User:Jarry1250/Cournot competition

Cournot competition is an economic model used to describe an industry structure in which firms compete on quantities, and where all firms announce their quantities simultaneously. Each firm will independently selects what quantity to produce based on their expectation of other firms' production decisions. It is named after Antoine Augustin Cournot (1801-1877), who outlined his model of competition in his 1838 work Recherches sur les Principes Mathematiques de la Theorie des Richesses as a way of describing the competition between a spring water duopoly.

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 rivals. Price is a commonly known decreasing function of total output. All firms know $$N$$, the total number of firms in the market, and take the output of the others as given. Each firm has a cost function $$c_i(q_i)$$. Normally the cost functions are treated as common knowledge. The cost functions may be the same or different among firms. 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.

History
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). The model was one of a number that Cournot set out "explicitly and with mathematical precision" in the volume. 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. 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).

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. This idea of stability was later taken up and built upon as a description of Nash equilibria, of which Cournot equilibria are a subset.

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 paribus will raise the price and thus increase profits for all firms involved.

Comparison to other models
The Cournot model of competition describes only one of two main possible starting point for analysing competition in markets. The other is that of Bertrand competition, named after Joseph Louis François Bertrand and formulated in his 1883 review of the work of Cournot. Bertrand reasoned that Cournot 'equilibria' could not be stable because, "whatever the common price adopted, if one of the owners, alone, reduces his price, he will... attract all of the buyers, and thus double his revenue". The ability of firms to expand capacity and 'steal the market' in this manner remains the crucial dividing assumption between the Bertrand and Cournot models. In general, if firms choose their capacities and are then subjected to restrictive capacity constraints, the outcome may be "closely approximated" by the Cournot model.

Although both models have similar assumptions, they have very different implications: However, when number of firms goes to infinity, Cournot model gives the same result as in Bertrand model: market price is pushed to marginal cost level.
 * 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.