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. It has the following features: 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. It has the following features: 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 {displaystyle 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 ) {displaystyle 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. 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. This section presents an analysis of the model with 2 firms and constant marginal cost. Equilibrium prices will be: This implies that firm 1’s profit is given by Π 1 = q 1 ( P ( q 1 + q 2 ) − c ) {displaystyle Pi _{1}=q_{1}(P(q_{1}+q_{2})-c)}