David Orrell
David John Orrell is a Canadian writer and mathematician. He received his doctorate in mathematics from the University of Oxford, his work in the prediction of complex systems such as the weather and the economy has been featured in New Scientist, the Financial Times, Adbusters, BBC Radio, Russia-1, CBC TV. He now conducts research and writes in the areas of systems biology and economics, runs a mathematical consultancy Systems Forecasting, he is the son of theatre historian and English professor John Orrell. His books have been translated into over ten languages. Apollo's Arrow: The Science of Prediction and the Future of Everything was a national bestseller and finalist for the 2007 Canadian Science Writers' Award. Economyths: Ten Ways Economics Gets It Wrong was a finalist for the 2011 National Business Book Award. A consistent topic in Orrell’s work is the limitations of mathematical models, the need to acknowledge these limitations if we are to understand the causes of forecast error, he argues for example that errors in weather prediction are caused by model error, rather than the butterfly effect.
Economic models are seen as unrealistic. In Truth or Beauty: Science and the Quest for Order, he suggests that many such theories, along with areas of physics such as string theory, are motivated by the desire to conform with a traditional scientific aesthetic, being subverted by developments in complexity science. In The Evolution of Money and two articles Orrell proposed a quantum theory of money and value, which states that money has dualistic properties because it combines the properties of an owned and valued thing, with those of abstract number; the fact that these two sides of money are incompatible leads to its complex and unpredictable behavior. In Quantum Economics: The New Science of Money he argues that these dualistic properties feed up to affect the economy as a whole. Orrell, David. Quantum Economics: The New Science of Money. Icon. ISBN 978-1785782299. Orrell, David. Economyths: 11 Ways Economics Gets It Wrong. Icon. ISBN 978-1848311480. Revised and extended edition of 2010 book. Wilmott, Paul.
The Money Formula: Dodgy Finance, Pseudo Science, How Mathematicians Took Over the Markets. Wiley. ISBN 978-1119358619. Orrell, David; the Evolution of Money. Columbia University Press. ISBN 978-0231173728. Orrell, David. Truth or Beauty: Science and the Quest for Order. Yale University Press. ISBN 978-0300186611. Sedlacek, Tomas. Soumrak Homo Economicus. 65th Square. ISBN 978-8087506073. Orrell, David. Introducing Economics: A Graphic Guide. Icon. ISBN 978-1848312159. Orrell, David. Economyths: Ten Ways Economics Gets It Wrong. Icon. ISBN 978-1848311480. Orrell, David; the Other Side of the Coin: The Emerging Vision of Economics and Our Place in The World. Key Porter. ISBN 978-1552639818. Orrell, David. Gaia. Lulu.com. ISBN 978-1409255178. Orrell, David. Apollo's Arrow: The Science of Prediction and the Future of Everything. HarperCollins. ISBN 978-0002007405. Published in the U. S. as The Future of Everything: The Science of Prediction. Anticipatory science forecasts Complex systems Mathematical model Computer model Chaos theory Systems biology David Orrell's homepage Systems Forecasting Video of talk on money given for Marshall McLuhan lecture, Berlin 2015 Video of talk on prediction given at TEDx Park Kultury, Moscow in 2012 Extract from Economyths in Adbusters magazine, viewable in English and Spanish ABC News - Good Morning America National Post's review of Apollo's Arrow Sunday Times review of Truth or Beauty
Mines ParisTech
MINES ParisTech, created in 1783 by King Louis XVI, is a French engineer school and a constituent college of Université PSL. MINES ParisTech is distinguished for the outstanding performance of its research centers and the quality of its international partnerships with other prestigious universities in the world, which include Massachusetts Institute of Technology, California Institute of Technology, Shanghai Jiao Tong University, University of Hong Kong, National University of Singapore, Novosibirsk State University, Pontifical Catholic University of Chile and Tokyo Tech; the École des Mines de Paris publishes a world university ranking based on the number of alumni holding the post of CEO in one of the 500 largest companies in the world: the Mines ParisTech: Professional Ranking of World Universities. The school is a member of the ParisTech alliance. Created by decree of the French King's Counsel on March 19, 1783, the first school of Mines was located in the Hôtel de la Monnaie, in Paris.
The school disappeared at the beginning of the French Revolution but was re-established by decree of the Committee of Public Safety in 1794, the 13th Messidor Year II. It moved to Savoie, after a decree of the consuls the 23rd Pluviôse Year X. After the Bourbon Restoration in 1814, the school moved to the Hôtel de Vendôme. From the 1960s onwards, it created research laboratories in Fontainebleau, Évry and Sophia Antipolis; the initial aim of the Ecole des mines de Paris, namely to train high-level mining engineers, evolved with time to adapt to the technological and structural transformations undergone by society. Mines ParisTech has now become one of the most prestigious French engineering schools with a broad variety of subjects, its students are trained to have management positions, work in research and development departments, or as operations officers, etc. They receive a well-rounded education in a variety of subjects, ranging from the most technical to economics, social sciences or art in order to be able to tackle the managing or engineering-related issues they are to face.
Exchange programs are possible during the third semester with prestigious universities around the world, such as Massachusetts Institute of Technology, California Institute of Technology, University of Hong Kong, National University of Singapore, Tokyo Tech, Seoul National University... Mines ParisTech provides different educational paths: The Ingénieurs civils degree, ranked among the best French Grande école engineering degrees, similar to that offered at École polytechnique, École des Ponts ParisTech or École Centrale Paris; the Corps of Mines, one of the greatest technical corps of the French state. It is a third cycle degree, lasting for three years, consisting in two long-term internships both in public and private economical institutions and courses in economics and public institutions; the admission to the Corps des Mines is selective as only the top students from École polytechnique, École normale supérieure, Mines ParisTech and Telecom ParisTech may apply Mastère Spécialisé degrees, post-graduate programs accredited by the Conférence des Grandes écoles, in the fields of Energy, Environment and Logistics, Informatics and management in industry and Materials engineering Doctoral and Master studies in various fields For students having studied in the Classe Préparatoire aux Grandes Ecoles, admission to Civil Engineer of Mines is decided through a nationwide competitive examination.
Every year, ten applications are accepted from students around the world according to their academic achievements. Admission to the Corps of Mines is possible for French students at the end of the studies in École polytechnique, École normale supérieure, École des télécommunications de Paris and École des mines de Paris, or from the other great technical corps of the French state. Admission in third year is open to one Ph. D graduate. A Student Union is elected every year after a one-week campaign, is in charge of enhancing the contact between students and various sponsoring industries as well as organizing events for the students. Various other organizations are part of the students' lives: the Students' Sport Committee, the Junior Enterprise, the Arts' Office, Cahier Vert, CAV, Catholic community, Fanfare band, Entrepreneur club, humanitarian organizations, photography club, Sailing club, among others. Maurice Allais, Nobel Prize in Economics, 1988 Jean-Louis Bianco, General Secretary of President of France, Minister of Social Affairs, Minister of Transport, députy of Alpes de Haute Provence's 1st constituency Louis Paul Cailletet and inventor Georges Charpak, Nobel Prize in Physics 1992 Jean-Baptiste Élie de Beaumont, founder of geology, Wollaston Medal 1843 Thierry Desmarest, former CEO of Total Jean-Martin Folz, former CEO of PSA Peugeot Citroën Noël Forgeard, former CEO of Airbus and EADS Charles de Freycinet, prime minister of France at the end of the 19th century Tidjane Thiam, CEO of Credit Suisse Car
Marginalism
Marginalism is a theory of economics that attempts to explain the discrepancy in the value of goods and services by reference to their secondary, or marginal, utility. The reason why the price of diamonds is higher than that of water, for example, owes to the greater additional satisfaction of the diamonds over the water. Thus, while the water has greater total utility, the diamond has greater marginal utility. Although the central concept of marginalism is that of marginal utility, following the lead of Alfred Marshall, drew upon the idea of marginal physical productivity in explanation of cost; the neoclassical tradition that emerged from British marginalism abandoned the concept of utility and gave marginal rates of substitution a more fundamental role in analysis. Marginalism is an integral part of mainstream economic theory. For issues of marginality, constraints are conceptualized as a margin; the location of the margin for any individual corresponds to his or her endowment, broadly conceived to include opportunities.
This endowment is determined by many things including physical laws, accidents of nature, the outcomes of past decisions made both by others and by the individual. A value that holds true given particular constraints is a marginal value. A change that would be affected as or by a specific loosening or tightening of those constraints is a marginal change. Neoclassical economics assumes that marginal changes are infinitesimals or limits. One is therefore told that "marginal" is synonymous with "very small", though in more general analysis this may not be operationally true. Economic analysis concerns the marginal values associated with a change of one unit of a resource, because decisions are made in terms of units; the marginal use of a good or service is the specific use to which an agent would put a given increase, or the specific use of the good or service that would be abandoned in response to a given decrease. Marginalism assumes, for any given agent, economic rationality and an ordering of possible states-of-the-world, such that, for any given set of constraints, there is an attainable state, best in the eyes of that agent.
Descriptive marginalism asserts that choice amongst the specific means by which various anticipated specific states-of-the-world might be affected is governed only by the distinctions amongst those specific outcomes. On such assumptions, each increase would be put to the specific, feasible unrealized use of greatest priority, each decrease would result in abandonment of the use of lowest priority amongst the uses to which the good or service had been put; the marginal utility of a good or service is the utility of its marginal use. Under the assumption of economic rationality, it is the utility of its least urgent possible use from the best feasible combination of actions in which its use is included. In 20th century mainstream economics, the term "utility" has come to be formally defined as a quantification capturing preferences by assigning greater quantities to states, services, or applications that are of higher priority, but marginalism and the concept of marginal utility predate the establishment of this convention within economics.
The more general conception of utility is that of use or usefulness, this conception is at the heart of marginalism. On the other hand, none of the early marginalists insisted that utility were not quantified, some indeed treated quantification as an essential feature, those who did not still used an assumption of quantification for expository purposes. In this context, it is not surprising to find many presentations that fail to recognize a more general approach. Under the special case in which usefulness can be quantified, the change in utility of moving from state S 1 to state S 2 is Δ U = U − U Moreover, if S 1 and S 2 are distinguishable by values of just one variable g, itself quantified it becomes possible to speak of the ratio of the marginal utility of the change in g to the size of that change: Δ U Δ g | c. P.. Mainstream neoclassical economics will assume that lim Δ g → 0 Δ U Δ g | c. p. {\displaystyle \lim _{\lef
Sociology
Sociology is the scientific study of society, patterns of social relationships, social interaction, culture of everyday life. It is a social science that uses various methods of empirical investigation and critical analysis to develop a body of knowledge about social order and change or social evolution. While some sociologists conduct research that may be applied directly to social policy and welfare, others focus on refining the theoretical understanding of social processes. Subject matter ranges from the micro-sociology level of individual agency and interaction to the macro level of systems and the social structure; the different traditional focuses of sociology include social stratification, social class, social mobility, secularization, sexuality and deviance. As all spheres of human activity are affected by the interplay between social structure and individual agency, sociology has expanded its focus to other subjects, such as health, economy and penal institutions, the Internet, social capital, the role of social activity in the development of scientific knowledge.
The range of social scientific methods has expanded. Social researchers draw upon a variety of quantitative techniques; the linguistic and cultural turns of the mid-20th century led to interpretative and philosophic approaches towards the analysis of society. Conversely, the end of the 1990s and the beginning of the 2000s have seen the rise of new analytically and computationally rigorous techniques, such as agent-based modelling and social network analysis. Social research informs politicians and policy makers, planners, administrators, business magnates, social workers, non-governmental organizations, non-profit organizations, people interested in resolving social issues in general. There is a great deal of crossover between social research, market research, other statistical fields. Sociological reasoning predates the foundation of the discipline. Social analysis has origins in the common stock of Western knowledge and philosophy, has been carried out from as far back as the time of ancient Greek philosopher Plato, if not before.
The origin of the survey, i.e. the collection of information from a sample of individuals, can be traced back to at least the Domesday Book in 1086, while ancient philosophers such as Confucius wrote about the importance of social roles. There is evidence of early sociology in medieval Arab writings; some sources consider Ibn Khaldun, a 14th-century Arab Islamic scholar from North Africa, to have been the first sociologist and father of sociology. The word sociology is derived from both Greek origins; the Latin word: socius, "companion". It was first coined in 1780 by the French essayist Emmanuel-Joseph Sieyès in an unpublished manuscript. Sociology was defined independently by the French philosopher of science, Auguste Comte in 1838 as a new way of looking at society. Comte had earlier used the term social physics, but that had subsequently been appropriated by others, most notably the Belgian statistician Adolphe Quetelet. Comte endeavoured to unify history and economics through the scientific understanding of the social realm.
Writing shortly after the malaise of the French Revolution, he proposed that social ills could be remedied through sociological positivism, an epistemological approach outlined in The Course in Positive Philosophy and A General View of Positivism. Comte believed a positivist stage would mark the final era, after conjectural theological and metaphysical phases, in the progression of human understanding. In observing the circular dependence of theory and observation in science, having classified the sciences, Comte may be regarded as the first philosopher of science in the modern sense of the term. Comte gave a powerful impetus to the development of sociology, an impetus which bore fruit in the decades of the nineteenth century. To say this is not to claim that French sociologists such as Durkheim were devoted disciples of the high priest of positivism, but by insisting on the irreducibility of each of his basic sciences to the particular science of sciences which it presupposed in the hierarchy and by emphasizing the nature of sociology as the scientific study of social phenomena Comte put sociology on the map.
To be sure, beginnings can be traced back well beyond Montesquieu, for example, to Condorcet, not to speak of Saint-Simon, Comte's immediate predecessor. But Comte's clear recognition of sociology as a particular science, with a character of its own, justified Durkheim in regarding him as the father or founder of this science, in spite of the fact that Durkheim did not accept the idea of the three states and criticized Comte's approach to sociology. Both Auguste Comte and Karl Marx set out to develop scientifically justified systems in the wake of European industrialization and secularization, informed by various key movements in the philosophies of history and science. Marx rejected Comtean positivism but in attempting to develop a science of society came to be recognized as a founder of sociology as the word gained wider meaning. For Isaiah Berlin, Marx may be regarded as the "true father" of modern sociology, "in so far as anyone can claim the title."To have given clear and unified answers in familiar empirical terms to those theor
Montreux
Montreux is a municipality in the district of Riviera-Pays-d'Enhaut in the canton of Vaud in Switzerland. It is located on Lake Geneva shoreline at the foot of the Alps and has a population, as of December 2017, of 26,574 and nearly 90,000 in the agglomeration; the earliest settlement was a Late Bronze Age village at Baugy. Montreux lies on the north east shore of Lake Geneva at the fork in the Roman road from Italy over the Simplon Pass, where the roads to the Roman capital of Aventicum and the road into Gaul through Besançon separated; this made it an important settlement in the Roman era. A Roman villa from the 2nd-4th centuries and a 6th–7th century cemetery have been discovered. In the 12th century, viticulture was introduced to the region, the sunny slopes of the lake from Lavaux to Montreux became an important wine-growing region. Montreux is first mentioned in 1215 as Mustruel. In 1295, the Bishop of Sion sold the parish of Montreux to Girard of Oron. In 1317, it was split between the Lords of Oron and the Counts of Savoy.
A Brotherhood of the Holy Spirit administered estates and a hospital in Montreux starting in about 1309. The region was subject to various princes, most notably the princes of Savoy from the south side of the lake, they unified the territory which comprises the present canton of Vaud and were popular sovereigns. After the Burgundian Wars in the 15th century, the Swiss in Bern occupied the region without resistance, an indication of the weakness of the princes of Savoy. Under Bernese rule it belonged to the Bailiwick of Chillon; the Reformation made the region around Montreux and Vevey an attractive haven for Huguenots from Italy, who brought their artisanal skills and set up workshops and businesses. The abbey of Les Echarpes blanches was founded in 1626. In 1798, Napoleon liberated the region from the Bernese. In the 19th century, the tourist industry became a major commercial outlet, with the grand hotels of Montreux attracting the rich and cultured from Europe and America. Starting in the 19th century there were three independent municipalities that shared a central authority.
This county council was made up of four deputies from Le Châtelard, two from Les Planches and one from Veytaux. The church, the market hall of La Rouvenaz, the secondary school and the slaughter-house were all owned by the county council; each municipality had a mayor. In 1962, the municipalities of Le Châtelard and Les Planches merged, while Veytaux remained independent. Montreux has an area, as of 2009, of 33.4 km2. Of this area, 8.47 km2 or 25.4% is used for agricultural purposes, while 16.93 km2 or 50.7% is forested. Of the rest of the land, 6.37 km2 or 19.1% is settled, 0.08 km2 or 0.2% is either rivers or lakes and 1.59 km2 or 4.8% is unproductive land. Of the built up area and buildings made up 10.9% and transportation infrastructure made up 6.3%. Out of the forested land, 47.0% of the total land area is forested and 3.1% is covered with orchards or small clusters of trees. Of the agricultural land, 0.4% is used for growing crops and 8.8% is pastures, while 1.6% is used for orchards or vine crops and 14.7% is used for alpine pastures.
All the water in the municipality is flowing water. The municipality was part of the Vevey District until it was dissolved on 31 August 2006, Montreux became part of the new district of Riviera-Pays-d'Enhaut; the municipality stretches from Lake Geneva to the foothills of the Swiss Alps. It includes the former municipalities of Montreux-Le Châtelard, it was formed in 1962 with the merger of the two former municipalities. The Köppen Climate Classification subtype for Montreux's climate is "Cfb". Montreux has a population of 26,574; as of 2008, 44.2% of the population are resident foreign nationals. Over the last 10 years the population has changed at a rate of 14.7%. It has changed at a rate of -0.8 % due to births and deaths. Most of the population speaks French as their first language, with German being second most common and Italian being third. There are 9 people; the age distribution, as of 2009, in Montreux is. Of the adult population, 4,216 people or 17.0 % of the population are between 29 years old.
3,016 people or 12.2% are between 30 and 39, 3,552 people or 14.4% are between 40 and 49, 3,048 people or 12.3% are between 50 and 59. The senior population distribution is 2,565 people or 10.4% of the population are between 60 and 69 years old, 1,795 people or 7.3% are between 70 and 79, there are 1,206 people or 4.9% who are between 80 and 89, there are 263 people or 1.1% who are 90 and older. As of 2000, there were 9,380 people who never married in the municipality. There were 9,758 married individuals, 1,631 widows or widowers and 1,685 individuals who are divorced; as of 2000, there were 9,823 private households in the municipality, an average of 2 persons per household. There were 4,198 households that consist of only one person and 402 households with five or more people. Out of a total of 10,236 households that answered this question, 41.0% were households made up of just one person and there were 53 adults who lived with their parents. Of the rest of the households, th
Fabian Society
The Fabian Society is a British socialist organisation whose purpose is to advance the principles of democratic socialism via gradualist and reformist effort in democracies, rather than by revolutionary overthrow. As one of the founding organisations of the Labour Representation Committee in 1900, as an important influence upon the Labour Party which grew from it, the Fabian Society has had a powerful influence on British politics. Other members of the Fabian Society have included political leaders from countries part of the British Empire, such as Jawaharlal Nehru, who adopted Fabian principles as part of their own political ideologies; the Fabian Society founded the London School of Economics and Political Science in 1895. Today, the society functions as a think tank and is one of 21 socialist societies affiliated with the Labour Party. Similar societies exist in Canada, in Sicily and in New Zealand; the Fabian Society was founded on 4 January 1884 in London as an offshoot of a society founded a year earlier called The Fellowship of the New Life.
Early Fellowship members included the visionary Victorian elite, among them poets Edward Carpenter and John Davidson, sexologist Havelock Ellis, early socialist Edward R. Pease, they wanted to transform society by setting an example of clean simplified living for others to follow. Some members wanted to become politically involved to aid society's transformation. All members were free to attend both societies; the Fabian Society additionally advocated renewal of Western European Renaissance ideas and their promulgation throughout the world. The Fellowship of the New Life was dissolved in 1899, but the Fabian Society grew to become the pre-eminent academic society in the United Kingdom in the Edwardian era, it was typified by the members of its vanguard Coefficients club. Public meetings of the Society were for many years held at Essex Hall, a popular location just off the Strand in central London; the Fabian Society was named — at the suggestion of Frank Podmore — in honour of the Roman general Quintus Fabius Maximus Verrucosus.
His Fabian strategy sought gradual victory against the superior Carthaginian army under the renowned general Hannibal through persistence and wearing the enemy down by attrition rather than pitched, climactic battles. An explanatory note appearing on the title page of the group's first pamphlet declared:For the right moment you must wait, as Fabius did most patiently, when warring against Hannibal, though many censured his delays. According to author Jon Perdue, "The logo of the Fabian Society, a tortoise, represented the group’s predilection for a slow, imperceptible transition to socialism, while its coat of arms, a'wolf in sheep’s clothing', represented its preferred methodology for achieving its goal." The wolf in sheep's clothing symbolism was abandoned, due to its obvious negative connotations. Its nine founding members were Frank Podmore, Edward R. Pease, William Clarke, Hubert Bland, Percival Chubb, Frederick Keddell, H. H. Champion, Edith Nesbit, Rosamund Dale Owen. Havelock Ellis is sometimes mentioned as a tenth founding member, though there is some question about this.
Upon its inception, the Fabian Society began attracting many prominent contemporary figures drawn to its socialist cause, including George Bernard Shaw, H. G. Wells, Annie Besant, Graham Wallas, Charles Marson, Sydney Olivier, Oliver Lodge, Ramsay MacDonald and Emmeline Pankhurst. Bertrand Russell became a member, but resigned after he expressed his belief that the Society's principle of entente could lead to war. At the core of the Fabian Society were Beatrice Webb. Together, they wrote numerous studies of industrial Britain, including alternative co-operative economics that applied to ownership of capital as well as land. Many Fabians participated in the formation of the Labour Representation Committee in 1900 and the group's constitution, written by Sidney Webb, borrowed from the founding documents of the Fabian Society. At the meeting that founded the Labour Representation Committee in 1900, the Fabian Society claimed 861 members and sent one delegate; the years 1903 to 1908 saw a growth in popular interest in the socialist idea in Great Britain and the Fabian Society grew accordingly, tripling its membership to nearly 2500 by the end of the period, half of whom were located in London.
In 1912, a student section was organised called the University Socialist Federation and by the outbreak of World War I this contingent counted its own membership of more than 500. The first Fabian Society pamphlets advocating tenets of social justice coincided with the zeitgeist of Liberal reforms during the early 1900s, including eugenics; the Fabian proposals however were more progressive than those that were enacted in the Liberal reform legislation. The Fabians lobbied for the introduction of a minimum wage in 1906, for the creation of a universal health care system in 1911 and for the abolition of hereditary peerages in 1917. Fabian socialists were in favour of reforming Britain's imperialist foreign policy as a conduit for internationalist reform, were in favour of a capitalist welfare state modelled on the Bismarckian German model, they favoured a national minimum wage i
Gérard Debreu
Gérard Debreu was a French-born economist and mathematician. Best known as a professor of economics at the University of California, where he began work in 1962, he won the 1983 Nobel Memorial Prize in Economic Sciences, his father was the business partner of his maternal grandfather in lace manufacturing, a traditional industry in Calais. Debreu was orphaned at an early age, as his father committed suicide and his mother died of natural causes. Prior to the start of World War II, he received his baccalauréat and went to Ambert to begin preparing for the entrance examination of a grande école. On, he moved from Ambert to Grenoble to complete his preparation, both places being in Vichy France during World War II. In 1941, he was admitted to the École Normale Supérieure in Paris, along with Marcel Boiteux, he was influenced by the Bourbaki writers. When he was about to take the final examinations in 1944, the Normandy landings occurred and he, enlisted in the French army, he was transferred for training to Algeria and served in the occupying French forces in Germany until July 1945.
Debreu passed the Agrégation de Mathématiques exams at the end of 1945 and the beginning of 1946. By this time, he had become interested in economics in the general equilibrium theory of Léon Walras. From 1946 to 1948, he was an assistant in the Centre National de la Recherche Scientifique. During these two and a half years, he made the transition from mathematics to economics. In 1948, Debreu went to the United States on a Rockefeller Fellowship which allowed him to visit several American universities, as well as those in Uppsala and Oslo in 1949–50. Debreu married Françoise Bled in 1946 and they had two daughters and Florence, born in 1946 and 1950 respectively. Debreu died in Paris at the age of 83 of natural causes on New Year's Eve, 2004. Debreu began working as a Research Associate and joined the Cowles Commission at the University of Chicago in the summer of 1950, he remained there for five years. In 1954, he published a breakthrough paper, entitled Existence of an Equilibrium for a Competitive Economy, together with Kenneth Arrow, in which they provided a definitive mathematical proof of the existence of a general equilibrium, using topological rather than calculus-based methods.
In 1955, he moved to Yale University. In 1959, he published his classical monograph, Theory of Value: An Axiomatic Analysis of Economic Equilibrium, one of the most important works in mathematical economics, he studied several problems in the theory of cardinal utility, in particular the additive decomposition of a utility function defined on a Cartesian product of sets. In this monograph, Debreu set up an axiomatic foundation for competitive markets, he established the existence of an equilibrium using a novel approach. The main idea of his argument is to show that there exists a price system for which the aggregate excess demand correspondence vanishes, he did so by proving a type of fixed-point theorem, based on the Kakutani fixed-point theorem. In Chapter 7, Debreu introduced the concept of uncertainty and showed how it could be incorporated into the deterministic model. Here, he introduced the notion of a contingent commodity, a promise to deliver a good should a certain state of nature be realized.
This concept is frequently used in financial economics, where it is known as the "Arrow–Debreu security". In 1960–61, he worked at the Center for Advanced Study in the Behavioral Sciences at Stanford and devoted most of his time to the complex proof that appeared in 1962 of a general theorem on the existence of an economic equilibrium. In January 1962, he started working at the University of California, where he held the titles of University Professor and Class of 1958 Professor of Economics and Mathematics Emeritus. During his sabbaticals in the late 1960s and 1970s, he visited universities in Leiden, Cambridge and Paris, his studies centred on the theory of differentiable economies, where he showed that, in general, aggregate excess demand functions vanish at a finite number of points – he showed that economies have a finite number of price equilibria. In 1976, he received the French Legion of Honour, he was awarded the 1983 Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel, for having incorporated new analytical methods into economic theory and for his rigorous reformulation of general equilibrium theory.
He was a member of the International Academy of Science. In 1990, he served as President of the American Economic Association. Debreu, Gérard; the theory of value: an axiomatic analysis of economic equilibrium. New York: Wiley. OCLC 270657. Debreu, Gérard. Mathematical economics: twenty papers of Gerard Debreu. Cambridge Cambridgeshire New York: Cambridge University Press. ISBN 9780521335614; the twenty papers: The coefficient of resource utilization · A social equilibrium existence theorem · A classical tax-subsidy problem · Existence of an equilibrium for a competitive economy · Valuation equilibrium and Pareto optimum · Representation of a preference ordering by a numerical function · Market equilibrium · Economics under uncertainty · Topological methods in cardinal utility theory · New concepts and techniques for equilibrium analysis · A limit theorem on the core of an economy · Contuinity properties of Paretian utility · Neighboring economic agents · Economies with a finite set of equilibria · Smooth preferences · Excess demand functions · The rate of convergence of the core of an economy · Four aspects of the mathematical theory of economic
