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Discuss examples where different models might be the most appropriate (think for example of market for raw materials or for air travel).
In this essay I am going to discuss models of oligopoly behaviour and analyse them and see whether they are realistic or not and evaluate them with certain examples where they may be most suitable.
Oligopoly is defined as a market form in which a market is dominated by a small number of sellers. There are many different models for oligopoly behaviour such as the Cournot Solution, the Sweezy Kinked Demand Curve Solution, the Stackelberg Model and the Bertrand Model.
The Cournot model focuses on the behaviour of quantities, prices and profits within a duopoly (if two firms are selling products in the same market). Within this model it is assumed that one firm will not react to all changes from the other firm’s decision. Firm 1 can choose an output of p1, assuming firm 2 had a fixed level of output at p2. The same assumption can be made the other way; for example, p2 is chosen supposing that p1 can be treated by the second firm as given. Within oligopolistic markets there are a huge number of firms so this hypothesis makes sense as firms can make their decisions without basing it on another’s decision. However, on the other hand, even though it is in a duopoly, in the Cournot equilibrium other firms will still notice change of the other firms if quantities are not changing.
Another way to analyse the Cournot equilibrium mathematically is to say the industry demand curve is:
An isoprofit curve is “the locus of points in a space defined by different levels of output for both firms 1 and 2 which yield the same level of profit to firm 1.”` They are generally concave and the level of profits decline with the height of the isoprofit curve above the horizontal axis. Before analysing the Cournot equilibrium, we need to define reaction functions or best-response functions. It specifies a firm’s optimal choice for something like output dependant on the choices of its rivals.
Another model that deals with oligopoly behaviour is the Bertrand model. It was derived by Joseph Bertrand a nineteenth-century French mathematician and economist. This model can be compared to the Cournot model, however, instead of using the assumption of a firm choosing output, it decides upon price. The main assumption in this case is that the firm’s rival keeps its price constant. There are three main principles of this model, firstly the idea of homogeneity is very important within the Bertrand model and if it is changed so are the results. Homogeneity is simply the idea of all firms selling the same product. Secondly, positive profits can be obtained by product differentiation and lastly each firm within the market has enough capacity to supply the market. Bertrand used isoprofit curves and best-response functions and its equilibrium is reached when it is characterised by equal prices and the 45 line at the origin. It can be stated that the Bertrand equilibrium is a Nash equilibrium for the price-setting game. The equilibrium price must equal marginal cost because if it exceeds it then if firm 1 will always lower its price as it will believe that firm 2 will not follow suit and consequently firm 1 will have the entire market at its disposal and visa versa. Price cuts will not occur if both firms charge the same price as marginal cost and therefore the industry profits will be zero. This leads to a perfectly competitive market despite the small number of firms in the market. Firms may decide to collude to avoid not making profits as forming cartels will seem more appealing than the Cournot solution.
“Heinrich von Stackelberg was a German economist who examined market organisation and the strategic interaction of firms. He proposed the leader-follower concept for duopolistic markets in Marktform und Gleichgewicht (Vienna:Julius Springer, 1934).” Consequently, he invented the Stackelberg model which is another model used with oligopolistic markets is based upon the idea of the Cournot model. Stackelberg used the Cournot model to examine what may happen if one firm tried to infer the reaction of the other firm. By using the in formation provided from the findings, Stackelberg hoped this would help improve the position of equilibrium of the firm finding out the information. This situation can be constituted as asymmetric, with one firm taking the role of the leader and the other firm pursuing in close suit as the follower. The Stackelberg model can be simply defined as an expansion of the Cournot model and the idea of the leader-follower can be extended upon. In terms of the Stackelberg mode, firm 1 is looking to maximise its profits knowing that firm 2 knows the decision of firm 1 is set. Consequently, firm 2 will always look to its reaction function for a decision, whereas firm 1 will assess the situation of firm 2’s reaction function and will therefore maximise its profits. The consequence of this is shown in figure 1.1 (17.7)
The kinked demand curve conjecture is a further model within oligopolisitic and duopolistic markets where it is responsible for the stability of these markets. The kinked demand curve conjecture is the idea by which firms will match a price decrease but not an increase.
By analysing the Cournot and Stackelberg models, we can see how the leader manipulates the situation to its benefit. With the Cournot model, firms adjust their decisions on the basis that the reaction of the other firms was not what they thought at first. In the Stackelberg model, firm 1 knows the behaviour of firm 2 so as a result it decides upon a higher output level than its own Cournot reaction function so it can maximise profits. Firm 2 responds to this and realises the behaviour of firm 1 and consequently finds out that they are in the Cournot equilibrium. Hence, it is producing less and making fewer profits that it thought it was and as a result firm 1 is making more and has higher profits. A cartel maybe harder in this type of situation than in Bertrand or Cournot conditions as it would be harder to follow the firm’s behaviour. Both firms may want to be leaders, but within the Stackelberg model it would not reach equilibrium. In Cournot conditions, they could decide upon collusion or a price war to choose who are the leader and the follower.
Each of these models can be deemed realistic in some ways and not in other ways. Bertrand and Cournot models are very different in their outcomes as with the Bertrand model it results in the quantity and welfare-optimal price while the Cournot equilibrium produces a price and a quantity between the levels of welfare-optimality and monopoly. This can be defined as the Bertrand proposition. In Cournot and Bertrand models firms assume a conjectural assumption of the behaviour of the firms as too restrictive so this leads to the no chance of a collusive agreement. The Cournot solution is somewhat not realistic as there seem to be many criticisms of it as a firm that is already in the industry may feel like a potential leader if other firms enter the market where they will act as followers. The Cournot model does not seem practical enough as it is hard to assume that one firm sets its price dependant on another’s output level. In some ways, it can be deemed realistic but there needs to be more evidence of it and this is provided by the Stackelberg model and consequently the idea of the leader-follower seems to be sensible and more in depth than the Cournot theory. It seems more obvious that if one firm sets a price that the other will follow suit and sets the same price or a lower price which is the essence of the Stackelberg model. The Bertrand model has two important concepts, one being its homogeneity and the other that the firms must have a big capacity. These two concepts provide enough substantiation for the model to be deemed realistic enough. This model is also a criticism of the Cournot model as the Cournot model assumes that firms compete in a market by choosing quantities of a good instead of prices they might change which is the reason why people feel it is unrealistic. The kinked demand curve conjecture appears slightly unrealistic due to a couple of slight problems it may encounter. Firstly, it cannot be exactly be illustrated as a game. If the game is simultaneous then matching is impossible and furthermore the matching process cannot be described as a sequential game either. Additionally, there can be any price if the marginal cost is lower than the price and if the price is lower than the monopoly price and therefore it is uncertain what price firms may agree on. In conclusion, the most realistic model in my opinion seems to be between the Bertrand model and Stackelberg model.
There are many different examples that can be used within all of these oligopolisitic models, for example, the market for raw materials or for air travel. Examples of oligopolies are the sale of petrol, supermarkets, telecommunications and banks and building societies.
Summarising the main companies in their categories:
An example where the Cournot model could be used is in the music industry if HMV and Virgin were competing to sell the same album. HMV would choose a price dependant on Virgin’s output and Virgin would make the same decision dependant on HMV’s output. The Bertrand model where firms set prices and then demand is split dependant on certain factors can be described best within the supermarket industry. For example, when Tesco, Asda/Wal Mart, Sainsbury and Safeway/Morrison set their prices for selling milk, consumers will buy milk from the cheapest supermarket and then the other supermarkets will choose its price assuming the competitor’s price is fixed. If all the prices of milk in all the supermarkets are equal then the demand between the consumers is split and all of them will make equal profits. The automobile industry can describe the Stackelberg model, for example, if a new firm starts to manufacture cars in America and has to compete with General Motors and Ford. It is evident that something like this would be unrealistic as it would be hard for the new company to compete with such a well-established company such as General Motors and Ford. An example of kinked demand curve conjecture is if, for instance, T-Mobile decides to increase price its competitors such as O2, Orange and Vodafone will not react. However, if T-Mobile were to decrease the price of a certain contracts, each of the other networks may develop a concept of matching the contract offered by T-Mobile. However, by doing this it would be sharing the market at a lower price and yielding less profit but it would be give no incentive for any of these firms to deviate.
In conclusion, it is fair to say that the Cournot model seems to be the more unrealistic of all the models discussed and that the Bertrand and Stackelberg models are more in depth and more sensible in the world of oligopoly.
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