Cournot competition
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.
The market price is set at a level such that demand equals the total quantity produced by all firms.
Each firm takes the quantity set by its competitors as a given, evaluates its residual demand, and then behaves as a monopoly.
The state of equilibrium... is therefore stable; i.e., if either of the producers, misled as to his true interest, leaves it temporarily, he will be brought back to it.Antoine Augustin Cournot (1801–1877) first outlined his theory of competition in his 1838 volume Recherches sur les Principes Mathématiques de la Théorie des Richesses as a way of describing the competition with a market for spring water dominated by two suppliers (a duopoly).
[4] Cournot's economic theory was little noticed until Léon Walras credited him as a forerunner.
This led to an unsympathetic review of Cournot's book by Joseph Bertrand which in turn received heavy criticism.
Irving Fisher found Cournot's treatment of oligopoly "brilliant and suggestive, but not free from serious objections".
[6] Reactions to this aspect of Cournot's theory have ranged from searing condemnation to half-hearted endorsement.
The diagrams were presumably included as an oversized plate in the original edition, and are missing from some modern reprints.
Cournot's discussion of oligopoly draws on two theoretical advances made in earlier pages of his book.
Cournot's discussion of monopoly influenced later writers such as Edward Chamberlin and Joan Robinson during the 1930s revival of interest in imperfect competition.
Cournot was wary of psychological notions of demand, defining it simply as the amount sold of a particular good (helped along by the fact that the French word débit, meaning 'sales quantity', has the same initial letter as demande, meaning 'demand' [7]).
Cournot remarks that the demand curve will usually be a decreasing function of price, and that the total value of the good sold is
Cournot insists that each duopolist seeks independently to maximize profits, and this restriction is essential, since Cournot tells us that if they came to an understanding between each other so as each to obtain the maximum possible revenue, then completely different results would be obtained, indistinguishable from the consumer's point of view from those entailed by monopoly.
Cournot presents a mathematically correct analysis of the equilibrium condition corresponding to a certain logically consistent model of duopolist behaviour.
Suppose that there are two owners of mineral water springs, each able to produce unlimited quantities at zero price.
The middle man finds the market-clearing price, which is determined by the demand function
It needs mental contortions to imagine the same market behaviour arising without a middle man.
[11] de Bornier expands on this by saying that "the obvious conclusion that only a single price can exist at a given moment" follows from "an essential assumption concerning his model, [namely] product homogeneity".
[12] Later on Cournot writes that a proprietor can adjust his supply "en modifiant correctement le prix".
If there is a single price, then it must be determined by the market as a consequence of the proprietors' decisions on matters under their individual control.
Cournot's account threw his English translator (Nathaniel Bacon) so completely off-balance that his words were corrected to "properly adjusting his price".
[14] Edgeworth regarded equality of price in Cournot as "a particular condition, not... abstractly necessary in cases of imperfect competition".
A. J. Nichol claimed that Cournot's theory makes no sense unless "prices are directly determined by buyers".
[16] Shapiro, perhaps in despair, remarked that "the actual process of price formation in Cournot's theory is somewhat mysterious".
, and therefore production beyond this point results in the firm losing money for each additional unit produced.
We can now find a Cournot-Nash Equilibrium using our "Best Response" functions above for the output quantity of firms 1 and 2.
[17][note 1] His summary of Cournot's theory of duopoly has remained influential: Cournot assumes that one of the proprietors will reduce his price to attract buyers to him, and that the other will in turn reduce his price even more to attract buyers back to him.
[18] Irving Fisher outlined a model of duopoly similar to the one Bertrand had accused Cournot of analysing incorrectly: A more natural hypothesis, and one often tacitly adopted, is that each [producer] assumes his rival's price will remain fixed, while his own price is adjusted.
