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Under this article we will discuss-
1) Cournot's Model,
2) Bertrand's model
3) Edgeworth's Model,
Introduction
We have studied price and output determination under three market forms, namely, perfect competition, monopoly and monopolistic competition.However, in the real world economices we find that many of the market or industries are oligopolistic. Oligopoly is an important form of imperfect competition. Oligopoly is said to prevail when there are few firms or sellers in the market producing or selling a product. Oligopoly is also ofter referred as "compeition among the few:. The simplest case of oligopoly is duopoly when there are only two producers or sellers of a product.
Oligopoly and Duopoly Defined
Among the various forms of market organisation that we come across in the real world, oligopoly is one of the most important market forms. By now, that is, in view of what you have already learnt about the various market forms, you may will be aware that perfect or pure competition as a market form is largely a mere conceptual construct and, therefore, this type of market form in its pure variety exists only in text-books. In real life there are few markets which can be said to near this market form. Monopoly is another pure market form which forms the opposite pole to perfect competition. Monopoly, though not as rare as perfect competition in real world, is not quite common either the real world market forms are monopolistic competition and oligopoly of the two,
it is oligopoly which is a peculiar feature of modern large scale industry.
But, what is oligopoly ? Well, we can define oligopoly as a market form in which there are only few freely competing firms in a given “industry” or “group” producing either standardised (homogenous) product or differentiated products such that an individual firm controls a substantial part of the total supply of the product or products. In view of it, any price-output decision taken by an individual firm has significant impact on the aggregate supply and the market price. When the
product is standardised, that is, homogenous, the oligopoly is said to be pure oligopoly. If the product is differentiated, it is said to be differentiated oligopoly. Duopoly is a special case of oligopoly when the number of firms in a
given “group” or “industry” is so small as two only. If in such a market form the product is standardised, the duopoly is said to be pure duopoly. On the other hand, if the product is differentiated, the Duopoly is said to be differentiated duopoly.
Analytical Difficulties
It is generally acknowledged that there are great difficulties in analysing the price-output determination under oligopoly. These difficulties arise from the peculiar structure of the market under oligopoly. As we observed above, the number of firms in an oligopolistic market is small that any change in the price and output effected by any one of the firms has a significant impact on the total condition in the “industry”. On account of it any change in the price and output of one firm is bound to provoke a counter-change by the rival firm in their own prices and output which may, in turn, provide a feature change in the price-output policy of the first firm. Such a chain reaction may go on till some sort of market equilibrium is attained. This shows that there is a great degree of inter-dependence of the firm's price-output policies under oligopoly, which suggest a seues of moves and counter-moves through determination under oligopoly a very intricate problem. It is important in this context to understand the structural difference between oligopoly, on the one hand, and other market firms like perfect competition and monopoly , on the other hand. Under perfect competition as well as monopoly and even under monopolistic competition an individual firm can disregard the behavioural reaction of the rival firms to its own price-output policy. But it can not do so under oligopoly. An individual firm in a perfectly competitive market can afford to disregard the behavioural reaction of the rival firms because it produces only an insignificant part of the total supply of the given commodity, on account of which achange in the output of a single individual firm does not change the total supply significantly and thus it has no influence on the price. The market structure of perfect competition is such that any individual firm can sell as must as it likes at the giving price. This is the meaning of the individual firm's demand or sale curve being
horizontal under perfect competition. So the rival firms are not expected to react and will not react to any price-output policy move made by any individual firm.
The monopolist also has hardly any need to bother about such a reaction because by the very definition of monopoly there is no rival facing a monopolist.Monopoly is as you know, a market form in which there is one and only one firm in a given industry producing a commodity which has no close substitute.
Under monopolistic competition, too, the individual firm will not normally bother about the rival firms reaction to its own policy moves. This is because the number of firms being very large under monpolistic competition, the adverse affect of any policy move by any one firm on the sales of the rival firms would be widely distributed. On account of it each of the rival firm will feel insignificant impact of it which will normally be ignored by it. Hence this is no reaction.
The structural conditions of oligopoly are different. The number of firms being very small under oligopoly, any move made by one of the firms is bound to be met with a counter—move by the rival firms. This makes the price-output decision under oligopoly a tricky one. An oligopolist has to make some assumption with regard to the probable behaviour reaction of the rival firm to his policy move before making the final decision. This behavioural assumption is crucial to the solution of the equilibrium problem under oligopoly. Different assumption in this regard lead to different solution. It is due to this that equilibrium output and price are said to be indeterminate under oligopoly. This is also the reason why there is a wilderingly large number of models of oligopoly.
It is only the position of sales curve of any oligopoly firm that is indeterminate, its slope which is broadly indicative of its elasticity is also indeterminate.This again depends on the nature of the behaviour reaction of rival firms to any price output more made by any one of them. Once again
taking the case of duopoly with only two firms, A and B, whether the sale curve facing an oligopolist firm, say, A will be elastic or inelastic depends on
A's assumption with regard to the behaviour reaction of the rival firm B to its price-output moves. For example, if A's assumption that whatever it does to its own output and price, B will stick to its own output and price, then the sales
curve of A will be rather elastic as shown by the curve dd' in the following Fig1. On the other hand, if any price-output move by A is limited or retaliated by B, then the sales curve of A will be rather inelastic like the curve DD' in Fig. 1.
Having explained the analytical difficulties with regard to equilibrium and price-output determination under oligopoly, we may now consider some important models of non-collusive oligopoly. Generally, we speak of two types of oligopoly on the basis of the organisational relationship between the firms belonging to a given oligopoly market, when firms belonging to a given oligopoly have a tactic or open agreement of some sort in order to eliminate mutual competition, the oligopoly is said to be collusive oligopoly. But, if the firm do not have any agreement on output and price, tactic or open, and rather compete freely with one another, the oligopoly is said to be non-collusive oligopoly.
Cournot's Model
Cournot's model is a model of non-collusive duopoly which can be easily extended to cover cases of oligopoly with more than two firms. August Cournot, an early nineteenth century, French economist, was probably the first economist who analysed the problem of equilibrium under duopoly. This model is based on the following explicit or implicit assumptions :
1. There are only two producers producing a homogeneous commodity. Incidently, the commodity assumed is mineral water whose production cost per unit is constant, though zero, it being a free gift of nature.
2. The two producers are assumed to have identical constant costs which, in his example if mineral water, are zero.
3. Both the Producers are assumed to be know with certainly the total demand curve for the commodity.
4. The demand curve is assumed to be negatively sloping straight line.
5. Absence of collusion and therefore presence of free competition between the two producers is assumed.
6. It is assumed that the objective of each producer is to maximize his individual profit. And, the most crucial assumption relates to the expected behaviour reaction of each producer.
7. Each producer assumes that whatever he may do to his own output, the rival producer will stick to the output that he is currently producing.
On the basis of the above assumption Cournot's analysis leads to the conclusion that under non-collusive duopoly the equilibrium output of the duopolistic “group” would be two thirds of the competitive equilibrium output which would be equally shared by the two producers that is, the equilibrium
output of each one of them would be one-third of the competitive output. How this result follows logically from the above assumptions, is explained below : Let us name of two producers as A and B, and let the total demand curve for their homogeneous commodity (mineral water) be represented by the straight line QR in Fig. 2 below. Since the cost per unit (average cost) is assumed to be
Now let B enter the market. He observes that one-half of market is already occupied by A. He assumes that whatever be his own output A will stick to the output OM which he is already producing. So he considers that only the remaining one-half of the market represented by the portion MR of the demand curve QR is open to him. He will behave like, a monopolist in this part of the market, producing one-half of MR, that is, MM, output (1 =1/4 of competitive output OR) which maximises his profit. Now the total output is OM1..... and consequently the price is brought down to OP1.This affects the profits of A adversely. So he makes a counter-move on the assumption that B will stick to MM1 (= 1/4 OR) output. So he believes that now only 3/4 of the market is open to him where in he can monopolistically, producing 3/8 of the competitive output OR.
Thus we find that the Cournot's model of non-collusive duopoly, the equilibrium total output is 2/3 of the equilibrium competitive output which is equally shared by the two producers. This output is greater than the equilibrium monopoly output and hence the price under duopoly will be, according to this model less than the monopoly price. As we remarked earlier, Cournot's model of duopoly can be extended to cover oligopoly cases with any number of firms. The general formula for this is that the equilibrium total output under oligopoly is n/n+1 of the competitive,output which is equally shared by all the firms, n in the above formula represents the number of firms. If there are three producers, for example, all other assumptions remaining the same, the equilibrium total output according to Cournot's model, would be 3/4th of the competitive output which will be equally shared by all the three producers, each producing 1/4th of the competitive output.
Bertrand's Model
Cournot's model was presented in 1838. About half a century later another french economist, Goseph Bertrand, presented an alternative model of duopoly by changing the crucial behavioural assumption of Cournot's model. Cournot had assumed that each producer expects his rival or rivals to stick to the output that he or they are currently producing regardless of what the
former does to his own output. This behavioural assumption of Cournot is replaced by Bertrand with the alternative behavioural assumption which states that each producer expects his rival to stick to the price which he is currently charging regardless of what the former does to his own price. Bertrand retains all other assumptions of Cournot's model.We assume that it is producer A who enters the market first. Being the sole producer, the whole market is open to him. But he would supply only such an output and charge such a price which would maximise his profit. So he will, obviously, settle for monopoly output and monopoly price. In terms of the diagram of Fig. 2, he will supply OM output and Charge OP price. Now B enters the market.
Assuming that whatever the price he may charge. A will continue to charge Op price, he fixes p1 price which is a little lower than OP which is being charged by A. Now the commodity being homogenous and competition free all the customers will switch over to B and the new customers will also buy from him. It is obvious that in such a situation A will not take things lying down. He is sure to retaliate by reducing the price even lower than that of B which will now take away all thecustomers of B to A. A too is assuming that B will stick to his price. Thus there will start what is known as a price war or cut-throat price competition between the two.
In the short period the price can fall even below the average cost of production.But no businessman will remain in a particular business in the long period, he is unable to recover his costs inclusive of his normal profit. This means that the price was between the duopolists (oligopolists) will go on till in the long period an equilibrium is attained. In this state of long-period equilibrium the price will equal the long-period average cost. In the case of the mineral water example of Cournot's model, the equilibrium Price will be zero as mineral water being a free gift of nature
has zero cost. And, the equilibrium output of the “industry” will be the same as under perfect competition. In term of the diagram of Fig. 2 above, the total equilibrium output will be OR, that is, the same as the competitive output and the equilibrium price also be the same as under perfect competition, that is, zero in this example. The total output and sales will be equally shared by all the producers who make up the given oligopolistic “industry”
Edgeworth's Model
The third classical model of duopoly (oligopoly) was formulated by the British economist, Edgeworth. In his model, there is no stable equilibrium : instead, there on perpetual oscillations of prices.The above rather interesting result in Edgeworth's model is also the result of a changed assumption. His assumptions are the same as those of Bertrand including the behavioural assumption of Betrand which stipulates that each producer assumes that whatever he may do to his own price, the rival producer will stick to the price which is currently charging. If Edgeworth adopts all the assumptions contained in Bertrand's model, then how is it that his result is different from that of Bertrand's model? The answer to this question lies in all
additional assumptions made in Edgeworth's model. He assumes that the combined output capacity of the two procucers is less than the competitive output. The detailed process of the price-output decisions making in Edgeworth's
model which rules out a stable equilibrium and instead points towards perpetual price oscillations is explained here under with the help of fig. 3.
OX1.This horizontal axis X1OX also represents the zero-cost line. The output capacity of A is OA and that of B is OB so that the combined output capacity of the two producers is AB which is less than the competitive output D1D2.DD1 is the demand curve facing A while DD2 is the demand curve facing B both of which are identical.
Supposing A enters the market first, he being the sole producer will behave monopolistically producing 1/2 of OD1(= PC) and charging price P which will maximise his profit. Now B enters the market and assuming that A will continue to charge price P puts in the market the whole of his capacity output (P1D = OB) and fixes a price lower than what A is charging, say at p1as shown in Fig. 3 above. Thus we will encroach on A's market as shown by P1D. Now A will retaliate by bringing into the market the whole of his capacity output and fixing a price lower than P1charged by B on the assumption that whatever he may do to his price, B will stick to his price P1 So A fixes the price, say, P2 and selling his capacity output P2E (= OA) encroaches on B's market. B will retaliate by a similar counter-move, lowering the prices still further. Thus there will be a price-war between the two producers as in Bertrand's model. Sooner or later one of the producers will have lowered the price to such a level at which the demand in his own pat of the market equals his capacity output. In terms of Fig. 3, this comes about when B lowers the price to the level P3 at which the demand in his our own part of the market is P3 F which equals his capacity output OB. Now there is no question of B encroaching of A's market. Now A seeing that B has done his worst to the price while his part of the market remains unencroached on by B1,will once again behave monopolistically assuming that B will stick to the price P3. So, once again, he fixes price P and producers and sells PC output. This attracts B to raise his price, though to a level lower than P. Thus there will start another round of price-cutting competition dragging the price once again to p3 and then again pulling it up to P. Thus there are perpetual price oscillations without any stable equilibrium.
Great sir
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