安東尼·奧古斯丁·庫爾諾

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安東尼·奧古斯丁·庫爾諾（Antoine Augustin Cournot，1801.8.28-1877.3.31）

　　安東尼·奧古斯丁·庫爾諾（Antoine Augustin Cournot）法國數學家、經濟學家和哲學家，數理統計學的奠基人。庫爾諾1801年8月28日出生於法國格雷，1877年3月31日在巴黎逝世；最先力圖用數學方法解決經濟問題，是數理經濟學的創始人之一。庫爾諾指出統計學的目的是協調各項觀察，以確定除去偶然因素的影響之外的數字關係和顯示出正常原因的作用。

　　庫爾諾的人生道路並不坎坷。他受教於著名的巴黎高等師範學校，獲巴黎大學博士學位。他曾在巴黎大學和里昂大學任教，擔任格勒諾布爾學院院長，成為法國勛級會榮譽軍團成員，並被任命為巴黎的教育巡視員。儘管他視力一直很差，晚年幾近失明，但生活還是安逸的。他在數學、科學哲學和歷史哲學、經濟學方面都有造詣。他在今天的名聲主要來自經濟學。

然而，庫爾諾生不逢時。當時法國學術界關註的是對大革命的爭論以及日益增長的社會主義思潮。聖西門和傅立葉的空想社會主義，蒲魯東對私有制的抨擊，路易·布朗的工人合作思想，這些都是人們關心爭論的話題。庫爾諾的思想不是時代的主旋律，同時，庫爾諾性情憂郁，性格孤僻，是個內向型的人，也不關心自己的作品是否有吸引力，沒有努力引起同時代人的關註，至死仍然默默無聞。也就在他臨終前，他的作品才引起傑文斯等名家的註意，認識到他的著作的深遠意義。

法國數學家、經濟學家和哲學家，數理統計學的奠基人。指出統計學的目的是協調各項觀察，以確定除去偶然因素的影響之外的數字關係和顯示出正常原因的作用。

　　最主要的貢獻在於下列幾方面的論述：

　　供給和需求的功能和在獨家壟斷、兩家壟斷和完全競爭情況下確立的平衡；賦稅的轉變；國際貿易問題等。

　　庫爾諾最早提出需求量是價格的函數這個需求定理，並建立了壟斷模型和分析寡頭的雙頭模型，直到今天雙頭模型(稱為庫爾諾模型)仍然是標準教科書中的重要內容。庫爾諾至今被重視的原因還在於他用數學方法分析這些問題。以後的經濟學家高度評價了他的這種貢獻，認為他對已有的，但形態模糊的經濟概念和經濟命題給予嚴密的數學表述。他的分析方法強有力地促使經濟學從文字的敘述轉向形式邏輯的和數字的表達。20世紀初的著名英國經濟學家埃奇沃思指出，庫爾諾的論著“是以數學形式把經濟科學里的某些高度概括的命題，陳述得最好的。”現代經濟學家還指出，庫爾諾是最早用博弈論思想分析經濟問題的先驅者，他的雙頭模型就成功地運用了博弈論。

• 《關於財富理論之數學原則的研究》 (Recherches sur les principes mathematiques de la theorie des richesses, 1838)。
• 《財富理論原理》(1863)
• 《經濟學說概要評論》 (1877)

　　Antoine Augustin Cournot

　　(August 28, 1801 - March 31, 1877)

　　Antoine Cournot attended the secondary school Collège de Gray between the years 1809 and 1816. He showed an interest in politics at a young age and in a France deeply divided between royalists and republicans, he sided with the royalist cause in his youth. After leaving school he spent four years in a lawyer's office but after he had read Laplace and the correspondence between Leibniz and Clarke he decided to enter university.

　　A preliminary course in mathematics at Collège Royal in Besançon in session 1820-21 prepared him for entry to École Normale Supérieur in Paris which he entered in 1821. However his time there was disrupted when the École Normale Supérieur was closed down. Cournot remained in Paris and, along with his fellow student Dirichlet, was taught mathematics at the Sorbonne by Lacroix and Hachette.

　　In 1823 Cournot became a tutor but continued his work in mathematics receiving his doctorate in 1829 for a thesis Le mouvement d'un corps rigide soutenu par un plan fixe. Poisson was impressed with Cournot and, in 1833, he obtained a position for him with the Academy in Paris. During this time he translated John Herschel's Treatise on astronomy into French, it was published in 1834.

　　Again with Poisson's recommendation, Cournot was appointed to a newly created chair in analysis at Lyon in 1834. In [6] Cournot writes of Poisson's opinion of his first papers in mechanics:-

　　Poisson discovered in them a philosophical depth - and, I must honestly say, he was not altogether wrong. Furthermore, from then he predicted that I would go far in the field of pure mathematical speculation but (as I have always thought and have never hesitated to say) in this he was wrong.

　　In 1835 Cournot became professor of mathematics at Grenoble and rector there. Three years later he became inspector general of public education. In this same year (1838) he published Recherches sur les principes mathématiques de la théorie des richesses in which he discussed mathematical economics, in particular supply- and- demand functions.

　　He also considered conditions for equilibrium with monopoly, duopoly and perfect competition. He considered the effect of taxes, treated as changes in production costs, and discussed problems of international trade. He gives a definition of a market which is the basis for that still used in economics:-

　　Economists understand by the term Market, not any particular market place in which things are bought and sold, but the whole of any region in which buyers and sellers are in such free intercourse with one another that the prices of the same goods tend to equality easily and quickly.

　　This work makes Cournot a pioneer of mathematical economics, 25 years before Jevons.

　　Cournot also worked on probability and although his investigations into a logical foundation for it were unsuccessful, his work did lead the way to future important developments. He, as Poisson and Condorcet did, applied probability to legal statistics.

　　Cournot also well known for his views on scientific knowledge. He wrote:-

... scientific knowledge is the sign of great achievement and alone is truly capable of cumulative and indefinitely pursued progress.

　　Article by: J J O'Connor and E F Robertson

　　Antoine Augustin Cournot From Wikipedia, the free encyclopedia.

　　Antoine Augustin Cournot (28 August 1801‑ 31 March 1877) was a French philosopher and mathematician.

　　Antoine Augustin Cournot was born at Gray, Haute-Saone. In 1821 he entered a teachers’ training college, and in 1829 he had earned a doctoral degree in mathematics, with mechanics as his main thesis supplemented by astrology. After graduating, Cournot held many positions as professor of analysis and mechanics, chief examiner for undergraduate students, and rector of Dijon Academy.

　　Cournot was mainly a mathematician, but did have some influence over economics. His theories on monopolies and duopolies are still famous. In 1838 Researches on the Mathematical Principals of the Theory of Wealth was published, and still has influence in economics today. In this book he used the application of the formulas and symbols of mathematics in economic analysis, which was highly criticized. This book was not very successful during Cournot’s lifetime, and he did try to rewrite it twice. Today many economists believe this book to be the point of departure for modern economic analysis. Cournot introduced the ideas of function and probability into economic analysis. He derived the first formula for the rule of supply and demand as a function of price.

　　Cournot believed that economists must utilize the tools of mathematics only to establish probable limits and to express less stable facts in more absolute terms. He further held that the practical uses of mathematics in economics do not necessarily involve strict numerical precision.

　　Today, Cournot’s work is recognized in a discipline called econometrics. He was also a teacher of political economy and mathematics to Auguste Walras, who was the father of Leon Walras. Cournot and Auguste Walras persuaded Leon Walras to try political economics. Cournot is also credited to be one of the sources of inspiration for Leon Walras and his equilibrium theory.

　　By the time Cournot died in 1877, he was nearly blind.

　　In the field of economics he is best known for his work in the field of oligopoly theory - Cournot competition

　　Antoine Augustin Cournot, 1801-1877

　　French philosopher, mathematician and economist, Augustin Cournot has been rightly hailed as one of the greatest of the Proto-Marginalists.　The unique insights of his major economics work, Researches into the Mathematical Principles of Wealth (1838) were without parallel.　Although neglected in his time, the impact of Cournot work on modern economics can hardly be overstated.

　　Augustin Cournot was born in the small town of Gray (Haute-Sa鬾e).　He was educated in the schools of Gray until he was fifteen. Subsequently, for the next four years,　he worked haphazardly as a clerk in a lawyer's office.　Cournot directed his own studies throughout this time, mostly centered around philosophy and law.　Inspired by the work of Laplace, Cournot realized that he had to learn mathematics if he was to pursue his philosophical aspirations.　So, at the relatively ripe age of nineteen, he enrolled in a mathematical preparatory course at a school in Besan鏾n.　He subsequently won entry into the 蒫ole Normale Sup閞ieure in Paris in 1821.　　

　　For political reasons, the ENS was closed down in 1822 and so Cournot transferred to the Sorbonne, obtaining a lecentiate in mathematics in 1823.　He threw himself wholeheartedly into the stimulating intellectual and scientific atmosphere of Paris, attending the seminars at the Academie des Sciences and the salon of the economist Joseph Droz. Among his main intellectual influences were Laplace, Lagrange and Hachette, a former disciple of Condorcet, who imbibed in him the principles of mathematique sociale, i.e. the idea that the social sciences, like the natural, could be dealt with mathematically.　Cournot counted the young mathematician Lejeune Dirichlet as a close friend.

　　From 1823, Cournot was employed as a literary advisor to Marshal Gouvoin Saint Cyr and a tutor to his son.　For the next ten years, Cournot would remain in Paris in this leisurely capacity, pursuing his studies and research in his own way.　In 1829, Cournot acquired a doctorate in sciences, focusing on mechanics and astronomy.　After Saint Cyr's death in 1830, Cournot took it upon himself to edit and publish the remaining volumes of his late employer's memoirs.　

　　Cournot's thesis and a few of his articles brought him to the attention of the mathematician Sim閛n-Denis Poisson who urged him to return to academia.　Cournot refused at first but, after his engagement with the Saint Cyr family ended in 1833, he took up a temporary appointment at the Academy in Paris.　It was during this time that he translated John Herschel's Astronomy (1834) and Dionysus Lardner's Mechanics (1835).

　　In 1834, through the good offices of Poisson, Cournot found a permanent appointment as professor of analysis and mechanics at Lyons.　 A year later, Poisson secured him a rectorship　at the Academy of Grenoble.　Although his duties were mostly administrative, Cournot excelled at them.　In 1838, (again, at the instigation of the loyal Poisson), Cournot was called to Paris as Inspecteur G閚閞al des 蓆udes.　In that same year, he was made a Knight of the L間ion d'honneur (he was elevated to an Officer in 1845).

　　It was in this year that Cournot published his economics masterpiece, the Recherches (1838). Cournot begins with some preliminary remarks on the role of mathematics applied to the social sciences.　His announces that his purpose in using mathematics is merely to guide his reasoning and illustrate his argument rather than lead to any numerical calculations.　He acknowledges (and disparages) N.F. Canard as his only predecessor.　

　　In his first three chapters, he runs through the definition of wealth, absolute vs. relative prices and the law of one price.　Then, in Chapter 4, he unveils his demand function. He writes it in general form as D = F(p).　He assumes that F(.) is continuous and takes it as an empirical proposition that the demand function is downward-sloping (the loi de d閎it, "law of demand") and proceeds to draw it in price-quantity space (Fig. 1).　He also introduces the idea of "elasticity", but does not write it down in a mathematical formula.

　　It is important to note that Cournot's "demand function" is not a demand schedule in the modern sense.　His curve, D = F(p) merely summarizes the empirical relationship between price and quantity sold, rather than the conceptual relationship between price and the quantity sought by buyers. Cournot refuses to derive demand from any "utility"-based theories of individual behavior.　As he notes, the "accessory ideas of utility, scarcity, and suitability to the needs and enjoyments of mankind...are variable and by nature indeterminate, and consequently ill suited for the foundation of a scientific theory" (Cournot, 1838: p.10).　He satisfies himself with merely acknowledging that the functional form of F(.) depends on "the utility of the article, the nature of the services it can render or the enjoyments it can procure, on the habits and customs of the people, on the average wealth, and on the scale on which wealth is distributed." (1838: p.47).

　　In Chapter 5, Cournot jumps immediately into an analysis of monopoly.　Here, the concept of a profit-maximizing producer is introduced.　Cournot introduces the cost function　f(D) and discusses decreasing, constant and increasing costs to scale.　He shows mathematically how a producer will choose to produce at a quantity where marginal revenue is equal to marginal cost (he re-expresses marginal cost as a function of price in its own right, f'(D(p)) = y(p)).　In Chapter 6, he examines the impact of various forms of taxes and bounties on price and quantity produced, as well as their impact on the income of　producers and consumers.　　

　　In Chapter 7, Cournot presents his famous "duopoly" model.　He sets up a mathematical model with two rival producers of a homogeneous product.　Each producer is conscious that his rival's quantity decision will also impact the price he faces and thus his profits.　Consequently, each producer chooses a quantity that maximizes his profits subject to the quantity reactions of his rival.　 Cournot mathematically derives a deterministic solution as the quantities chosen by the rival producers are in accordance with each other's anticipated reactions.　Cournot showed how this equilibrium can be drawn as the intersection of two "reaction curves".　He depicts a stable and an unstable equilibrium in Figures 2 and 3 respectively.　

　　Comparing solutions, Cournot notes that under duopoly, the price is lower and the total quantity produced greater than under monopoly. He runs with this insight, showing that as the number of producers increases, the quantity becomes greater and the price lower.　 In Chapter 8, he introduces the case of unlimited competition, i.e. where the quantity of producers is so great that the entry or departure of a individual producer has a negligible effect on the total quantity produced.　He goes on to derive the prices and quantities in this "perfectly competitive" situation, in particular showing that, at the solution, price is equal to marginal cost.　

　　In the remainder of his book, Cournot takes up what he calls the "communication of markets", or trade of a single good between regions.　In Ch. 10, he analyzes two isolated countries and one homogeneous product.　He shows that the impact of opening trade between the two countries leads to the equalization of prices, with the lower cost producer exporting to the higher cost country.　Cournot tries to prove that there are conditions where the opening of trade will lead to a decline in the quantity of the good and lower revenue.　He then proceeds to discuss the impact of import and export taxes and subsidies (and algebraic error here was spotted later by Edgeworth (1894)) .　On account of this, Cournot raises doubts in Chapter 12 about the "gains from trade" and defends the profitability of import duties.　

　　Finally, Cournot also acknowledges that the solutions obtained via his "partial equilibrium" method are incomplete.　He recognizes the need to take multiple markets into account and trying to solve for the general equilibrium, but "this would surpass the powers of mathematical analysis" (Cournot, 1838: p.127).　

　　Cournot's 1838 work received hardly any response when it came out.　The denizens of the French Liberal School, who dominated the economics profession in France at the time, took no notice of it, leaving Cournot crushed and bitter.　In 1839, plagued by ill-health, Poisson asked Cournot to represent him at the concours d'agr間ation de math閙atiques at the Conseil Royal.　After Poisson died in 1840, Cournot continued on at the Conseil as a deputy to Poisson's successor, the mathematician Louis Poinsot.　　

　　In 1841, Cournot published his lecture notes on analysis from Lyons, dedicating the resulting Trait? to Possion.　In 1843, he made his first stab at probability theory in his Exposition.　He differentiated between three types of probabilities: objective, subjective and philosophical.　The former two follow their standard ontological　and epistemological definitions.　The third category refers to probabilities "which depend mainly on the idea that we have of the simplicity of the laws of nature." (1843: p.440).　

　　After the 1848 Revolution, Cournot was appointed to the Commission des Hautes 蓆udes.　It was during this time that he wrote his first treatise on the philosophy of science (1851).　In 1854, he became rector of the Academy at Dijon.　However, Cournot's lifelong eye-sight problem began getting worse.

　　Cournot retired from teaching in 1862 and moved back to Paris.

　　In 1859, Cournot wrote his Souvenirs, a haunting autobiographical memoir (published posthumously in 1913).　Despite the dark pessimism about the decline of his creative powers, he wasn't quite yet finished.　He published two more philosophical treatises in 1861 and 1872 which sealed his fame in the French philosophy community, but did nothing to advance his economics.　He took another stab at economics with his Principes (1863), which, on the whole, was merely a　restatement of the 1838 Recherches without the math and in more popular prose.　Once again, it was completely neglected.　A Journal des 閏onomistes review churlishly claimed that Cournot had "not gone beyond Ricardo", etc.　Cournot's bitterness increased accordingly.

　　However, by this time the Marginalist Revolution had already started.　L閛n Walras (1874), who had read Cournot's work early on, argued that his own theory was but a multi-market generalization of Cournot's partial equilibrium model (indeed, the notation is almost identical).　W. Stanley Jevons, who had not read him, nonetheless hailed him as a predecessor in later editions of his Theory (1871). Francis Ysidro Edgeworth (1881) went to Cournot to pick up his theory of perfect competition.　Alfred Marshall claimed to have read him as far back as 1868, and extensively acknowledged Cournot's influence in his 1890 textbook, particularly in his discussion of the theory of the firm.　

　　Cournot lived long enough to greet the works of Walras and Jevons with a warm sense of vindication.　This is evident in Cournot's Revue sommaire (1877), a long, non-mathematical statement of his earlier work.　He seemed particularly grateful that Walras had bravely climbed the steps of the Institute de France and accused the academicians of injustice towards Cournot.　He died that same year.　

　　Walras, Jevons and the other young blades complained loudly that Cournot had been unjustly neglected by his contemporaries.　So, in 1883, the French mathematician Joseph Bertrand took it upon himself to finally provide the first review of the Cournot's Recherches (jointly with a Walras book) in the Journal des savants.　It was not a kind review.　Bertrand argued that Cournot had reached the wrong conclusion on practically everything, and reworked Cournot's duopoly model with prices, rather than quantities, as the strategic variables -- and obtained the competitive solution immediately.　Edgeworth (1897) revisited the model and assailed both Cournot and Bertrand for obtaining deterministic solutions, arguing that the equilibrium solution in the case of a small number of producers should always be indeterminate.

　　The development of monopolistic competition in the 1930s drew much inspiration from Cournot's work.　As the theory of games advanced in the 1950s, Mayberry, Nash and Shubik (1953) restated Cournot's duopoly theory as　a non-cooperative game with quantities as strategic variables.　They showed that Cournot's solution was nothing other than its "Nash equilibrium" (Nash, 1951).　Cournot's influence on modern theory continues unabated, having been given a particular boost in the attempt to develop non-cooperative foundations for Walrasian general equilibrium theory (e.g. Novshek and Sonnenschein (1978) and the 1980 JET Symposium).