How price and output is determined under cartel aiming at joint profit maximization explain?

In this article we will discuss about the determination of price and output under collusive oligopoly.

There is an element of uncertainty prevailing within oligopoly resulting in price wars and cut throat competition among the firms. There are certain measures that the firms working under oligopolistic environment pursue like entering into agreement regarding a uniform price output policy so as avoid the uncertainty. These agreements are basically tacit or hidden. These agreements form a part of the discussion under Collusive Oligopoly.

The collusions can be classified into:

(a) Cartels- In cartels firms jointly fix the price and output through a process of agreement.

(b) Price leadership- In this form Collusive Oligopoly one firm sets the price and others follow it. There is a price leader who is followed by the followers.

Price leadership is one more form of collusion of Oligopoly firms. This form of Collusion is basically a secret affair among firms. One firm is considered as the leader and is allowed to take fix price and related decisions. Under price leadership it should be noted that all the existing firms in the industry will pursue the rules fixed by the leader. The likelihood of competition between leader and individual firms is far cry. Price leadership takes three different forms viz., low cost price leadership, dominant price leadership, barometric price leadership.

(a) Cartels:

Cartel refers to a grouping of some firms into a group aiming at an identical objective. It is observed that if a large number of firms or industries unite to form a group they enjoy additional powers. Cartel as a group is capable of exerting considerable pressure on the market conditions.

The members of the cartel can take the liberty of charging exorbitantly high prices to maximize their profits. In legal terms cartels are in general banned in many countries. Cartels do exist in some implicit or explicit forms in different parts of the world. The most famous example of cartels in the OPEC – (Organization of the Petroleum Exporting Countries)

Earlier, the cartel as a term was used to refer to the agreement under which there used to be a common sales agency which would undertake the selling operations and decisions of all the member firms. Later on, all types of formal or informal and tacit agreements reached among the oligopolistic firms of an industry are known as cartels.

Cartels cause serious obstruction and curtailment of the competitive environment in the economy. Therefore as discussed above, the cartels are banned in many countries like U.S.A. where cartel are banned under the Anti-Trust Laws.

Cartels which are the formal collusion or agreement among the oligopolists take various forms.

Joint profit maximization by the cartel:

To secure maximum joint profits for the members of the cartel, an extreme form of collusion is formed in which there is a Central Administrative Agency and the member firms agree to surrender completely their rights of price and output determination upon the agency.

Such a formal collusion is referred to as perfect cartel. The main aim is to maximize joint profit for the members. It is interesting to note that under the perfect cartel type of collusive oligopoly, the Central Administrative Agency plays the crucial role of price and output determination of the whole industry as well as of each member firm.

In this form of collusive oligopoly, the total profits are distributed among the member firms in a way already agreed between them. The share of each member firm from the total profits is not necessarily in proportion to its output and the cost.

The amount of output to be produced by each firm is decided by the central administrative agency in such a way that the total costs of the total output produced is minimum. Similarly, the price that the members can charge is determined by the central agency.

Let us try to understand how the output allocation of member firms takes place in order to minimize the total cost. This is possible when the various firms in the cartel produce outputs separately in such a way that their marginal costs are equal.

Figure 9.8, Price and Output Determination Under Cartel: Joint Profit Maximization

The process in which the cartel works and determines its price and output is shown in figure 9.8. For our understanding it is assumed that there are two firms’ viz., firm1 and firm2 that have formed a cartel by entering into an agreement. It is further assumed that the cartel aims at maximizing joint profits for the member firms.

At the outset the cartel would make an estimate of the market demand of the product. In the figure 9.8 (c) we can see that the aggregate demand curve DDc of the consumers of the product of the cartel is sloping downward. MRc curve is the marginal revenue curve.

The marginal cost curve (MCc) of the Cartel is obtained by the horizontal addition of the marginal cost curves of the two member firms. Thus, in figure*(c) the MCc Curve is the horizontal summation of marginal cost curve MC1 of firm1 and marginal cost curve MC2 of firms 2 .

MCc indicates the minimum possible total cost of producing each industry output on it. The output of the industry is being distributed among the two firms in such a way that their marginal costs are equal.

The cartel will maximise its profits by fixing the industry’s output at the level at which MRc and MCc curves of the cartel intersect each other. It can be observed in figure9.8. (c) that MRc and MCc curves cut each other at point E or output OQc. It will also be seen from the demand curve DDc that the output OQc will determine price equal to QcT or OP.

As shown in the figure 9.8 (c) OQc is the total output to be produced, the central agency of cartel will allot output quota to be produced by each firm so that the marginal cost of each firm is the same. This can be ascertained by drawing a horizontal straight line from point E towards the Y-axis.

It will be seen from the figure that when firm 1 produces OQ1 and firm 2 produces OQ2 the marginal costs of the two firms are equal. Accordingly, the output quota of firm 1 will be OQ1 and of firm 2 will be OQ1. It is worth noting that the total output OQc will be equal to the sum of OQ1 and OQ2.

Therefore it can be seen that when firm1 produces OQ1 level of output and firm2 produces OQ2 level of output the maximum joint profits for the member firms of the cartel is ascertained.

It can further be observed from Figure 9.8 that with output OQ1 and cartel price OP. the profits made in firm 1 are equal to PLMN and with output OQ2, and cartel price OP the profits made in firm 2 are equal to PABC.

Market-Sharing Cartels:

The formation of perfect cartels, has been quite rare in the real world even where their formation is not illegal. In a perfect cartel not only the price but also the output to be produced by each member of a cartel is decided by a central management authority and profits made in all of them are pooled together and distributed among the members according to the terms of a prior agreement.

But when cartels are loose, instead of being perfect, the distribution of profits and fixation of outputs of individual firms are not determined in a manner perfect cartel does. In a loose type of cartel the market-sharing by the firms occurs. Further, there are two methods of market sharing-non-price competition and quotas.

Market-Sharing by Non-Price Competition:

Under market sharing by non-price competition, only a uniform price is set and, the member firms are free to produce and sell the amount of outputs which will maximise their individual profits. Though the firms agree not to sell at a price below the fixed price they are free to vary the style of their product and the advertising expenditure and to promote sales in other ways.

That is, the price being a fixed datum, the firms compete on non-price basis. If the different member firms have identical costs, then the agreed uniform price will be the monopoly price which will ensure maximisation of joint profits. But when there are cost differences between the firms as is generally the case, the cartel price will be fixed by bargaining between the firms. The level of this price will be such as will ensure some profits to high-cost firms.

But with cost differences such loose cartels are quite unstable. This is because the low cost firms will have an incentive to cut price to increase their profits and therefore they will tend to break away from the cartel. However, they may not openly charge lower price than the fixed one and instead cheat the other firms by giving secret price concessions to the buyers. However, as the rivals gradually lose their customers, the cheating by the low-cost firms will be ultimately discovered and consequently open price war may commence and cartel breaks down.

Market-Sharing by Output Quota:

The second type of market-sharing cartel is the agreement reached between the oligopolistic firms regarding quota of output to be produced and sold by each of them at the agreed price. If all firms are producing homogeneous product and have same costs, the monopoly solution (that is, the maximisation of joint profits) will emerge with the market being equally shared by them.

However, when costs of member-firms are different, the different quotas for various firms will be fixed and therefore their market shares will differ. The quotas and market shares in case of cost differences are decided through bargaining between the firms. During the bargaining process, two criteria are usually adopted to fix the quotas of the firms.

The second common basis for the quota system and market sharing is the division of market region-wise, that is, the geographical division of the market between the cartel firms. In this arrangement, price and also style of the product of cartel firms may vary.

It is worth noting that all types of cartels are unstable when there exists cost differences between firms. The low cost firms always have a tendency to-reduce price of the product to maximise their profits which ultimately results in the collapse of the collusive agreement.

Further, if the entry of firms in the oligopolistic industry is free, the instability of the cartel is intensified. The new entrants may not join the cartel and may fix a lower price of the product to sell a large quantity. This may start a price war between the cartel firms and the new entrants. We thus see that the stability of the cartel arrangement is always in danger.

(b) Price Leadership:

Types and Price-Output Determination:

Price leadership is one more form of collusion of oligopoly firms. This form of Collusion is basically a secret affair among firms. Price leadership maybe considered as an imperfect form of collusion among the oligopoly firms. One firm is considered as the leader and is allowed to fix price and related decisions. Under price leadership it should be noted that all the existing firms in the industry will pursue the rules fixed by the leader. The likelihood of competition between leader and individual firms is far cry. Price leadership takes three different forms viz., low cost price leadership, dominant price leadership, barometric price leadership.

Types of Price Leadership:

Price leadership is of various types:

(1) Price Leadership by a Low-Cost Firm:

The low-cost firm in the industry in order to maximize profits sets a lower price than the profit-maximizing price of the high-cost firms. As a result, the high-cost firms will not be able to sell their product at the higher price; these high cost firms will therefore be forced to agree to fix the low price set by the low-cost firm. The low -cost firm becomes the price leader. However, the price leader i.e., the low-cost firm has to make sure that the price which it sets must yield some amount of profits to the followers.

(2) Price Leadership of the Dominant Firm:

In this form of leadership it is observed that there is one firm among the few firms in the industry which contributes a very huge proportion of the total production of the industry. This firm owing to its market share dominates the market for the product. This dominant firm which acquires the leadership exercises a profound influence over the market for that product. The other small firms are normally don’t have such influence on the market.

Attaining the leadership status, the dominant firm estimates its own demand curve and fixes a price which maximizes its own profits. The small firm who turns out to be the followers have no individual effects on the price of the product in the market. They therefore follow the dominant firm and accepting the price set by the price leader will adjust their output accordingly.

(3) Price Leadership by a Barometric Firm:

As the name suggest in this form of price leadership there is a firm which is an old, matured, experienced, largest or most prestigious firm. This firm becomes the price leader and undertakes the responsibility of a guardian to protect the interests of the other firms.

The barometric price leader assesses the changes in the market conditions with regard to the change in demand, change in production cost, competition from the related products and other similar changes and accordingly takes initiatives to meet the challenges keeping in view interest and welfare of all the firms in the industry. The followers in this from follow the barometric price leadership.

(4) Price Leadership by an Exploitative Firm (Also Termed as Aggressive Price Leadership):

In this form of price leadership there is usually a very large or dominant firm. This particular firm takes the help of aggressive price policies in order to assume the status of the Price leader. The aggressive price leader forces the other firms in the industry accept its leadership. An exploitative firm often threatens to compete with the others firms to throw them out of market if they do not follow its leadership.

There are many models explaining the price leadership and the price-output determination therein. All the models are based on different assumptions about the behaviour of price leader and his followers. In order to develop an understanding about the working mechanism of price leadership from of collusive oligopoly we initiate our discussion with the price-output determination underprice leadership by a low-cost firm.

Let us make the following assumptions before we commence our discussion:

(1) In the model, there are two only firms, 1 and 2. The firm 1 has a lower cost of production than firm 2.

(2) A homogeneous product is produced by the two firms.

(3) The share of each firm in the market is equal. This assumption implies that the demand curve facing each firm will be the same and will be half of the total market demand curve of product.

The process price and output determination underprice leadership is represented in figure 9.9. Each firm is feeing demand curve DD1 which is half of the total market demand curve DD for the product. MR is the marginal revenue curve of each firm. AC1 and MC1 are the average and marginal cost curves of firm A and AC2 and MC2 are the average and marginal cost curves of firm B. As assumed above Cost curves of firm 1 lie below the cost curves of firm 2.

The firm 1 maximizes its profits by selling OS level of output and setting price OP, since at output OS, its marginal cost is equal to the marginal revenue firm 2’s profits will be maximum when it fixes price OP1 and sells output OR. It will be seen from the figure that profit- maximising price OP of firm 1 is lower than the profit- maximising price OP1 of firm 2.

Since the two firms are producing a homogeneous product, they cannot charge two different prices. Because the profit- maximising price OP of firm 1 is lower than the profit-maximising price OP1 of firm 2, firm 1 will dictate the price to the firm 2 or, in other words, firm 1 will win if there is price war between the two and will emerge as a price leader and firm 2 will be compelled to follow. Given these facts, the agreement reached between them, even though tacit it maybe, will require that the firm 1 will act as the price leader and firm 2 as the price follower.

It should be noted that firm 2 after having accepted firm 1 as the price leader will actually charge price OP and produce and sell OS. This is because at price OP, it can sell OS output like firm 1 because the demand curve facing each firm is the same.

Thus both the firms will charge the same price OP and sell the same amount (OS). Note that the total output of the two firms will be OS + OS = OQ which will be equal to the market demand for the good at price OP. But there is an important difference between the two.

While firm 1, the price leader, will be maximising its profits by selling output OS and charging price OP, the firm 2 will not be making maximum profits with this price- output combination because its profits are maximum at output OR and price OP1. Profits earned by firm 2 by producing and selling output OS and charging price OP will be smaller than those of firm 1 because its costs are greater.

When the products of the price leader and his price-followers are differentiated, then the price charged by them will be different but the prices charged by the followers will be only slightly different either way from that of the price leader and they will conform to a definite pattern of differentials.

Price-Output Determination under Price Leadership by the Dominant Firm:

We assume that the dominant firm is aware of the total market demand curve for the product.

Further, it is assumed that the dominant firm knows the marginal cost curves of the smaller firms. The lateral summation of the supply of the small firms at various prices provides the total supply of the product. The dominant firm based on its experience can fairly estimate the likely supply of the product by the small firms at various prices. Having the access to this range of information, the dominant firm leader can derive its demand curve.

Now as represented in the figure 9.10, we can see in panel (I) of Figure 9.10 where DD1 is the market demand curve for the product S is the supply curve the product of all the small firms taken together. At each price the leader will be able to sell the part of the market demand not fulfilled by the supply from the small firms.

Thus at price P1 the small firms supply the whole of the quantity of the product demanded at that price. Therefore, demand for leader’s product is zero. At price P2, the small firms supply P2J and therefore the remaining part of JN of the market demand will constitute the demand for the leader’s product. The demand for leader’s product has been separately shown in panel (II) of Figure 9.10 by the curve DPL.

P2W in panel (II) is equal to JN in panel (I). At price P3, the supply of the product by the small firms is zero. Therefore, the whole market demand P3I will have to be satisfied by the price leader. Likewise, the other point of the demand curve for the price leader can be obtained.

In panel (II) of figure 9.10 the MRPL is the marginal revenue curve of the price leader corresponding to his demand curve DSPL , ACPL and MCPL are his average and marginal cost curves. The dominant price leader will maximize his profits by producing output OQ (or PF) and setting price OP. The followers, that is, the small firms will charge the price OP and will together produce PL. [PF in panel (II) equals LM of panel (I) in Figure 9.10].

It is worth noting that in order that profits of the leader are maximised it is not enough that followers should charge profit-maximizing price OP set by him, he will also have to ensure that they produce output PL. If the followers produce more or less than this, given the market demand DD1, the leader will be pushed to a non-profit maximising position. This implies that if price- leadership is to remain, there must be some definite market-sharing agreement even though it may be a tacit agreement.