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Математика Firms behavior in Oligopoly
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Oligopoly

An oligopoly is a market that is characterized by the interdependence of firms. The typical characteristics that constitute an oligopoly are:

1) A “few” firms; the concept of “few” means that there are few enough sellers that they recognize their interdependence.

2) The output may be homogeneous or differentiated. Primary metals industries are examples of oligopolies with homogeneous goods. Instant breakfast drink mixes are an example of an oligopoly with differentiated products.

3) In an oligopoly there are usually significant barriers to entry.

4) The outcomes that follow from the decisions of one firm are dependent on what the other firms do.

Augustin Cournot (1801-1877), a French mathematician/economist developed the theory of monopoly and then considered the effects of two interdependent competitors (sellers) in a duopoly. Cournot’s analysis of two sellers of spring water clearly established that the price and output of one seller was a reaction to the price and output of the other seller. If the two collude they can act as a single monopolist and divide monopoly profits.

Cournot’s recognition of the interdependence of sellers provided the foundation for a variety of approaches to explain the interdependent behavior of oligopolists. In the 1930’s the “kinked demand” model (published by Paul Sweezy in August 1939 and by R.L. Hall and C.J. Hitch in May 1939) and the “administered price hypothesis” (Gardner C. Means in 1935) were developed as an attempt to explain price rigidities in some markets during the great depression. In 1943 John von Neumann and Oskar Morgenstern published a path breaking work on game theory. Game theory has been used to try to explain the behavior of independent competitors. There have been a variety of other models that attempted to explain the interdependent behavior in oligopolies. The number of models is evidence that it is a difficult task and there are problems with most approaches. The kinked demand model is used here to emphasize the interdependence of oligopolistic behavior rather than to explain the determination of price.

If the market of a particular commodity consists of more than one seller but the number of sellers is few, the market structure is termed oligopoly. The special case of oligopoly where there are exactly two sellers is termed duopoly.

In analysing this market structure, we assume that the product sold by the two firms is homogeneous and there is no substitute for the product, produced by any other firm.

Given that there are a few firms, the output decisions of any one firm would necessarily affect the market price and therefore the amount sold by the other firms as also their total revenues. It is, therefore, only to be expected that other firms would react to protect their profits. This reaction would be through taking fresh decisions about the quantity and price of their own output. There are various ways in which this can be theorised. We briefly explain two of them.

Firstly duopoly firms may collude together and decide not to compete with each other and maximise total profits of the two firms together. In such a case the two firms would behave like a single monopoly firm that has two different factories producing the commodity.

Secondly, take the case of a duopoly where each of the two firms decides how much quantity to produce by maximising its own profit assuming that the other firm would not change the quantity that it is supplying.

We can examine the impact using a simple example where both the duopolist firms have zero cost.

Assume that Firm B supplies zero units of the good, then Firm A realizing that maximum demand is 20 units, would decide to supply half of it, i.e. 10 units. Given that Firm A is supplying 10 units, Firm B would realize that out of the maximum demand of 20 units, a demand of 10 units (i.e. 20 minus 10) still exists and hence would supply half of it, i.e. 5 units. Since firm B has changed its supply from zero to 5 units, Firm A would realize that the total demand is 15 units (i.e., 20 minus 5) and supply half to it, i.e., 7.5 units. In the fashion, the two firms would keep making moves. It can be shown that these lead to an equilibrium. Let us examine these steps:

And so on.

Therefore both the firms would finally supply an output equal to

The total quantity supplied in the market equals the sum of the quantity supplied by the two firms is which is greater than the quantity supplied under a monopoly market structure and less than the quantity supplied under a perfectly competitive structure.

Since price depends on the quantity supplied by the formula p = 10 – 0.5q, for q = 40/3, price is 10 – 20/3 = 3,33. This is lower than the price under monopoly and higher than under perfect competition.

Even in the case where there are positive costs, the mathematics only becomes more complex, but the results are similar. That through a very large number of moves and countermoves, the two firm reach an equilibrium quantity of total output. The quantity produced by both firms together is more than what a pure monopoly would have produced and lesser than that produced if the market structure was perfectly competitive. The equilibrium market price is naturally lower than in the case of pure monopoly and higher than under perfect competition.

Thirdly, some economists argue that oligopoly market structure makes the market price of the commodity rigid, i.e. the market price does not move freely in response to changes in demand. The reason for this lies in the way in which oligopoly firms react to a change in price initiated by any firm. If one firm feels that a price increase would generate higher profits, and therefore increases the price at which it sells its output, other firms do not follow. The price increase would therefore lead to a huge fall in the quantity sold by the firm leading to a fall in its revenue and profit. It is therefore not rational for any firm to increase the price. On the other hand, a firm may estimate that it could earn a larger revenue and profit by selling a larger quantity of output and therefore lowers the price at which it sells the commodity. Other firms would perceive this action as a threat and therefore follow the first firm and lower their price as well. The increase in the total quantity sold due to the lowering of price is therefore shared by all the firms, and the firm that had initially lowered the price is able to achieve only a small increase in the quantity it sells. A relatively large lowering of price by the first firm leads to a relatively small increase in the quantity sold. Thus, this firm experiences an inelastic demand curve and its decision to lower price leads to a lowering of its revenue and profit. Any firm therefore finds it irrational to change the prevailing price, leading to prices that are more rigid compared to perfect competition.


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