. Pure oligopoly – have a homogenous product. Pure because the only source of market power is lack of competition. An example of a pure oligopoly would be the steel industry, which has only a few producers but who produce exactly the same product. Impure oligopoly – have a differentiated product. Impure because have both lack of.
A model of oligopoly was first of all put forward by Cournota French economist, in 1838. Cournot’s model of oligopoly is one of the oldest theories of the behaviour of the individual firm and relates to non-collusive oligopoly.
In Cournot model it is assumed that an oligopolist thinks that his rival will keep their output fixed regardless of what he might do. That is, each oligopolist does not take into account the possible reactions of his rivals in response to his actions.
Another important model of non-collusive oligopoly which we will discuss below was put forward by E.H. Chamberlin in his famous work “The Theory of Monopolistic Competition”. Chamberlin made an important improvement over the classical models of oligopoly, including that of Cournot.
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In sharp contrast to Cournot and other classical models Chamberlin assumes in his model that oligopoly firms recognise their inter-dependence while fixing their output and price. Through his model Chamberlin arrives at a monopoly solution of pricing and output under oligopoly wherein oligopolistic firms in an industry jointly maximise their profits.
1. Cournot’s Duopoly Model:
As said above, Augustin Cournot, a French economist, published his theory of duopoly in 1838. But it remained almost unnoticed until 1880’s when Walras called the attention of the economists to Cournot’s work. Cournot dealt with the case of duopoly.
Let us first state the assumptions which are made by Cournot in his analysis of price and output under duopoly. First, Cournot takes the case of two identical mineral springs operated by two owners who are selling the mineral water in the same market. Their waters are identical. Therefore, his model relates to the duopoly with homogeneous products.
Secondly, it is assumed by Cournot, for the sake of simplicity, that the owners operate mineral springs and sell water without incurring any cost of production. Thus, in Cournot’s model, cost of production is taken as zero; only the demand side of the market is analysed.
It may be noted that the assumption of zero cost of production is made only to simplify the analysis. His model can be presented when cost of production is positive. Thirdly, the duopolists fully know the market demand for the mineral water; they can see every point on the demand curve. Moreover, the market demand for the product is assumed to be linear, that is, market demand curve facing the two producers is a straight line.
Lastly, Cournot assumes that each duopolist believes that regardless of his actions and their effect upon market price of the product, the rival firm will keep its output constant, that is, it will go on producing the same amount of output which it is presently producing.
In other words, the duopolist will decide about the amount of output which is most profitable for him to produce in the light of his rival’s present output and assumes that it will remain constant. In other words, for determining the output to be produced, he will not take into account reactions of his rival in response to his variation in output and thus decides its level of output independently.
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Cournot’s Approach to Equilibrium of the Duopolists:
Suppose the demand curve confronting the two producers of the mineral water is the straight line MD as shown in Fig. 29A.1. Further suppose that ON = ND is the maximum daily output of each mineral spring. Thus, the total output of both the springs is OD = ON + ND.
It will be seen from the figure that when the total output OD of both the springs is offered for sale in the market, the price will be zero. It may be noted here that if there was a perfect competition, the long-run equilibrium price would have been zero and actual output produced equal to OD. This is because cost of production being assumed to be zero; price must also be zero so as to provide a zero profit long-run equilibrium under perfect competition.
Assume for the moment that one producer A of the mineral water starts the business first. Thus, to begin with he will be the monopolist. He will then produce daily ON output because his profits will be maximum at output ON’ and will be equal to ONKP (since the costs are zero, the whole of total revenue ONKP will represent profits).
The price which that producer will charge will be OP. Suppose now that the owner of the other spring enters into the business and starts operating his spring. This new producer B sees that the former producer A is producing ON amount of output.
According to the assumption made by Cournot, the producer B believes that the former producer A will continue producing ON (= 1/2 OD) amount of output, regardless of what output he himself decides to produce. Given this belief, the best that the new producer B can do is to regard segment KD as the demand curve confronting him. With his demand curve KD, and corresponding marginal revenue curve MRB, the producer B will produce NH (= 1/2 ND) amount of output. The total output will now be ON + NH = OH, and as a result the price will fall to OP’ or HL per unit.
The total profits made by the two producers will be OHLP’ which are less than ONKP. Out of total profits OHLP’, profits of producer A will be ONGP’ and profits of producer B will be NHLG. Thus entry into the market by producer B and producing output NH by him, the producer A’s profits has been reduced.
A will therefore reconsider the situation. But he will assume that producer B will continue to produce output NH. With producer B producing output NH, the best that the producer A can do is to produce 1/2 (OD -NH). He, will, therefore, reduce his output.
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Now that the producer B has been surprised by the reduction of output by producer A and will also find that his share of total profits is less than that of producer A, he will reconsider his situation. Learning nothing from his earlier experience and believing that producer A will continue producing its new current level of output, the producer B will find that he will now be making maximum profits by producing output equal to 1/2 (OD – New output of A).
Producer B, accordingly, will increase his output. With this move of producer B, producer A will find his profits reduced. The producer A will therefore again reconsider his position and will find that he can increase his profits by producing output equal to 1/2 (OD – Current output of producer B).
This process of adjustment and readjustment will continue and producer A being forced gradually to reduce his output and producer B being able to increase his output gradually until the total output OT is produced (OT = 2/3 OD) and each is producing the same amount of output equal to 1/3 OD.
In this final position, producer A produces OC amount of output and producer B produces CT amount of output, and OC = CT. Throughout this process of adjustment and readjustment, each producer assumes that the other will keep his output constant at the present level and then always finds his maximum profits by producing output equal to 1/2, (OD – the present output of the other).
As seen above, producer A starts by producing ON = (1/2 OD) and continuously reduces his output until he produces OC. The final output OC of producer A will be equal to 1/3 OD (= 1/2 OT). On the other hand, producer B begins by producing 1/4th of OD and continuously increases his output until he produces CT. His final output CT will be equal to 1/3 OD (= 1/2 OT). Thus, the two producers together will produce total output equal to 1/3 OD + 1/3 OD= 2/3 OD (= OT).
Cournot’s Duopoly Equilibrium:
It will be seen from Fig. 29A.1 that when each producer is producing 1/3 OD (that is, when producer A is producing OC and producer B equal to CT), the best that his rival can do is to produce 1/2 (OD – 1/3 OD) which is equal to 1/3 OD = OC – CT. Thus, when each producer is producing 1/3 OD so that the total output of the two together is 2/3 OD, no one will expect to increase his profits by making any- further adjustment in output. Thus, in Cournot’s model of duopoly, stable equilibrium is reached when total output produced is 2/3rd of OD and each producer is producing 1/3rd of OD.
It will be useful to compare the Cournot’s duopoly equilibrium with the monopolistic and the purely competitive equilibriums. If the two producers had combined and formed a coalition, then the output produced by them together will be the monopoly output ON and. therefore, the price set will be the monopoly price OP.
Monopoly output ON produced in case of coalition is much less than the output OT produced in Cournot’s duopoly equilibrium. Further, the monopoly price OP charged in case of coalition is much greater than the price OP” determined in Cournot’s duopoly equilibrium.
In case of coalition, they will enjoy the monopoly profits ONKP which are maximum possible joint profits, given the demand curve MD. These monopoly or maximum joint profits can be shared equally by them. It will be seen from Fig. 29A. 1, that these monopoly profits ONKP made in case of coalition are much greater than the total profits OTSP” made by them in Cournot’s duopoly equilibrium.
It is thus clear that in case of the duopolists competing with each other as conceived by Cournot’s duopoly solution, the price and the profits are lower and output is greater than if they had combined together and formed a monopoly.
On the other hand, if the market were perfectly competitive, the output would have been OD and price would have been zero. This is because with assumed marginal cost being equal to zero, perfectly competitive equilibrium will be reached at the output level where price is equal to zero. That is, perfectly competitive solution would have resulted in greater output and lower price than under Cournot’s duopoly equilibrium.
To sum up, under Cournot’s duopoly equilibrium, output is two thirds of the maximum possible output (i.e., perfectly competitive output) and price is two-thirds of the most profitable price (i.e., monopoly price).
Following Cournot, the cost of production in the above discussion of Cournot’s oligopoly solution has been taken to be zero. However, it should be noted that above conclusions will not change if the cost curves with positive cost of production are introduced into the discussion.
Reaction Functions and Cournot Duopoly Solution:
Cournot solution of duopoly problem can also be obtained with reaction functions of the two firms. An output reaction function depicts the profit-maximising output of a firm, on the assumption that the other firm’s output remains constant.
We have seen above that the profit-maximising output of a Cournot’s duopolist is one-half of the difference between the other firm’s output and the market demand for output at which price equals marginal cost.
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This is called reaction function of a firm. This output at which price equals marginal cost (MC) is the maximum output which can be produced because any output beyond this will cause the price to go below marginal cost (which is equal to AT under constant cost conditions) and will therefore not be worthwhile to produce.
The following example will make clear the concept of reaction functions. Let the market demand function is: Q = 100 – P and marginal cost is Rs. 10. In order to determine reaction functions of two duopolist firms, we set price equal to the given marginal cost to determine market demand at price (P) = MC. Thus, from the given demand function
P= 100-0…. (i)
Setting it equal to MC we have
100-0=10
Or
Q=100-10 = 90
Thus, the reaction function of firm A is:
Qa = 90 – Qb/2… (ii)
Where Qa and Qb are the outputs of firm A and B respectively.
Similarly, reaction function of firm B is:
Qb = 90-Qa/2 …. (iii)
The above two equations (ii) and (iii) can be solved simultaneously to determine Qa and Qb. To do so we substitute the value of Qb = 90-Qa/2 in equation (ii) and have:
Cournot Equilibrium as Nash Equilibrium:
John F. Nash, a noted American Mathematician and a Nobel Prize winner in economics, has put forward the concept of equilibrium known as Nash Equilibrium. Cournot duopoly equilibrium is an example of Nash equilibrium.
According to Nash equilibrium, competing firms reach their equilibrium state when each of them thinks that it is doing its best that is, maximising its profits in response to the given strategy adopted by others which think they are also maximising their profits with the given strategies. As a result, no one has a tendency to change its strategy.
Therefore, we have a stable equilibrium. Since in Cournot duopoly equilibrium each firm chooses to produce an output level hat maximises its profits, given the profit-maximising level of output of the other firm, Cournot duopoly is generally called Cournot-Nash duopoly equilibrium.
Cournot’s Duopoly Equilibrium Explained with the Aid of Reaction Curves:
Some economists have employed the reaction curves to explain Cournot’s duopoly equilibrium. The reaction curves may be output reaction curves or price reaction curves depending upon whether it is the output or the price which is the adjustment viable.
Since, in Cournot’s model, it is the output which is subject to the adjusting variation, output reaction curves are relevant. It should be carefully noted that these reaction curves refer not to the reactions which a seller expects will be forthcoming from his rivals but to the sellers’ own reactions to the moves of his rival.
In Fig. 29A.2 output reaction curves of two producers (sellers) A and B are shown, MN is the output reaction curve of A and RS is the output reaction curve of B. The output reaction curve MN of seller A shows how A will react to any change in output by B, that is, A’s output reaction curve shows how much output A will decide to produce for each given output of producer B.
In other words, A’s output reaction curve MN indicates the most profitable output for A for each given output of B. Likewise, B’s output reaction curve RS shows how much output B will decide to produce (that is, what will be B’ s most profitable output) for each given output of A.
For example, if B produces output OB1.A’s output reaction curve MN shows that A will produce output OA2 in response to B’s output OB1. Similarly, for all other outputs on the other hand, if A produces OA2, B’s output reaction curve shows that B will produce OB2 and so forth for all other outputs.
It will be seen from Fig. 29 A.2, that output reaction curves have been drawn to be straight lines. This is because we are assuming that market demand curve for the product of duopolist is a straight line and that the marginal costs of production of both producers A and B are constant (at zero).
It should be noted that output OM is the monopoly output since producer A will produce output OM if producer B’s output is zero. In other words, producer A will produce and sell output OM if he were the monopolist. On the other hand, A will produce zero output if B ‘S output is ON.
Given the marginal cost equal to zero, a producer will be forced to produce zero output when the price has fallen to zero and, therefore, production is no longer profitable. Output ON will be produced under conditions of perfect competition since at output ON the price will be zero and therefore equal to marginal cost which is assumed to be zero in the present case.
Thus, while OM is the monopoly output, ON is the perfectly competitive output. We assume the two producers A and B to be completely identical, OR will, therefore, be equal to OM, and OS will be equal to ON.
Output reaction curves, as interpreted above, can be used to explain Cournot’s duopoly equilibrium. Each producer, as before, assumes that his rival will continue producing the same amount of output regardless of what he might himself decide to produce. To begin with, suppose producer A goes into business first and is therefore initially a monopolist.
Therefore, in the beginning A will produce output OM which is a monopoly output as output by the firm B is zero. Suppose now B also enters into business, B will assume that A, will keep his output constant at OM. B’s output reaction curve RS reveals that for output OM of A, he will produce OB, But when A sees that B is producing OB1 he will reconsider his last decision but will assume that B will go on producing OB1.
Output reaction curve NM of seller A shows that he will produce OA2 in reaction to output OB1, of firm B. Now when B sees that A is producing OA2, he will think of readjusting his output but will assume that A will continue producing OA2. B’s output reaction curve RS, shows that he will produce output OB2 for output OA2 of producer A, but when A knows that B is producing OB2 he will again readjust his output and will produce OA3.
This process of adjustments and readjustments will continue until point E is reached where the two reaction curves intersect each other and A and B are producing OAn and OBn respectively. The duopolists attain stable equilibrium at the intersection point, since they will not feel induced to make any further adjustments in their outputs.
With B producing OBn, A’s most profitable output is OAn as indicated by his reaction curve NM, and with A producing OAn, the most profitable output for B is OBn as shown by his reaction curve RS, Therefore, no one will have a tendency to make any further changes in their output. It is thus evident also from the reaction curve analysis that Cournot’s solution yields a unique and stable equilibrium under duopoly.
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A Critique of Cournot’s Oligopoly Model:
Cournot model of oligopoly is perhaps the first model which describes the behaviour of an individual firm under conditions of monopoly and competition. Therefore, it has occupied an important place in economic theory as a reference model or as a starting point of explaining the behaviour of individual firms under oligopolistic market structure.
In our analysis of Cournot’s duopoly model, we have seen that he makes an important assumption, namely, while deciding about his output policy each duopolist believes that his riyal will hold output constant at the present level whatever output he himself might produce. Further, a producer remains unshaken in this erroneous belief even when he constantly finds himself to be proved incorrect since after his action the rival does react and changes his output. This is a chief logical error in Cournot’s model.
Furthermore, by assuming that duopolist (oligopolist), will think that his rival will continue producing the current level of output Cournot model ignores the mutual interdependence between the duopolist which is the chief characteristic of oligopoly, Thus, Cournot model provides solution for oligopoly problem by removing from it its most important feature.
2. Bertrand’s Duopoly Model:
Joseph Bertrand, a French mathematician, criticized Cournot’s duopoly solution and put forward a substitute model of duoply. According to Betrand, there was no limit to the fall in price since each producer can always lower the price by underbidding the other and increasing his supply of output until the price becomes equal to his unit cost of production.
There are some important differences in assumptions of Bertrand and Cournot’s models of duopoly. In Bertrand’s model, producers do not produce any output and then sell whatever price it can bring in. Instead, the producers first set the price of the product and then produce the output which is demanded at that price. Thus, in Bertrand’s model adjusting variable is price and not output.
In Cournot’s model, each producer adjusts his output believing that rival will continue to produce the same output as he is doing at present, but in Bertrand’s model each producer believes that his rival will keep his price constant at the present level whatever price he might himself set. Thus, in Bertrand’s adjusting variable is price and not output.
Furthermore, in Bertrand’s model, it is not very important that the producers should know the correct market demand of their product, or should have identical view about the market demand. It is enough for each producer to know that he can capture the whole market by undercutting his rival.
The other assumptions of Bertrand’s model are the same as those of Cournot’s model though their implications may be somewhat different. Thus, in Bertrand s model the products produced and sold by the two producers are completely identical and in no way differentiated.
Its implications are that if a producer underbids the other, it can conquer the whole market (that is, snatch away all the customers from his rival). Further, the two producers have identical costs and also work under condition of constant marginal cost. Moreover, the productive capacity of the producers is unlimited, that is, there is no limit to their increase in the supply of output up to the maximum requirement of demand.
Bertrand’s duopoly model is illustrated through Fig. 29A.3. Let there be two producers A and B. Market demand curve for the product produced by them is given by linear curve DD’. Suppose that producer A goes into business first.
Because A is the only producer at present he sets the price at the monopoly level, which is the most profitable for him. This monopoly price is Pm and producer A produces monopoly output ON which is half of perfectly competitive output 0 assuming constant average and marginal cost equal to OG.
Now, suppose that B also enters into the business and starts producing the same product as produced by A. But B assumes that A will go on charging the same price Pm which he is doing at present, irrespective of whatever price he himself might set.
Further B finds that he can capture the whole market by slightly undercutting the price and thereby make substantial amount of profits. Accordingly, B sets a price slightly lower than A’s price Pm and as a result gets the entire demand of the product. A’s sales, for the moment, falls to zero. Now threatened with the loss of his entire business, producer A will reconsider his price policy. But while deciding about his new price policy he assumes that S will continue to charge the same price which he is doing at present.
There are two alternatives open to him. First, he may match the price cut made by B, that is, he may charge the same price as B is now charging. In this case, he will secure half the market, the other half going to the producer B.
Secondly, he may undercut B and set a slightly lower price than that of B In this case, A thinks he will seize the entire market. Evidently, the latter course looks more profitable and thus A undercuts B and sets a price lower than S’s price.
But with the above move of A, producer B finding himself deprived of all his sales will react and think of changing his price. Since B also assumes A’s price to remain fixed at the present level, whatever price he himself might set. Producers have similarly two alternatives: he may match A’s price or undercut him. Finding the undercutting more profitable, B will set a bit lower price than A and thus seize the whole market.
But again, A will be forced to undercuts. This price war (i.e. the process of undercutting) will go on until the price falls to the competitive levels, that is, equal to average or marginal cost of production. Once the price has fallen to the level of average or marginal cost of production, neither of them will like to cut the price further because in that case total cost would exceed total revenue and will therefore bring losses to the duopolists.
Also, neither of them would like to raise the price, since in doing so each of them would be afraid of losing his entire business given the belief that the other will go on charging the same lower price. Thus, when the price has fallen to the competitive level of average cost of production, neither of the duopolists would have any incentive to lower the price further or to raise it and, therefore, the equilibrium has been achieved. In Bertrand’s model equilibrium is achieved when as a result of price war market price has fallen to the average cost of production and the combined equilibrium output of the two duopolists is equal to the competitive output.
It is evident from the above analysis of the Cournot and Bertrand’s models of duopoly that the fundamental assumption about the behaviour of the duopolists in the two models is similar. The duopolists in both models have erroneous and incorrigible belief that the rival will continue to do what he is presently doing regardless of what he himself might do.
However, the basic assumption in the two models is not exactly the same. In Cournot’s model, the basic assumption relates to the output policy, but in Bertrand’s model, it relates to the price policy. Therefore, the two models yield different results.
According to Cournot’s model, equilibrium output is less than the perfectly competitive output and, therefore, under it price is higher than the perfectly competitive price. But, according to Bertrand’s model, output and price under duopoly are equal to those under pure competition.
3. Edgeworth Duopoly Model:
F.Y. Edgeworth, a famous French economist, also attacked Cournot’s duopoly solution. He criticised Cournot’s assumption that each duopolist believes that his rival will continue to produce the same output irrespective of what he himself might produce.
According to Edgeworht (as in Bertrand’s model), each duopolist believes that his rival will continue to charge the same price as he is just doing irrespective of what price he himself sets. With his assumption, and taking the example of Cournot’s “mineral wells’ with zero cost of production, Edgeworth showed that no determinate equilibrium would be reached in duopoly.
The main difference between Edgeworth’s model and Bertrand’s model is that whereas in Bertrand, productive capacity of each duopolist is practically unlimited so that he could satisfy any amount of demand but in Edgeworth’s model, the productive capacity of each duopolist is limited so that neither duopolist can meet entire demand at the lower price ranges.
Each duopolist accepts as much demand of the product at a price as he can meet. It is not essential in Edgeworth’s model that the products of duopolist should be perfectly homogeneous; his argument will apply even if the products were close substitutes so that a slight price differential is sufficient for a good proportion of customers to switch from a higher priced product to a lower-price product.
However, in our analysis below we assume that the products of the two duopolists are perfectly homogeneous. Moreover, the cost conditions of the two duopolists need not be exactly same but must be similar.
Fig. 29A.4 illustrates Edgeworth’s model of duopoly. Since it is assumed that the products of two duopolists are completely identical, the market would be equally divided between the two duopolists at the same price of the product.
Suppose DC and DC’ represent the demand curves facing each duopolist. Further suppose OB and OB’ are the maximum possible outputs of the two duopolist respectively. If the duopolists form a collusion, they will set the monopoly price OP and will make maximum joint profits. Price OQ represents the price at which both duopolists sell their maximum possible outputs.
Assume that the two duopolists happen to charge the price OP, then producers 1 and 2 will be producing and selling OA and OA’ amounts of output respectively. Suppose now producer 1 thinks of revising his price policy. Producer 1 will believe that producer 2 will keep his price unchanged at OP regardless of whatever price he himself might charge.
With producer 2’s price remaining fixed at OP, producer 1 realises that if he sets the price slightly lower than OP, he will be able to attract a sufficient number of producer 2’s customers so that the he can sell his whole maximum output which he can produce. This would yield greater profits to producer 1 than he is making at present.
Thus in Fig. 29A.4 if producer 1 lowers his price from OP to OR, he will be able to sell his entire maximum and will be earning profits equal to the area OBSR which are greater than OAEP. Thus A would increase his profit by lowering his price.
But when producer 1 reduces his price, producer 2 will find most of his customers deserting him and his sales considerably reduced. Profits of producer 2 will therefore fall considerably. As a result, producer 2 will think of making a counter move, but he too will assume that producer 1 will hold his price constant at OR.
Producer 2 sees that if he cuts his price slightly below producer 1’s price OR, say he fixes OR’ he can take away enough customers of A to sell his entire maximum possible output OB’. Thus when producer 2 cuts his price to OR’, he sells his entire output OB’ and makes profits equal to OR’S’B which are greater than the profits he was making before.
As a result of this, sales and profits of producer 1 will greatly decline. Producer 1 will then react and will think that if he reduces his price a bit below OR’, he will be able to sell his whole maximum possible output OB by attracting customers of producer 2, still believing that producer 2 will keep his price fixed at OR’.
Thus when producer 1 reduces his price, his profits will rise for a moment. But producer 2 will then reacts and reduce his price further in order to increase his profits. In this way, according to Edgeworth, the price cutting by two producers will continue until the price falls to the level OQ at which both producers sell their entire maximum possible outputs.
It will be seen in Fig. 29A.4 that at price OQ, producers 1 and 2 are selling OB and OB’ respectively 0OB = OB’) and are making profits equal to OBTQ and OB’TQ respectively. When the price has been bid down to the level OQ, none of the producers will see any advantage to cut the price further.
Since at price OQ each is selling the entire output he can produce, he will not be able to increase his profits because of his inability to increase his output further. But, according to Edgeworth, equilibrium is not attained at price OQ. Edgeworth argues that each producer will have no incentive to lower the price below OQ, but each will have incentive to raise it above OQ.
Thus, Edgeworth says: “At this point it might seem that equilibrium would have been reached. Certainly it is not in the interest of either monopolist to lower the price still further. But it is in the interest of each to raise it.” At price OQ, one of the two producers, say producer 1, may realise that his rival producer 2 is selling his entire possible output OB’ and serving half of the customers and cannot increase his output further to serve more customers.
Thus producer 1 realises that he can serve the other half of the customers at the price which is most profitable for him and he will accordingly raise the price to OP at which he sells OA and earns profits OAEP which are larger than profits OBTQ at price OQ.
Thus knowing that his rival has done his worst by putting his entire possible output on the market and that producer 2 cannot attract any of his OA units of demand because of his inability to produce more, producer 1 raises the price to OP and thereby increases his profits.
But when producer 1 has raised the price to OP, producer 2 will realise that if he sets his price slightly below OP, he would still be able to sell OB’ by attracting enough customers of producer 1 who is charging the price OP and, will therefore increase his profits.
Accordingly, producer 2 raises his price to the level slightly below OP. But producer 1 then finding his customers deserting him and sales being reduced will believe that he can increases his profits by reducing his price slightly below producer 2’s level.
When he does so, then producer 2 will react, and so on. Thus, once again the process of competitive price cutting starts and the price again ultimately reaches the level OQ. But once the price has reached OQ, any of the producers will again raise it to OP and so on.
In this way, price will oscillate between OP and OQ, gradually downward but upward in a jump. As said above, price OP is the monopoly price and price OQ is the competitive price. It follows from above that Edgeworth duopoly solution is one of perpetual disequilibrium, price constantly oscillating between the monopoly price and competitive price. Thus no determinant and unique equilibrium of duopoly is suggested by edgeworth’s duopoly model.
Comments over the above Classical Models of Duopoly (Oligopoly):
In our analysis of three classical models of duopoly we saw that one common assumption in them is that the duopolists have zero conjectural variation, that is, while deciding about his output or price policy, each duopolist believes that his rival will hold output or price constant at the present level whatever he himself might do.
Further, a producer remains unshaken in this erroneous belief even when he constantly finds himself to be proved incorrect since after his action the rival does react and changes his output or price. This is a chief logical error in classical models.
Furthermore, by assuming zero conjectural variation on the part of the duopolists (oligopolists), classical models ignore the mutual interdependence which is the chief characteristic of oligopoly. Thus, classical models provide solution for oligopoly problem by removing from it is most important feature.
4. Chamberlin’s Oligopoly Model:
In his now famous work “The Theory of Monopolistic Competition” Chamberlin made an important contribution to the explanation of pricing and output under oligopoly. His oligopoly model makes an advance over the classical models of Cournot, Edgeworth and Bertrand in that, in sharp contrast to above classical models, his model is based on the assumption that the oligopolists recognise their interdependence and act accordingly.
Chamberlin criticises the behavioural assumption of Cournot, Bertrand and Edgeworth that the oligopolists behave independently in the sense that they ignore their mutual dependence and while ‘deciding about their output or price assume that their rivals will keep their output or price constant at the present level.
According to him, oligopolists behave quite intelligently as they recognise their interdependence and learn from the experience when they find that their action in fact causes the rivals to react and adjust their output level.
This realisation of mutual dependence on the part of the oligopolists leads to the monopoly output being produced jointly and thus charging of the monopoly price. In this way, according to Chamberlin, maximisation of joint profits and stable equilibrium are achieved by the oligopolists even though they act in a non-collusive manner. Given identical costs, they will also equally share these monopoly profits.
Chamberlin’s Approach to Stable Joint Profit-Maximising Equilibrium under Oligopoly:
The process by which stable equilibrium under oligopoly is reached in Chamberlin’s oligopoly model is illustrated in Figure 29 A.5. Chamberlin considers the case of a duopoly with zero cost of production of the two producers, A and B. Like Cournot he also assumes that the market demand curve for the product is linear.
In Figure 29A.5, MD represents this linear market demand curve for the homogeneous product of the duopolists. As in Cournot’s model, suppose producer A is the first to start production. He will view the whole market demand curve MD facing him and corresponding to it MRa is the-marginal revenue curve. In order to maximise his profits he will equate marginal revenue with marginal cost (which is here taken to be equal to zero). It will be seen from Fig. 29A.5 that he will be in equilibrium by making MR = MC when he produces OQ output (i.e. half of OD) which is in fact the monopoly output, and will fix price equal to OP.
Now, suppose producer B enters the market. He thinks, as in Cournot’s model, that producer A would continue to produce OQ output and therefore views ED portion of the market demand curve as the relevant demand curve facing him and corresponding to it MRa is the marginal revenue curve. With marginal cost being equal to zero, for maximum profits he will produce half of QD, that is, QL or at point L at which his marginal revenue curve MR intersects the .Y-axis along which output is measured. With aggregate output OL(OL = OQ of A + QL of B), price will fall to the level LK or OP ‘with the result that profits earned by producer B will be equal to the area of rectangle QLKT, and due to the fall in price the profit of producer A will decrease from OPEQ to OP’TQ.
Oligopoly Models Pdf Notes For Beginners
However, from this point onward Chamberlin’s analysis deviates from Cournot’s model. Whereas in Cournot’s model, the firm A will readjust his output and will continue to assume that his rival will keep his output constant at QL level, but in Chamberlin’s model producers learns from his experience that they are interdependent.
With the realisation of mutual dependence, producer A decides to produce output OH equal to output QL of producer B and half of monopoly output OQ so that the aggregate output of both of them is the monopoly output (OQ = OH of A + QL of B).
With OQ as the aggregate output level, price will rise to QE or OP. Firm B also realises that in view of interdependence it is in the best interest for both of them to produce half of monopoly output and will therefore maintain output at the QL or OH level which is half of the monopoly output.
Thus, each producer producing half of monopoly output will result in maximisation of joint profits though they do not enter into any formal collusion. In this way Chamberlin explains that duopolists behaving intelligently and realising their interdependence reach a stable equilibrium and together produce monopoly output and charge monopoly price each sharing profits equally.
A Critical Evaluation:
Chamberlin’s model is an advance over the classical models in that the firms behave intelligently and recognise their interdependence. Their behaviour leads them to the monopoly solution of output and pricing which ensures maximisation of joint profits though they do not formally collude.
This implies that firms have full information about the market demand curve and quickly learn from the experience and realise that the ultimate consequence of alternative chain of adjustments to rival’s moves will be less profitable than sharing the monopoly profits equally with him.
Further, it is assumed in Chamberlin’s model that the oligopolists know fully the costs of production of their rivals which enable them to arrive at a monopoly output and price which is in the best interest of all of them.
Thus, unless all oligopolists have identical costs and demands, it seems impossible that the oligopolists will be able to reach monopoly solution, that is, maximisation of joint profits without collusion. It may be noted that even in a formal collusion there is always incentive on the part of rival firms to cheat by under-cutting price to increase their individual profits.
In Chamberlin’s model of oligopoly without collusion, incentive for the firms to undercut price to increase their share of profit will be relatively more. Besides, Chamberlin’s model has another great flaw as it ignores the entry of new firms and is thus a closed model.
Price Leadership Model Of Oligopoly
Due to the attraction of monopoly profits jointly earned by the existing firms, the new firms are likely to enter the industry. With the entry of new firms the attainment of stable equilibrium of oligopoly is unlikely to occur.