after he had completed university. He qualified as a barrister
in London
in 1877 but did not practice.
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
.
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 would be judged as incomprehensible. However, one of the most influential economists of the time, Alfred Marshall
, commented in his review of Mathematical Psychics:
Edgeworth's close friend William Stanley Jevons
said of Mathematical Psychics:
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 A.L. Bowley
published a book entitled and devoted to F. Y. Edgeworth's Contributions to Mathematical Statistics.
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'.
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 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 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.
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----
----
Edgeworthstown
Edgeworthstown or Mostrim is a town in County Longford, Ireland. The Edgeworthstown name is derived from the Edgeworth Family who have a long association with the town as the family estate of Henry Essex Edgeworth de Firmont was nearby, while Mostrim is an anglicisation of the town's pre-conquest...
– 13 February 1926, Oxford
Oxford
The city of Oxford is the county town of Oxfordshire, England. The city, made prominent by its medieval university, has a population of just under 165,000, with 153,900 living within the district boundary. It lies about 50 miles north-west of London. The rivers Cherwell and Thames run through...
) was an Irish
Irish people
The Irish people are an ethnic group who originate in Ireland, an island in northwestern Europe. Ireland has been populated for around 9,000 years , with the Irish people's earliest ancestors recorded having legends of being descended from groups such as the Nemedians, Fomorians, Fir Bolg, Tuatha...
philosopher and political economist who made significant contributions to the methods of statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
during the 1880s. From 1891 onward he was the editor of a leading academic journal in economics
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
and his own writings in economics were influential.
Life
Edgeworth was born in EdgeworthstownEdgeworthstown
Edgeworthstown or Mostrim is a town in County Longford, Ireland. The Edgeworthstown name is derived from the Edgeworth Family who have a long association with the town as the family estate of Henry Essex Edgeworth de Firmont was nearby, while Mostrim is an anglicisation of the town's pre-conquest...
, County Longford
County Longford
County Longford is a county in Ireland. It is part of the Midlands Region and is also located in the province of Leinster. It is named after the town of Longford.Longford County Council is the local authority for the county...
, Ireland
Ireland
Ireland is an island to the northwest of continental Europe. It is the third-largest island in Europe and the twentieth-largest island on Earth...
. He did not attend school, but was educated by private tutors at the Edgeworthstown estate until he reached the age to enter university. Richard Lovell Edgeworth
Richard Lovell Edgeworth
Richard Lovell Edgeworth was an Anglo-Irish politician, writer and inventor.-Biography:Edgeworth was born in Pierrepont Street, Bath, England, grandson of Sir Salathiel Lovell through his daughter, Jane Lovell....
was his grandfather, and Maria Edgeworth
Maria Edgeworth
Maria Edgeworth was a prolific Anglo-Irish writer of adults' and children's literature. She was one of the first realist writers in children's literature and was a significant figure in the evolution of the novel in Europe...
his aunt. His father was Francis Beaufort Edgeworth who "was a restless philosophy student at Cambridge
Cambridge
The city of Cambridge is a university town and the administrative centre of the county of Cambridgeshire, England. It lies in East Anglia about north of London. Cambridge is at the heart of the high-technology centre known as Silicon Fen – a play on Silicon Valley and the fens surrounding the...
on his way to Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
when he decided to elope with a teenage Catalonia
Catalonia
Catalonia is an autonomous community in northeastern Spain, with the official status of a "nationality" of Spain. Catalonia comprises four provinces: Barcelona, Girona, Lleida, and Tarragona. Its capital and largest city is Barcelona. Catalonia covers an area of 32,114 km² and has an...
n refugee he met on the steps of the British Museum
British Museum
The British Museum is a museum of human history and culture in London. Its collections, which number more than seven million objects, are amongst the largest and most comprehensive in the world and originate from all continents, illustrating and documenting the story of human culture from its...
. One of the outcomes of their marriage was Ysidro Francis Edgeworth (the name order was reversed later) ..."
As a student at Trinity College, Dublin
Trinity College, Dublin
Trinity College, Dublin , formally known as the College of the Holy and Undivided Trinity of Queen Elizabeth near Dublin, was founded in 1592 by letters patent from Queen Elizabeth I as the "mother of a university", Extracts from Letters Patent of Elizabeth I, 1592: "...we...found and...
, and Balliol College, Oxford
Balliol College, Oxford
Balliol College , founded in 1263, is one of the constituent colleges of the University of Oxford in England but founded by a family with strong Scottish connections....
, Edgeworth studied ancient and modern languages. A voracious autodidact, he studied mathematics or economics only after he had completed university. He qualified as a barrister
Barrister
A barrister is a member of one of the two classes of lawyer found in many common law jurisdictions with split legal professions. Barristers specialise in courtroom advocacy, drafting legal pleadings and giving expert legal opinions...
in London
London
London is the capital city of :England and the :United Kingdom, the largest metropolitan area in the United Kingdom, and the largest urban zone in the European Union by most measures. Located on the River Thames, London has been a major settlement for two millennia, its history going back to its...
in 1877 but did not practice.
On the basis of his publications in economics
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
and mathematical statistics
Mathematical statistics
Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and analysis...
in the 1880s, he was appointed to a chair in economics at King's College London
King's College London
King's College London is a public research university located in London, United Kingdom and a constituent college of the federal University of London. King's has a claim to being the third oldest university in England, having been founded by King George IV and the Duke of Wellington in 1829, and...
in 1888, and in 1891 was appointed Drummond Professor of Political Economy
Drummond Professor of Political Economy
The Drummond Professorship of Political Economy at All Souls College, Oxford has been held by a number of distinguished individuals, including three Nobel laureates. The professorship is named after and was founded by Henry Drummond...
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
Indifference curve
In microeconomic theory, an indifference curve is a graph showing different bundles of goods between which a consumer is indifferent. That is, at each point on the curve, the consumer has no preference for one bundle over another. One can equivalently refer to each point on the indifference curve...
and the famous Edgeworth box
Edgeworth box
In 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...
, which is now familiar to undergraduate students of microeconomics
Microeconomics
Microeconomics is a branch of economics that studies the behavior of how the individual modern household and firms make decisions to allocate limited resources. Typically, it applies to markets where goods or services are being bought and sold...
. He is also known for the Edgeworth conjecture
Edgeworth conjecture
In 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....
which states that the core
Core (economics)
The core is the set of feasible allocations that cannot be improved upon by a subset of the economy's consumers. A coalition is said to improve upon or block a feasible allocation if the members of that coalition are better off under another feasible allocation that is identical to the first...
of an economy shrinks to the set of competitive equilibria
General equilibrium
General equilibrium theory is a branch of theoretical economics. It seeks to explain the behavior of supply, demand and prices in a whole economy with several or many interacting markets, by seeking to prove that a set of prices exists that will result in an overall equilibrium, hence general...
as the number of agents
Agent (economics)
In economics, an agent is an actor and decision maker in a model. Typically, every agent makes decisions by solving a well or ill defined optimization/choice problem. The term agent can also be seen as equivalent to player in game theory....
in the economy gets large. In statistics Edgeworth is most prominently remembered by having his name on the Edgeworth series
Edgeworth series
The Gram–Charlier A series , and the Edgeworth series are series that approximate a probability distribution in terms of its cumulants...
.
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
Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...
, French
French language
French is a Romance language spoken as a first language in France, the Romandy region in Switzerland, Wallonia and Brussels in Belgium, Monaco, the regions of Quebec and Acadia in Canada, and by various communities elsewhere. Second-language speakers of French are distributed throughout many parts...
and Ancient Greek
Ancient Greek
Ancient Greek is the stage of the Greek language in the periods spanning the times c. 9th–6th centuries BC, , c. 5th–4th centuries BC , and the c. 3rd century BC – 6th century AD of ancient Greece and the ancient world; being predated in the 2nd millennium BC by Mycenaean Greek...
. The mathematics was similarly difficult, and a number of his creative applications of mathematics to economic or moral issues would be judged as incomprehensible. However, one of the most influential economists of the time, Alfred Marshall
Alfred Marshall
Alfred Marshall was an Englishman and one of the most influential economists of his time. His book, Principles of Economics , was the dominant economic textbook in England for many years...
, 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
William Stanley Jevons
William Stanley Jevons was a British economist and logician.Irving Fisher described his book The Theory of Political Economy as beginning the mathematical method in economics. It made the case that economics as a science concerned with quantities is necessarily mathematical...
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.
The Royal Statistical Society
Royal Statistical Society
The Royal Statistical Society is a learned society for statistics and a professional body for statisticians in the UK.-History:It was founded in 1834 as the Statistical Society of London , though a perhaps unrelated London Statistical Society was in existence at least as early as 1824...
awarded him the Guy Medal
Guy Medal
The Guy Medals are awarded by the Royal Statistical Society in three categories; Gold, Silver and Bronze. The Gold Medal is awarded triennially, the other two are awarded annually...
in 1907. Edgeworth served as the president of the Royal Statistical Society, 1912-14. In 1928 A.L. Bowley
Arthur Lyon Bowley
Sir Arthur Lyon Bowley was an English statistician and economist who worked on economic statistics and pioneered the use of sampling techniques in social surveys....
published a book entitled and devoted to F. Y. Edgeworth's Contributions to Mathematical Statistics.
Contributions to economics
In Mathematical Psychics (1881), his most famous and original book, he criticised Jevons's theory of barterBarter
Barter is a method of exchange by which goods or services are directly exchanged for other goods or services without using a medium of exchange, such as money. It is usually bilateral, but may be multilateral, and usually exists parallel to monetary systems in most developed countries, though to a...
exchange
Trade
Trade is the transfer of ownership of goods and services from one person or entity to another. Trade is sometimes loosely called commerce or financial transaction or barter. A network that allows trade is called a market. The original form of trade was barter, the direct exchange of goods and...
, 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
Martin Shubik
Martin Shubik is an American economist, who is Professor Emeritus of Mathematical Institutional Economics at Yale University. He was educated at the University of Toronto and Princeton University...
(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), 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
Utility
In economics, utility is a measure of customer satisfaction, referring to the total satisfaction received by a consumer from consuming a good or service....
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
Tariff
A tariff may be either tax on imports or exports , or a list or schedule of prices for such things as rail service, bus routes, and electrical usage ....
".
- 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
Duopoly
A true duopoly is a specific type of oligopoly where only two producers exist in one market. In reality, this definition is generally used where only two firms have dominant control over a market...
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
Marginal cost
In economics and finance, marginal cost is the change in total cost that arises when the quantity produced changes by one unit. That is, it is the cost of producing one more unit of a good...
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
War finance
The term war finance, a branch of defense economics, denotes a number of measures including fiscal and monetary initiatives to fund the expenditure of a war. Such measures, broadly classified in three categories, are levy of taxes, raising of debts, and creation of fresh money supply...
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 equilibrium of supply and demand in a free market. See Edgeworth's limit theorem
Edgeworth's limit theorem
Edgeworth'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...
.
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
Verbosity
Verbosity in language refers to speech or writing which is deemed to use an excess of words. Adjectival forms are verbose, wordy, prolix and garrulous.-History:...
and coining obscure words without providing definition for the reader.
Collections/Selections
- F. Y. Edgeworth (1925) Papers relating to political economy 3 vols. Available online at Gallica
- Philip Mirowski (ed.)(1994). Edgeworth's Writings on Chance, Economic Hazard, and Statistics, Rowman & Littlefield.
- Charles R. McCann Jr. (ed.)(1966) F.Y. Edgeworth: Writings in Probability, Statistics and Economics, 3 vols. Cheltenham, Glos.: Elgar.
- Peter Newman (ed.) (2003) F.Y. Edgeworth : Mathematical psychics, and further papers on political economy Oxford University Press.
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Individual works
- "Mr. Mathew Arnold on Bishop Butler's Doctrine of Self-Love", 1876, Mind
- New and Old Methods of Ethics, 1877.
- "The Hedonical Calculus", 1879, Mind
----
- Mathematical Psychics: An essay on the application of mathematics to the moral sciences, 1881.
- "Mr. Leslie Stephen on Utilitarianism", 1882, Mind
- "The Law of Error", 1883, Phil Mag
- "The Method of Least Squares", 1883, Phil Mag
- "The Physical Basis of Probability", 1883, Phil Mag
- "On the Method of Ascertaining a Change in the Value of Gold", 1883, JRSS
- "Review of Jevons's Investigations", 1884, Academy
- "The Rationale of Exchange", 1884, JRSS
- "The Philosophy of Chance", 1884, Mind
- "On the Reduction of Observations", 1884, Phil Mag
- "A Priori Probabilities", 1884, Phil Mag
- "Chance and Law", 1884, Hermathena
- "Methods of Statistics", 1885, Jubilee Volume of RSS.
- "The Calculus of Probabilities Applied to Psychic Research, I & II", 1885, 1886, Proceedings of Society for Psychic Research
- "On Methods of Ascertaining Variations in the Rate of Births, Deaths and Marriages", 1885, JRSS
- "Progressive Means", 1886, JRSS
- "The Law of Error and the Elimination of Chance", 1886 Phil Mag
- "On the Determination of the Modulus of Errors", 1886, Phil Mag
- "Problems in Probabilities", 1886, Phil Mag
- "Review of Sidgwick's Scope and Method", 1886, Academy
- "Review of Jevons's Journals", 1886, Academy
- "Four Reports by the committee investigating best method of ascertaining and measuring variations in the monetary standard", 1887, Reports of the BAAS (Parts I & 3; Part 2)
- "Observations and Statistics: An essay on the theory of errors of observation and the first principles of statistics", 1887, Transactions of Cambridge Society.
- Metretike, or the method of measuring probability and utility, 1887.
- "On Observations Relating to Several Quantities", 1887, Hermathena
- "The Law of Error", 1887, Nature
- "The Choice of Means", 1887, Phil Mag
- "On Discordant Observations", 1887, Phil Mag
- "The Empirical Proof of the Law of Error", 1887, Phil Mag
- "On a New Method of Reducing Observations Relating to Several Quantities", 1888, Phil Mag
- "New Methods of Measuring Variation in General Prices, 1888, JRSS
- "The Statistics of Examinations", 1888, JRSS
- "The Value of Authority Tested by Experiment", 1888, Mind
- "Mathematical Theory of Banking", 1888, JRSS
- "On the Application of Mathematics to Political Economy: Address of the President of Section F of the British Association for the Advancement of Science", 1889, JRSS
- "The Mathematical Theory of Political Economy: Review of Walras's Elements", 1889, Nature
- "Review of Wicksteed's Alphabet", 1889, Academy
- "Review of Bohm-Bawerk's Kapital und Kapitalismus", 1889, Academy
- "Review of Bertrand's Calcul des Probabilites", 1889, J of Education
- "Points at which Mathematical Reasoning is Applicable to Political Economy", 1889, Nature
- "Appreciation of Gold", 1889, QJE
----
- "The Element of Chance in Competitive Examinations", 1890, JRSS
- "Economic Science and Statistics", 1889, Nature
- "Review of Marshall's Principles", 1890, Nature
- "Review of Jevons's Pure Logic", 1890, Academy
- "Review of Walras's Elements", 1890, Academy
- "Review of Bohm-Bawerk's Capital and Interest", 1890, Academy
- "La Théorie mathématique de l'offre et de la demande et le côut de production", 1891, Revue d'Economie Politique
- "Osservazioni sulla teoria matematica dell' economica politica", 1891, GdE (trans. "On the Determinateness of Economic Equilibrium")
- "Ancora a proposito della teoria del baratto", 1891, GdE
- "Review of Ricardo's Principles", 1891, J of Education
- "Review of Keynes's Scope and Method", 1891, EJ
- "An Introductory Lecture on Political Economy", 1891, EJ
- "Review of Sidgwick's Elements of Politics", 1891, EJ
- "Review of Second Edition of Marshall's Principles", 1891, EJ
- "Mathematical Investigations in the Theory of Value and Prices," Connecticut Academy, 1892.
- "Correlated Averages", 1892 , Philos Magazine
- "The Law of Error and Correlated Averages", 1892, Philos Magazine.
- "Recent Attempts to Evaluate the Amount of Coin Circulating in a Country", 1892, EJ
- "Review of Marshall's Economics of Industry", 1892, Nature
- "Review of Cantillon's Essai", 1892, EJ
- "Review of Palgrave's Dictionary", 1892, EJ
- "Review of Bohm-Bawerk's Positive Theory of Capital", 1892, EJ
- "Review of Smart's Introduction to the Theory of Value", 1892, EJ
- "Review of Dusing's Das Geschlechtverhaltniss", 1892, EJ
- "Review of Benson's Capital, Labor and Trade", 1892, EJ
- "Review of Smart's Women's Wages", 1893
- "Review of Bonar's Philosophy", 1893, Mind
- "Review of Walsh's Bimetallism", 1893, EJ
- "Review of Fisher's Mathematical Investigations", 1893, EJ
- "Professor Böhm-Bawerk on the Ultimate Standard of Value", 1894, EJ
- "One More Word on the Ultimate Standard of Value", 1894, EJ
- "Review of Wiser's Natural Value", 1894, EJ
- "Theory of International Values: Parts I, II and III", 1894, EJ
- "Recent Writings on Index Numbers", 1894, EJ
- "The Measurement of Utility by Money", 1894, EJ
- "Asymmetric Correlation between Social Phenomenon", 1894, JRSS
- Entries: "Average", "Census", "Cournot", "Curves", "Demand Curves", Difficulty of Attainment", "Distance in Time", "Error", 1894, in Palgrave, editor, Dictionary of Political Economy, Vol. 1.
- "Review of the Webbs' History of Trade Unionism", 1894, EJ
- "Review of Third Edition of Marshall's Principles", 1895, EJ
- "Mr. Pierson on the Scarcity of Gold", 1895, EJ
- "Thoughts on Monetary Reform", 1895, EJ
- "The Stationary State in Japan", 1895, EJ
- "A Defense of Index-Numbers", 1896, EJ
- "Statistics on Unprogressive Communities", 1896, JRSS
- "The Asymmetrical Probability Curve (Abstract)", 1894, Proceedings of Royal Society
- "The Asymmetrical Probability Curve", 1896, Phil Mag
- "The Compound law of Error", 1896, Phil Mag
- Entries: "Gossen", "Index Numbers", "Intrinsic Value", "Jenkin", "Jennings", "Least Squares" and "Mathematical Method", 1896, in Palgrave, editor, Dictionary of Political Economy, Vol. 2.
- "Review of Price's Money", 1896, EJ
- "Review of Nicholson's Strikes and Social Problems", 1896, EJ
- "Review of Pierson's Leerboek, Vol. 1", 1896, EJ
- "Review of Pierson's Leerkook, Vol. 2", 1897, EJ
- "Review of Bastable, Theory of International Trade", 1897, EJ
- "Review of Grazani's Istituzioni", 1897, EJ
- "La teoria pura del monopolio", 1897, GdE, (trans."The Pure Theory of Monopoly")
- "The Pure Theory of Taxation: Parts I, II and III", 1897, EJ
- "Miscellaneous Applications of the Calculus of Probabilities", Parts 1, 2, 3, 1897, 1898, JRSS
- "Review of Cournot's Recherches", 1898, EJ
- "Professor Graziani on the Mathematical Theory of Monopoly", 1898, EJ
- "Review of Darwin's Bimetallism", 1898, EJ
- "On the Representation of Statistics by Mathematical Formulae", Part 1 (1898), Parts 2, 3, 4 (1899)
- "On a Point in the Theory of International Trade", 1899, EJ
- "Review of Davidson, Bargain Theory of Wages", 1899, EJ
- "Professor Seligman on the Mathematical Method in Political Economy", 1899, EJ
- Entries: "Pareto", "Pareto's Law", "Probability", Supply Curve" and "Utility", 1899, in Palgrave, editor, Dictionary of Political Economy, Vol. 3
- "Answers to Questions by Local Taxation Commission", 1899, Reprint of Royal Commission for Local Taxation
- "The Incidence of Urban Rates, Parts I, II and III" 1900, EJ
- "Defence of Mr. Harrison's Calculation of the Rupee Circulation", 1900, EJ
- "Review of J.B. Clark's Theory of Distribution", 1900, EJ
- "Review of Smart's Taxation of Land-Values", 1900, EJ
- "Review of Bastable, Theory of International Trade (3rd edition)", 1897, EJ
- "Review of Bonar and Hollander, Letters of Ricardo", 1900, EJ
- "Mr. Walsh on the Measurement of General Exchange Value", 1901, EJ
- "Disputed Points in the Theory of International Trade", 1901, EJ
- "Review of Gide's Cooperation", 1902, EJ
- "Review of Wells's Anticipations", 1902, EJ
- "Methods of Representing Statistics of Wages and Other Groups Not *"Fulfilling the Normal Law of Error", with A.L. Bowley, 1902, JRSS
- "The Law of Error", 1902, Encycl Britannica
- "Review of Cannan's History of Theories of Production", 1903, EJ
- "Review of Bortkiewicz's Anwendungen and Pareto's Anwendungen", 1903, EJ
- "Review of Bastable's Public Finance", 1903, EJ
- "Review of Bastable's Cartels et Trusts", 1903, EJ
- "Review of Pigou's Riddle of the Tarriff", 1904, EJ
- "Review of Nicholson's Elements", 1904, EJ
- "Review of Bowley's National Progress", 1904, EJ
- "Review of Plunkett's Ireland", 1904, EJ
- "Review of Northon's Loan Credit", 1904, EJ
- "Review of Graziani's Istituzione", 1904, EJ
- "Review of Dietzel's Vergeltungzolle", 1904, EJ
- "Preface", 1904, in J.R. MacDonald, editor, Women in the Printing Trades.
- "The Theory of Distribution", 1904, QJE
- "The Law of Error", 1905, Transactions of Cambridge Society
- "Review of Nicholson's History of English Corn Laws", 1905, EJ
- "Review of Cunynghame's Geometrical Political Economy", 1905, EJ
- "Review of Carver's Theory of Distribution", 1905, EJ
- "Review of Taussig's Present Position", 1905, EJ
- "Review of Henry Sidgwick: A memoir", 1906, EJ
- "The Generalised Law of Error, or Law of Great Numbers", 1906, JRSS
- "Recent Schemes for Rating Urban Land Values", 1906, EJ
- "On the Representation of Statistical Frequency by a Series", 1907, JRSS
- "Statistical Observations on Wasps and Bees", 1907, Biometrika
- "Review of de Foville's Monnaie and Guyot's Science economique", 1907, EJ
- "Appreciations of Mathematical Theories", Parts I & II (1907), Parts III & IV (1908), EJ
- "On the Probable Errors of Frequency Constants", I, II & III (1908), Add. (1909), JRSS
- "Review of Andreades's Lecture on the Census", 1908, EJ
- "Review of Rea's Free Trade", 1908, EJ
- "Review of Withers's Meaning of Money", 1909, EJ
- "Review of Mitchell's Gold Prices", 1909, EJ
- "Review of Jevons's Investigations", 1909, EJ
- "Application du calcul des probabilités à la Statistique", 1909, Bulletin de l'Institut international de statistique
- "On the Use of the Differential Calculus in Economics to Determine Conditions of Maximum Advantage", 1909, Scientia
- "Applications of Probabilities to Economics, Parts I & II", 1910, EJ.
- "The Subjective Element in the First Principles of Taxation", 1910, QJE
- "Review of John Stuart Mill's Principles", 1910, EJ
- "Review of Colson's Cours", 1910, EJ
- "Review of J. Maurice Clark's Local Freight Discriminations", 1910, EJ
- "Review of Hammond's Railway Rate Theories", 1911, EJ
- "Probability and Expectation", 1911, Encycl Britannica
- "Monopoly and Differential Prices", 1911, EJ
- "Contributions to the Theory of Railway Rates", Part I & II (1911), Part III (1912), Part IV (1913), EJ
- "Review of Moore's Laws of Wages", 1912, EJ
- "Review of Pigou's Wealth and Welfare", 1913, EJ
- "On the Use of the Theory of Probabilities in Statistics Relating to Society", 1913, J of RSS
- "A Variant Proof of the Distribution of Velocities in a Molecular Chaos", 1913, PhilMag
- "On the Use of Analytical Geometry to Represent Certain Kinds of Statistics", Parts I-V, 1914, J of RSS
- "Recent Contributions to Mathematical Economics, I & II", 1915, EJ
- On the Relations of Political Economy to War, 1915.
- The Cost of War and ways of reducing it suggested by economic theory, 1915.
- "Economists on War: Review of Sombart, etc.", 1915, EJ
- "Review of Pigou's Economy and Finance of War", 1916, EJ
- "Review of Preziosi's La Germania alla Conquista dell' Italia", 1916, EJ
- "British Incomes and Property", 1916, EJ
- "On the Mathematical Representation of Statistical Data", Part I (1916), Parts II-IV (1917), J of RSS
- "Review of Gill's National Power and Prosperity", 1917, EJ
- "Review of Lehfeldt's Economics in Light of War", 1917, EJ
- "Some German Economic Writings about the War", 1917, EJ
- "After-War Problems: Review of Dawson at al.", 1917, EJ
- "Review of Westergaard's Scope and Methods of Statistics", 1917, JRSS
- "Review of Anderson's Value of Money", 1918, EJ
- "Review of Moulton and Phillips on Money and Banking", 1918, EJ
- "Review of Loria's Economic Causes of War", 1918, EJ
- "Review of Arias's Principii", 1918, EJ
- "Review of Smith-Gordon, Rural Reconstruction of Ireland and Russell's National Being", 1918, EJ
- "On the Value of a Mean as Calculated from a Sample", 1918, EJ
- "An Astronomer on the Law of Error", 1918, PhilMag
- Currency and Finance in Time of War, 1918.
- "The Doctrine of Index-Numbers According to Prof. Wesley Mitchell", 1918, EJ
- "Psychical Research and Statistical Method", 1919, JRSS
- "Methods of Graduating Taxes on Income and Capital", 1919, EJ
- "Review of Cannan's Money", 1919, EJ
- "Review of Andreades's Historia", 1919, EJ
- "Review of Lehfeldt's Gold Prices", 1919, EJ
- A Levy on Capital for the Discharge of the Debt, 1919.
- "Mathematical Formulae and the National Commission on Income Tax", 1920, EJ
- "On the Application of Probabilities to the Movement of Gas Molecules", Part I (1920), Part II (1922), Phil Mag
- "Entomological Statistics", 1920, Metron
- "Review of Gustav Cassel's Theory of Social Economy", 1920, EJ
- "Review of Bowley's Change in Distribution of National Income", 1920, JRSS
- "Review of the Webbs' History of Trade Unionism", 1920, EJ
- "Molecular Statistics", Part I (1921), Part II (1922), JRSS
- "On the Genesis of the Law of Eror", 1921, PhilMag
- "The Philosophy of Chance", 1922, Mind
- "The Mathematical Economics of Professor Amoroso", 1922, EJ
- "Equal Pay to Men and Women for Equal Work", 1922, EJ
- "Review of Keynes's Treatise on Probability", 1922, JRSS
- "Review of Pigou's Political Economy of War", 1922, EJ
- "Statistics of Examinations", 1923, JRSS
- "On the Use of Medians for Reducing Observations Relating to Several Quantities", 1923, Phil Mag
- "Mr. Correa Walsh on the Calculation of Index Numbers", 1923, JRSS
- "Index Numbers According to Mr. Walsh", 1923, EJ
- Women's Wages in Relation to Economic Welfare, 1923, EJ
- "Review of Marshall's Money, Credit and Commerce", 1923, EJ
- "Review of The Labour Party's Aim", 1923, EJ
- "Review of Bowley's Mathematical Groundwork", 1924, EJ
- "Review of Fisher's Economic Position of the Married Woman", 1924, EJ
- "Untried Methods of Representing Frequency", 1924, JRSS
- Papers Relating to Political Economy, 3 volumes, 1925.
- "The Plurality of Index-Numbers", 1925, EJ
- "The Element of Probability in Index-Numbers", 1925, JRSS
- "The Revised Doctrine of Marginal Social Product", 1925, EJ
- "Review of J.M. Clark's Overhead Costs", 1925, EJ.
- "mathematical method in political economy," 1926, Palgrave's Dictionary of Political Economy, reprinted in 1987, The New Palgrave: A Dictionary of Economics, v. 3.
- "Mr Rhode's Curve and the Method of Adjustment", 1926, JRSS
See also
- Core (economics)Core (economics)The core is the set of feasible allocations that cannot be improved upon by a subset of the economy's consumers. A coalition is said to improve upon or block a feasible allocation if the members of that coalition are better off under another feasible allocation that is identical to the first...
- Exponential familyExponential familyIn probability and statistics, an exponential family is an important class of probability distributions sharing a certain form, specified below. This special form is chosen for mathematical convenience, on account of some useful algebraic properties, as well as for generality, as exponential...
in parametric statisticsParametric statisticsParametric statistics is a branch of statistics that assumes that the data has come from a type of probability distribution and makes inferences about the parameters of the distribution. Most well-known elementary statistical methods are parametric.... - Fisher informationFisher informationIn mathematical statistics and information theory, the Fisher information is the variance of the score. In Bayesian statistics, the asymptotic distribution of the posterior mode depends on the Fisher information and not on the prior...
- Likelihood functionLikelihood functionIn statistics, a likelihood function is a function of the parameters of a statistical model, defined as follows: the likelihood of a set of parameter values given some observed outcomes is equal to the probability of those observed outcomes given those parameter values...