# 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.[1] It has the following features:

• There is more than one firm and all firms produce a homogeneous product, i.e. there is no product differentiation;
• Firms do not cooperate, i.e. there is no collusion;
• Firms have market power, i.e. each firm’s output decision affects the good’s price;
• The number of firms is fixed;
• Firms compete in quantities, and choose quantities simultaneously;
• The firms are economically rational and act strategically, usually seeking to maximize profit given their competitors’ decisions.

An essential assumption of this model is the “not conjecture” that each firm aims to maximize profits, based on the expectation that its own output decision will not have an effect on the decisions of its

History

 “ 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, Recherches sur les Principes Mathematiques de la Theorie des Richesses (1838), translated by Bacon (1897).

Antoine Augustin Cournot (1801-1877) first outlined his theory of competition in his 1838 volume Recherches sur les Principes Mathematiques de la Theorie des Richesses as a way of describing the competition with a market for spring water dominated by two suppliers (a duopoly).[2] The model was one of a number that Cournot set out “explicitly and with mathematical precision” in the volume.[3] Specifically, Cournot constructed profit functions for each firm, and then used partial differentiation to construct a function representing a firm’s best response for given (exogenous) output levels of the other firm(s) in the market.[3] He then showed that a stable equilibrium occurs where these functions intersect (i.e. the simultaneous solution of the best response functions of each firm).[3]

The consequence of this is that in equilibrium, each firm’s expectations of how other firms will act are shown to be correct; when all is revealed, no firm wants to change its output decision.[1] This idea of stability was later taken up and built upon as a description of Nash equilibria, of which Cournot equilibria are a subset.[3]

## Implications

• Output is greater with Cournot duopoly than monopoly, but lower than perfect competition.
• Price is lower with Cournot duopoly than monopoly, but not as low as with perfect competition.
• According to this model the firms have an incentive to form a cartel, effectively turning the Cournot model into a Monopoly. Cartels are usually illegal, so firms might instead tacitly collude using self-imposing strategies to reduce output which, ceteris paribuswill raise the price and thus increase profits for all firms involved.

## Bertrand versus Cournot

Although both models have similar assumptions, they have very different implications:

• Since the Bertrand model assumes that firms compete on price and not output quantity, it predicts that a duopoly is enough to push prices down to marginal cost level, meaning that a duopoly will result in perfect competition.
• Neither model is necessarily “better.” The accuracy of the predictions of each model will vary from industry to industry, depending on the closeness of each model to the industry situation.
• If capacity and output can be easily changed, Bertrand is a better model of duopoly competition. If output and capacity are difficult to adjust, then Cournot is generally a better model.
• Under some conditions the Cournot model can be recast as a two-stage model, where in the first stage firms choose capacities, and in the second they compete in Bertrand fashion.

However, as the number of firms increases towards infinity, the Cournot model gives the same result as in Bertrand model: The market price is pushed to marginal cost level.

## References

1. ^ Jump up to:ab Varian, Hal R. (2006). Intermediate microeconomics: a modern approach (7th ed.). W. W. Norton & Company. p. 490. ISBN 0-393-92702-4.
2. ^Van den Berg et al. 2011, p. 1
3. ^ Jump up to:ab c d Morrison 1998
4. ^Etro, Federico. Simple models of competition Archived 2011-10-05 at the Wayback Machine, page 6, Dept. Political Economics — Università di Milano-Bicocca, November 2006

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