Explain Cournot, Bertrand and Stackelberg models of oligopoly assuming that the firms have identical costs. Describe circumstances where each model is appropriate.
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Explain Cournot, Bertrand and Stackelberg models of oligopoly assuming that the firms have identical costs. Describe circumstances where each model is appropriate. The theory of the firm is a set of economic theories that describe the nature, existence and behaviour of a firm and its relationship with the market. Some of the questions it aims to answer are why firms enter or exit the market, why there are boundaries between the firm and the market, and why firms are structured in a specific way. An oligopoly is a common market form in which a market or industry is dominated by a small number of sellers. There are several different ways for firms to behave in an oligopolistic environment, and whereas the Stackelberg and Cournot models compete on quantity produced, the Bertrand model is based on price competition between firms. Stackelberg The Stackelberg model is a leadership game in which the leading firm makes the first move and the follower firms adjust their own product decisions accordingly. The total industry output is based on the output of the leader, y1 and that of the follower, y2. The profit maximising output of the leader depends on how the follower will react and assuming that the follower will also want to profit maximise, his problem will be: .
This leads to the profit maximisation problem () and functional relationship (firm one's reaction curve: and firm two's reaction curve: ) similar to the Stackelberg model. The Cournot equilibrium combination of output choices satisfy and as is the optimal output level for firm one, assuming that firm two is producing , and the optimal output level for firm two is , assuming that firm one keeps consistent and produces at . The Nash solution will always emerge in this situation because if the two firms decided to produce at a level of outputas illustrated, firm one will cut its production to settle on its own reaction function and the new outputs will be. In response to this, firm two will increase its production such that the new pair of outputs will be. A similar process will repeat itself until the stable equilibrium level of is reached. Additionally, if there were several firms involved in Cournot equilibrium, an n-firm concentration ratio, each firm would have to take into account the expected output choices of all the incumbent firms and the total output of n firms would therefore be. The profit maximising condition where marginal revenue equals marginal cost would lead to: where si is firm i's share of the total output market.
Examples and Implications A typical example of the Bertrand model is that of shops and bars that publish non-negotiable prices. This is not very popular as firms would still prefer to make a significant profit rather than undercutting the other incumbents on price. A popular example of the Stackelberg model is Google who is a significant large player in the internet market. It started off providing a search engine but now has diversified into maps and emails which Microsoft have tried to imitate. Lastly, Cournot competition is widely seen in many oligopoly markets and a prime example is the aircraft industry where there are initially high set up costs and only two providers, Airbus and Boeing. A comparison of the three models shows that the Stackelberg price is greater than the Bertrand price but lower than the Cournot. Stackelberg aggregate output and consumer surplus is greater than Cournot, but it is lower than Bertrand aggregate output and consumer surplus. Stackelberg aggregate output is also greater than a pure monopoly or cartel but less than a perfectly competitive output. Finally, Stackelberg price is lower than a pure monopoly or cartel but greater than the perfectly competitive price. ?? ?? ?? ?? Page 1
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