Antoine-Augustin Cournot
Antoine-Augustin Cournot (born August 28, 1801 in Gray , † March 31, 1877 in Paris ) was a French mathematician and economic theorist . He can be counted to classical economics and is considered to be a co-founder of mathematical economic theory.
Life
Augustin Cournot's mathematical training took place at the Lycée de Besançon, and he continued his studies in 1821 at the École Normale in Paris. In 1834 he became a professor of mathematics in Lyon. His Recherches sur les principes mathématiques de la théorie des richesses appeared in 1838, but went largely unnoticed at that time. He therefore simplified it in the following years and published it again in 1863 and 1876.
Influence on mathematical economic theory
The name Cournot is usually the first to be associated with the duopoly theory. Most economics students come across his name through the Nash-Cournot equilibrium . Occasionally the profit maximum of a monopoly is also called Cournot's point . However, he played a key role in introducing the application of mathematics to economics. Many of his ideas are still almost unchanged today as part of microeconomics .
The research
construction
Cournot uses the first three chapters of his research to define “wealth”, to compare absolute prices with relative prices, and to stipulate that only one price can apply to homogeneous goods in a common market. It also defines that all acting individuals in an economy act in a profit-maximizing manner.
Chapter 4 serves to explain the demand function he used in the further course . Beginning with the analysis of the monopoly in Chapter 5, Cournot approaches his best-known investigation: He first considers a good that is only manufactured by a single producer, then expands the model in Chapter 7 to include one or more competitors and thus achieves his famous oligopoly theory , whereby the special case with two competitors, i.e. the duopoly, is described in detail both graphically and analytically. Chapter 8 concludes this basic consideration by introducing full competition with an infinite number of competitors. Chapter 6 deals with the effects of taxing a monopoly.
The remaining four chapters deal with the “communication” of markets, i.e. trade between different regions, and the effects on total national income.
Investigation of the forms of competition
It should be noted that the "investigation of the forms of competition" is actually an investigation of the price of goods under certain conditions. Cournot initially defines wealth as the product of the quantity and price of a good, although he admits that this “wealth” does not necessarily maximize welfare. As an example, he cites the destruction of spices by the Dutch East India Society, which is an "actual creation of wealth in the commercial sense of the word". With the household theory developed later, and with it in particular the consumer surplus, it is possible to show the negative consequences of an artificial shortage of goods from a provider with market power for general welfare. Cournot, however, had no choice but to choose an intuitive explanation based on examples.
The law of demand
It can be assumed that Cournot studied Adam Smith's Wealth of Nations thoroughly. In the seventh chapter, Smith shows an intuitive understanding of the properties of a demand function, but without designating them as such or even defining them precisely. It was Cournot who was the first to translate the concept of a demand dependent on the price of a good into mathematics and describe it as a function.
Cournout defines the demand D as a continuous and monotonically decreasing function F (p) , i.e. as dependent on the price p of the respective good.
At this point it should be pointed out that Cournot's demand function differs from that used in today's microeconomics, since Cournot did not derive it from a utility function of the demanders. Although he was aware that the law of demand depends on the utility of the good, he was of the opinion that the reasons for the demand were too subjective and could not be expressed in algebraic formulas. He therefore justifies the properties of the demand function exclusively through empirical observations that suggest a negative relationship between price and quantity. The explanation of the steady course, on the other hand, corresponds to today's one: he admits that in a small market with few buyers there can be sudden changes in demand; however, as soon as the market becomes large enough, the assumption of continuity is justified.
The importance of this definition of demand will become clear in the further course of the research . By depicting demand as a function, Cournot succeeds in building his study of the various forms of market in a rigorous, consistent manner.
Reactions and influences
Cournot was a well-respected and recognized scientist during his lifetime, but his research was almost completely ignored. It was only after his death that his influences on the development of economic theory began to emerge.
What can be stated is that the mathematical treatment of the simple monopoly case has remained unchanged to this day. Hardly any standard textbook in microeconomics does without repeating this investigation, but without referring to Cournot.
Furthermore, Cournot seems to have had a great influence on many later economists who used mathematical methods. For example, Walras wrote in 1874:
“I am indebted to my father, Auguste Walras, for the fundamental principles of my economic doctrine; and to Augustin Cournot for the idea of using the calculus of functions in the elaboration of this doctrine. "
and Marshall 1890:
"Cournot's genius must give a new mental activity to everyone who passes through his hands."
One of the best-known investigations of Cournot's duopole theory is the 1883 criticism by the French mathematician Joseph Bertrand . In his derivation of the equilibrium, Cournot assumed the quantity of goods offered as the decisive variable, while Bertrand selected the price. In the case of two suppliers with the same cost structure competing for the sale of a homogeneous good, one of the competitors can set its price minimally below that of the other, whereupon it would receive the entire demand and thus increase its profit. However, this would cause the other provider to undercut the new price - a process would have been set in motion that would only end when the marginal costs were reached.
The result of this competition is known as the Bertrand Paradox : although there are only two suppliers, the goods are sold at a price that corresponds to that of unlimited competition. Today, a competition based on Cournot's scheme is known as a quantity competition, while the Bertrand competition is also known as a price competition.
The equilibrium described in the duopoly case is known today as the Nash-Cournot equilibrium . Friedman compares Cournot's performance in considering the duopoly with that of Adam Smith in relation to the demand function: although Smith had a vague idea of the nature of a demand function, he could not describe it exactly, just as Cournot had a vague idea of the later Nash- Had balance, but could not describe it exactly.
Cournot treated his analysis of the situation as if it were dynamic, which is wrong. The great attention paid to this aspect of his investigation today is due to the application of this equilibrium calculation to static considerations, the apparent non-cooperative result being that of Cournot.
literature
- Joseph Bertrand : Théorie Mathématique de la Richesse Sociale . In: Journal des Savants , 1883
- Augustin Cournot: Investigations into the mathematical foundations of the theory of wealth , Jena 1924 (French original: Recherches sur les principes mathématiques de la théorie des richesses , 1838)
- Augustin Cournot: Souvenirs 1760–1860 (memoirs of Cournot). 1859
- Irving Fisher: Cournot and Mathematical Economics . In: Quarterly Journal of Economics , 1898, pp. 119-138
- James W. Friedman: An Experimental Study of Cooperative Duopoly . In: Econometrica , Vol. 35, 1967, No. 3/4, pp. 379-397
- James W. Friedman: The Legacy of Augustin Cournot . University of North Carolina, Department of Economics, Working Paper, 1999, pp. 99-05
- G. Granger: Cournot, Antoine-Augustin . In: Charles Coulston Gillispie (Ed.): Dictionary of Scientific Biography . tape 3 : Pierre Cabanis - Heinrich von Dechen . Charles Scribner's Sons, New York 1971, p. 450-454 .
- Marco LiCalzi, Achille Basile: Economists and Mathematics from 1494 to 1969: Beyond the Art of Accounting . In: M. Emmer (Ed.): Matematica e Cultura 2000. Springer, Milano 2000, pp. 95-107
- Thierry Martin: Bibliography Cournotienne . In: ISIS , 90 (3), 1999, pp. 1045-1046
- Thierry Martin: La philosophie de l'histoire de Cournot . In: Revue d'Histoire des Sciences Humaines , No. 12, 2005/1, pp. 141–162
- Robert Remak : Can economics become an exact science? (1929) In: Martin J. Beckmann, Ryuzo Sato (Ed.): Mathematical Economic Theory . Kiepenheuer & Witsch, Cologne 1975, pp. 16-27
- Léon Walras : Principe d'une théorie mathématique de l'échange . In: Journal des économistes , 1874
- The little encyclopedia . Encyclios-Verlag, Zurich, 1950, Volume 1, p. 318
Web links
- Literature by and about Antoine-Augustin Cournot in the catalog of the German National Library
- Dirk Wigant: Antoine Augustin Cournot on the 200th birthday: life and work . In: Ecochron.
| personal data | |
|---|---|
| SURNAME | Cournot, Antoine-Augustin |
| BRIEF DESCRIPTION | French mathematician and economic theorist |
| DATE OF BIRTH | August 28, 1801 |
| PLACE OF BIRTH | Gray |
| DATE OF DEATH | March 31, 1877 |
| Place of death | Paris |