The main models of oligopoly in which firms compete according to output

The study of oligopolistic markets is inherently more difficult than that of monopolistic or perfectly competitive markets as it deals with the way firms interact with each other as well as with consumers। In an oligopoly, a small number of large firms dominate a particular industry and produce identical or closely substitutable products। Firms in an oligopolistic industry are interdependent, thus the central problem faced by a firm in oligopoly is that its decisions affect the price and quantity choices of its rivals; the likely response of other firms is a major factor influencing its own price and output decisions। An oligopolist therefore cannot take its demand curve as given as equilibrium output depends on enterprise behaviour. Possibilities range from the competitive outcome of the Cournot model with competing firms to the monopoly equilibrium characteristic of a cartel. Hence there is a general indeterminacy that lies at the heart of the oligopoly market structure.

This article reviews the theory of oligopolistic competition from the perspective of the non-collusive, conjectural variation models of Cournot and Stackleberg, within which firms compete according to output.

In 1838 Antoine Augustin Cournot, using the analogy of mineral water to illustrate his claims, laid out the foundation of oligopoly theory by proposing a solution concept to oligopolistic interaction. The Cournot model, in which the firm’s basic decision variable is output, assumes that each firm takes the level of output of its rivals as given in choosing its own. Hence in the Cournot model all firms are assumed to have zero conjectural variation. In equilibrium, the expectations of each firm about the output choice of its competitors are realised. The outcome in terms of the Cournot market structure can be categorised by the price-cost margin:

From this formula it is clear that the price-cost margin in the Cournot equilibrium declines as the number of firms increases. The outcome will therefore approximate the competitive equilibrium as the number of firm’s approaches infinity. This indicates the incentive for firms to collude to ensure that a zero-profit outcome is avoided.

The Cournot model is best explained diagrammatically with reference to isoprofit curves and reaction functions. In a duopoly, in which both firms have equal cost functions, the profits attainable for a firm depend on the output decision of its rival because the price obtained for the product depends on the total industry output. Equilibrium occurs at the intersection of the two reaction functions. Each reaction function plots the profit maximising level of output for each firm given every conceivable expected value of production which could be chosen by its rival. Therefore, at the equilibrium point each firm is choosing to produce the level of output expected by its rival.




It is clear from the diagram displayed above that a strong incentive to collude exists at the Cournot equilibrium. Although firms generate positive profits, industry profits are not maximised. The equilibrium point yields a greater output and a lower price, implying lower profits, when compared to a pure monopoly (M1 or M2) . Both firms could increase profits by reducing output, and moving into the shaded region, provided that its rival responded equally. This establishes the result that, whilst the behavioural assumptions of the Cournot model lead to a stable non-collusive equilibrium, there is a strong incentive for firms to co-operate to maximise industry profits which would suggest that collusion is a potential outcome in oligopolistic markets.

The hierarchal Stackleberg model, incorporating the idea of commitment, can be developed as an extension of the Cournot framework. In the Stackleberg model, the leader recognizes its interdependence, and seeks to improve upon its position in equilibrium in the knowledge that the followers will act according to the behavioural assumption of the Cournot model, and treat the leader’s output decisions as given. Hence, in duopoly, the follower will adjust output in response to the leader’s level of production according to its own reaction function. The leader, however, chooses an output level above that implied by its own reaction function in order to maximise profits subject to the followers reaction function. The resulting Stackleberg equilibrium occurs where the leader’s isoprofit curve is tangent to the followers reaction function. The Stackleberg model is therefore characterised by the fact that the leader and the follower have different conjectural variations. The follower act’s the same as all firms do in the Cournot model, and therefore the conjectural variation term for them is zero. The conjectural variation term for the leader is given by the slope of the follower’s reaction function, as it builds its knowledge about the follower’s reaction function into its decision making. A problem arises in the Stackleberg model if both firms seek to be leaders. If both firms understand the other’s Cournot behaviour, then they will either agree to collude or enter a price war until the competitive price, which equals marginal cost, has been reached and the Stackleberg warfare point is attained, clearly if non-collusion and competition lead to a zero profit outcome, the formation of cartels will seem more attractive.

A comparison of the Cournot and Stackleberg equilibria provides some intuition about how the leader uses its knowledge to its advantage.



The Stackleberg equilibrium is more competitive than since the leader selects a high output in order to induce subsequent firms to cut back, making the equilibrium price unambiguously higher in the Cournot case. A further dissimilarity lies in the fact that Von Stackleberg’s leader, with its higher output is expected to earn greater profits than under the Cournot behavioural assumption, whilst the follower with a smaller share of industry output will receive fewer profits when compared to firms in the Cournot model. Thus whilst the incentive to collude to maximise joint profits still exists, the leader is likely to be less sympathetic towards the formation of a cartel under these circumstances than it would under the Cournot conditions.
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