Antoine-Augustin Cournot

Antoine -Augustin Cournot ( born August 28, 1801 in Gray, † March 31, 1877 in Paris) was a French mathematician and economist. He can be counted on classical economics and is a co-founder of mathematical economic theory.

Life

Augustin Cournot's mathematical education was at the Lycée de Besançon, his studies he set in 1821 at the École Normale in Paris continued. In 1834 he became professor of mathematics in Lyon. His Recherches sur les principes Mathématiques de la théorie of richesses published in 1838, remained at this time, however, largely ignored. He therefore simplified in the following years and published them in 1863 and 1876 again.

Influence on the mathematical economic theory

The name Cournot is usually brought first to the duopoly theory related. His name encountered the most students of economics by the Nash - Cournot equilibrium. Occasionally, the maximum profit of a monopoly is called Cournot point. But he had a major role in the introduction of the application of mathematics to economics share. Many of his ideas are still virtually unchanged part of microeconomics.

The Recherches

Construction

The first three chapters of his Recherches Cournot uses to define "wealth", absolute to compare relative prices and specify that for homogeneous goods in a common market only a single price may apply. He also defines that all individuals acting in an economy act profit-maximizing.

Chapter 4 is used to explain the demand function used by him in the course. Starting with the analysis of the monopoly in Chapter 5, Cournot approaches his most famous investigation: He first considered a commodity that is produced by a single manufacturer, the model is extended in Chapter 7 or a number of competitors, thus achieving his famous oligopoly theory, where the special case with two competitors, so the duopoly, graphically describes how analytically in detail. Chapter 8 concludes this basic observation from the implementation of full competition with an infinitely large number of competitors. Chapter 6 deals with the effects of the taxation of a monopolist.

The remaining four chapters deal with the " communication " of markets, so trade between different regions, and the impact on the entire national income.

Examination of the forms of competition

It should be noted that the " study of the forms of competition " is actually an investigation of the price of goods, subject to certain conditions. Cournot defined in the introduction wealth as the product of quantity and price of a good, where he admits that this "wealth" is not necessarily welfare- maximizing. As an example, he cites the destruction of spices by the Dutch East India Company, which was an " actual creation of wealth in the commercial sense of the word ." With the later-developed budget theory and therefore particularly in consumer surplus, it is possible to show the negative consequences of an artificial scarcity of goods of a market power owning party for the general welfare. However, Cournot had no choice but to choose intuitively easy to understand explanation with examples.

The law of demand

It is assumed that Cournot Adam Smith's Wealth of Nations has quite thoroughly studied. Smith shows in the seventh chapter of an intuitive understanding of the properties of a demand function, without being identified as such or even to define exactly. It was Cournot, which transferred first, the concept of a dependent from the price of a good demand in the mathematics and described it as a function.

Cournout defines the demand D as a continuous and monotonically decreasing function F (p), ie, as dependent on the price of the commodity p.

At this point it should be noted that Cournot's demand function is different from the usual in today's microeconomics, since Cournot not herleitete from a utility function of the demand. Although he was aware that the law of demand depends on the benefit of the estate, however, took the view that the reasons for asking too subjective and therefore can not be expressed in algebraic formulas are. He therefore founded the properties of the demand function only by empirical observations that suggest a negative relationship between price and quantity. The explanation of the steady progression corresponds to contrast today: he admits that in a small market with few buyers can certainly occur sudden changes in demand; However, once the market is large enough, however, the assumption of continuity is justified.

What does this definition of demand, it becomes clear later in the Recherches. Through the representation of demand as a function succeeds Cournot to build his study of the various market forms in rigorous, consistent form.

Reactions and influences

During his lifetime, Cournot was indeed a well respected and renowned scientist, but his Recherches were almost completely ignored. Only after his death, his influence on the development of economic theory began to emerge.

What can be said is that the mathematical treatment of the simple monopoly case has remained unchanged. Hardly a standard textbook of microeconomics need to repeat this study, however, to refer without resorting to Cournot.

Furthermore Cournot seems to many later economists, mathematical, applied their methods to have had a major impact. For example, writes Walras 1874:

" I am indebted to my father, Auguste Walras, for the fundamental principles of my economic doctrine; Augustin Cournot and to 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 most famous studies of Cournot Duopoltheorie is the 1883 published criticism of the French mathematician Joseph Bertrand. Cournot went out in his derivation of the equilibrium by the quantity of goods offered as a crucial variable, while Bertrand chose the price. In the case of two suppliers with the same cost structure, which compete for the sale of a homogeneous good, one of the competitors can determine its price slightly below that of the other, and he would receive the total demand and thus increase its profit. However, this would cause the other providers to its part to undercut the new price - so it would be a process was set in motion that would only end with the achievement of marginal costs.

The result of this competition is known as the Bertrand paradox: Although there are only two providers, the good is sold at a price equal to that of unlimited competition. Today is called a Cournot competition after schema as quantity competition, while Bertrand competition is also known as price competition.

The equilibrium described in the duopoly case is now known as the Nash - Cournot equilibrium. Friedman compares Cournot's performance in the consideration of the duopoly with that of Adam Smith in terms of the demand function: although Smith had a vague idea about the nature of a demand function, he could not describe exactly the same as Cournot a vague idea about the later Nash had balance, but this could not describe exactly.

Cournot treated his analysis of the situation as if it were a dynamic, but this is wrong. The great attention that is now given to this aspect of its investigation based on the fact that applying this calculation of the equilibrium static considerations, the obvious non-cooperative result corresponds to that of Cournot.

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