Antoine Augustin Cournot | |
---|---|

Born | |

Died | 31 March 1877 75) | (aged

Nationality | French |

Alma mater | Sorbonne University |

Known for | Cournot competition Oligopoly |

Scientific career | |

Fields | Economics Mathematics |

Institutions | University of Grenoble |

Influences | Nicolas-François Canard |

Influenced | Gabriel Tarde Léon Walras |

**Antoine Augustin Cournot** (28 August 1801 –31 March 1877) was a French philosopher and mathematician who also contributed to the development of economics.

Antoine Augustin Cournot was born at Gray, Haute-Saône. In 1821 he entered one of the most prestigious Grande École, the École Normale Supérieure, and, according to Sandmo:

in 1823 he took a license degree in mathematics at Sorbonne University. He then became the private secretary of a field marshal who required assistance in writing his memoirs. This position does leave Cournot with considerable time for his own pursuits, for in the course of his ten years in the field marshal's employment he took two doctoral degrees, one in mechanics and one in astronomy. In addition, he published a number of articles and even acquired a degree in law.

^{ [1] }

Subsequently, Cournot held positions as professor of mathematics, chief examiner for undergraduate students, and rector of Dijon Academy.

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

Cournot was mainly a mathematician, but did have some influence over economics. His theories on monopolies and duopolies are still famous.^{[ citation needed ]} In 1838 the book *Researches on the Mathematical Principles of the Theory of Wealth*^{ [2] } was published, in which he used the application of the formulas and symbols of mathematics in economic analysis. This book was highly criticized and not very successful during Cournot's lifetime. He did attempt to rewrite it twice. However, it still has influence in economics today. Today many economists believe this book to be the point of departure for modern economic analysis. Cournot introduced the ideas of functions and probability into economic analysis. He derived the first formula for the rule of supply and demand as a function of price and in fact was the first to draw supply and demand curves on a graph, anticipating the work of Alfred Marshall by roughly thirty years. The Cournot duopoly model developed in his book also introduced the concept of a (pure strategy) Nash equilibrium, the Reaction function and best-response dynamics.

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 econometrics. He was also a teacher of political economy and mathematics to Auguste Walras, who was the father of Léon Walras. Cournot and Auguste Walras persuaded Léon Walras to try political economics. Cournot is also credited to be one of the sources of inspiration for Léon Walras and his equilibrium theory.^{[ citation needed ]}

In the field of economics he is best known for his work in the field of oligopoly theory—Cournot competition which is named after him.^{ [3] }

Cournot worked on determinism (in physics) and chance.

Unlike Pierre-Simon de Laplace, who thought that nothing happen by chance, and Aristotle, who thought that randomness and causality had nothing to do which each other, Cournot combine them both and define randomness as

encounter of two independent causal series

^{ [4] }.

This definition allows randomness even in perfectly deterministic events, and is used to generate random number by the combination of unrelated signal (for instance, temperature and sound).

**Game theory** is the study of mathematical models of strategic interaction among rational decision-makers. It has applications in all fields of social science, as well as in logic, systems science and computer science. Originally, it addressed zero-sum games, in which each participant's gains or losses are exactly balanced by those of the other participants. Today, game theory applies to a wide range of behavioral relations, and is now an umbrella term for the science of logical decision making in humans, animals, and computers.

In economics, **general equilibrium theory** attempts to explain the behavior of supply, demand, and prices in a whole economy with several or many interacting markets, by seeking to prove that the interaction of demand and supply will result in an overall general equilibrium. General equilibrium theory contrasts to the theory of *partial* equilibrium, which only analyzes single markets.

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**Gérard Debreu** was a French-born economist and mathematician. Best known as a professor of economics at the University of California, Berkeley, where he began work in 1962, he won the 1983 Nobel Memorial Prize in Economic Sciences.

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**Bertrand competition** is a model of competition used in economics, named after Joseph Louis François Bertrand (1822–1900). It describes interactions among firms (sellers) that set prices and their customers (buyers) that choose quantities at the prices set. The model was formulated in 1883 by Bertrand in a review of Antoine Augustin Cournot's book *Recherches sur les Principes Mathématiques de la Théorie des Richesses* (1838) in which Cournot had put forward the Cournot model. Cournot argued that when firms choose quantities, the equilibrium outcome involves firms pricing above marginal cost and hence the competitive price. In his review, Bertrand argued that if firms chose prices rather than quantities, then the competitive outcome would occur with price equal to marginal cost. The model was not formalized by Bertrand: however, the idea was developed into a mathematical model by Francis Ysidro Edgeworth in 1889.

**Cournot competition** is an economic model used to describe an industry structure in which companies compete on the amount of output they will produce, which they decide on independently of each other and at the same time. It is named after Antoine Augustin Cournot (1801–1877) who was inspired by observing competition in a spring water duopoly. It has the following features:

**Michio Morishima** was a heterodox economist and public intellectual who was the Sir John Hicks Professor of Economics at the London School of Economics from 1970–88. He was also professor at Osaka University and member of the British Academy. In 1976 he won the Order of Culture.

A **Walrasian auction**, introduced by Léon Walras, is a type of simultaneous auction where each agent calculates its demand for the good at every possible price and submits this to an auctioneer. The price is then set so that the total demand across all agents equals the total amount of the good. Thus, a Walrasian auction perfectly matches the supply and the demand.

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The **Lausanne School** of economics, sometimes referred to as the **Mathematical School**, refers to the neoclassical economics school of thought surrounding Léon Walras and Vilfredo Pareto. It is named after the University of Lausanne, at which both Walras and Pareto held professorships. Polish economist Leon Winiarski is also said to have been a member of the Lausanne School.

* Foundations of Economic Analysis* is a book by Paul A. Samuelson published in 1947 by Harvard University Press. It is based on Samuelson's 1941 doctoral dissertation at Harvard University. The book sought to demonstrate a common mathematical structure underlying multiple branches of economics from two basic principles: maximizing behavior of agents and stability of equilibrium as to economic systems. Among other contributions, it advanced the theory of index numbers and generalized welfare economics. It is especially known for definitively stating and formalizing qualitative and quantitative versions of the "comparative statics" method for calculating how a change in any parameter affects an economic system. One of its key insights about comparative statics, called the correspondence principle, states that stability of equilibrium implies testable predictions about how the equilibrium changes when parameters are changed.

* Value and Capital* is a book by the British economist John Richard Hicks, published in 1939. It is considered a classic exposition of microeconomic theory. Central results include:

**Auguste Walras** was a French school administrator and (amateur) economist. He was the father of Léon Walras, who was deeply influenced by his father's view on economics.

**Mathematical economics** is the application of mathematical methods to represent theories and analyze problems in economics. By convention, these applied methods are beyond simple geometry, such as differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, and other computational methods. Proponents of this approach claim that it allows the formulation of theoretical relationships with rigor, generality, and simplicity.

**Griffith Conrad Evans** was a mathematician working for much of his career at the University of California, Berkeley. He is largely credited with elevating Berkeley's mathematics department to a top-tier research department, having recruited many notable mathematicians in the 1930s and 1940s.

The **progressive theory of capital** is an economic theory posited by Léon Walras in 1874 in part 5 of his book *Elements of Pure Economics*.

**Xavier Vives** is a Spanish economist regarded as one of the main figures in the field of industrial organization and, more broadly, microeconomics. He is currently Chaired Professor of Regulation, Competition and Public Policies, and academic director of the Public-Private Sector Research Center at IESE Business School in Barcelona.

**Charles Frederick Roos** was an American economist who made contributions to mathematical economics. He was one of the founders of the Econometric Society together with American economist Irving Fisher and Norwegian economist Ragnar Frisch in 1930. He served as Secretary-Treasurer during the first year of the Society and was elected as President in 1948. He was director of research of the Cowles Commission from September 1934 to January 1937.

- ↑ Sandmo, Agnar (2011).
*Economics evolving*. Princeton: Princeton university press. p. 146. ISBN 9780691148427. - ↑ Antoine Augustin Cournot (1897).
*Researches Into the Mathematical Principles of the Theory of Wealth*. Macmillan. - ↑ Varian, Hal R. (2006),
*Intermediate microeconomics: a modern approach*(7 ed.), W. W. Norton & Company, p. 490, ISBN 0-393-92702-4 - ↑ Thierry Martin. "Cournot (A)".
*encyclo-philo.fr*(in French). Retrieved 16 January 2017..

- Touffut, Jean-Philippe, ed. (2007).
*Augustin Cournot: Modelling Economics*. Cheltenham: Edward Elgar. ISBN 1-84720-654-9. - For an early 20th century evaluation see: Chisholm, Hugh, ed. (1911).
*Encyclopædia Britannica*.**7**(11th ed.). Cambridge University Press. p. 321. .

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