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The collusive models of oligopoly suggest that duopolists or oligopolists can gain by colluding, i.e., by choosing the output level which maximises total industry profits and then sharing the profits among themselves. A cartel is formed when firms jointly fix prices and outputs with a view to maximising total industry profits. A cartel is often called monopoly of oligopolists.
In the early 1970s, several different firms in the oil industry colluded and jointly restricted output in order to raise prices and thereby increase their profits. This type of collusion is known as a cartel. The reason is that a cartel (such as the- OPEC) is nothing other than a group of firms that jointly control the total supply of a commodity (such as oil) like a pure monopolist and maximise the sum of their profits. So in a cartel situation we find the adoption of a new strategy, viz., joint profit maximisation.
Output Allocation by Producers’ Cartel:
A cartel is a group of producers that collectively determines the price and output in a market. When a cartel works on the basis of the intentions of its members, it acts like a single monopolist firm that maximises total industry profits. This is known as joint profit maximisation. Profit allocation among members is based on allocation of output, i.e., by fixing production quotas of members on the basis of their respective marginal costs.
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The problem a producers cartel faces in allocating output levels among members is the same as the one faced by a multi-plant monopolist in allocating output across its individual p an s Output is allocated on the basis of MC of each firm – the lower the MC the higher the output In Fig. 24.9 we show that the cartel consists of two firms, with marginal cost, functions MC (Q1) and MC2 (Q2).
At the profit-maximising level of output, the cartel a locates its total output between the two firms, so that marginal costs are equalised and the common MC equals the industry-wide MR. Let Q* and P* be the optimal total output and price for the cartel as a whole and Q1* and Q2* are the output levels of the individual members.
In this case the profit-maximising condition of the cartel can be expressed as;
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MR (Q*) = MC1 (Q1*)
MR (Q*) = MC2 (Q2*)
The cartel’s marginal cost curve is MCT, which is the horizontal summation of the MC curves of the individual firms in the cartel. The cartel’s profit-maximising output is fixed where MCT = MR or Q* units. To equalize the marginal costs of individual producers, firm 2 should produce Q2* units and firm 1 should produce Q1* units. The cartel’s profit- maximising price is P*.
In Fig. 24.9 the profit-maximising output of the cartel is Q* at this price. The cartel then allocates output between its two members to equalize their marginal costs. Firm 1, with higher MC is allocated a smaller share of total cartel output (Q1* units). Firm 2, with lower MC is allocated Q2* units of output. Thus, the cartel does not necessarily divide the market equally among its members. The low-marginal cost firms supply a bigger share of total cartel output than do the high-marginal cost firms.
Joint Profit Maximisation:
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The basic cartel model of duopoly suggests that the profit-maximisation problem facing the two firms is to choose their outputs q1 and q2 so as to maximise total industry profits;
From equation (2) it is clear that when firm 1 is expanding its output by Δq1, two effects are produced. It makes some extra profits from selling more output. But at the same time some profit is lost due to price cut. In this case firm 1 has to take into account the effort of price cut on both q1 (its own output) and q2 (the output of its rival). The reason is that it is now interested in maximising total industry profits, not just its own profits as is found under non-collusive oligopoly situations.
The optimality condition is MR1 = MR2, irrespective of whether the extra output is produced by firm 1 or firm 2′. For this condition to hold MC1 (q1*) has to be equal to MC2 (q2*). In other words, MR – MC equality for each firm, in a cartel situation, implies that the marginal costs of the two firms have to be the same in equilibrium. However, if MC1 (q1*) < MC2 (q2*), then firm 1 will necessarily produce more in equilibrium so as to increase the size of total cartel profit.
Instability Due to Cheating:
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The problem with the cartel solution is that there is always an inducement to cheat. This is why a cartel arrangement is inherently unstable. Let us suppose, for example, that the two duopolists are producing outputs which maximise industry profits (q1*, q2*), and firm 1 is planning to produce a little more output.
The marginal profits accruing to firm 1 will be:
Thus, if firm 1 thinks that firm 2 will keep its output unchanged, then it can increase its own profits by cheating, i.e., by increasing its level of output. In a cartel solution, joint profits are maximised by jointly restricting output and raising the price of the product. If a firm cheats and produces more than its quota, the entire market will be spoilt.
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But if each firm believes that at the output levels that maximise joint profits its only rival will observe the cartel norm and stick to its output quota and keep its output fixed then each will be tempted to increase its own profits by unilaterally expanding its output.
Worse still, if firm 1 thinks that its rival will increase its output, then firm 1 will try to increase its output as quickly as possible and make profits as long as it can (like the early bird which catches the worm). Thus, in order to make a cartel effective, the firms must find a way to detect and punish cheating. Otherwise a cartel is likely to break down sooner or later.
The Cournot Solution in a Cartel Situation:
We may now find out the Cournot solution to the cartel problem assuming that marginal costs of both the duopolists are zero and market demand curve is linear.
The aggregate profit function is the same as the total revenue function (since total cost is zero):
So the condition of profit maximisation is:
What is important in this context is total industry output. The division of output between the two firms is inconsequential since marginal cost is zero. The Cournot solution to the cartel problem is shown in Fig. 24.10. Since the objective of the cartel is to maximise joint profits, optimum output combinations are those that lie along the line a/2b which is the locus of the points of tangency of the iso-profit curves. The reason is easy to find out.
If industry profits are maximised, then the marginal profit from producing more output in either firm must be the same. Otherwise, total profits will increase and both firms stand to gain if more output is produced by the more profitable firm. This implies that iso-profit curves must be tangent to each other at the profit maximising levels of output, i.e., their slopes have to be the same.
Here E, F, etc. are such tangency points. Each one is a point of Cournot equilibrium. This is why the output combinations that maximise total industry profits (i.e., the cartel solution) are those that lie along the line illustrated in Fig. 24.10.
Fig. 24.10 also illustrates the temptation to cheat that is present in the cartel solution. Let us consider a case where the two firms divide the market between them equally. In this case, if firm 1 increases its output and firm 2 keeps its output constant, then firm 1 would move to a lower iso-profit curve — which means that firm 1 would increase its profits.
If one firm believes that the other’s output will remain constant, it will be tempted to increase its own output with a view to making more profits. Thus we see that the cartel solution is unstable but the Cournot solution is inherently stable.
Cartel Instability:
Cartel agreements are fragile because the members generally have an incentive to cheat on the agreement to earn higher than expected profits at the expense of their partners. This point is illustrated in Fig. 24.11. If a firm left the cartel and charged the profit-maximising price P1 (to sustain sales of output Q1, where MC= MR), then the firm’s profit would equal Q1 x BP1. This would be higher than if adhered to the price and sales quota established by the cartel (i.e., price P0 and sales quota Q0).
Punishment Strategies:
A cartel is inherently unstable because it is always in the interest of each firm to increase its production above the level which maximises industry profit. A cartel can operate successfully if some measure is adopted to ‘stabilise’ its behaviour. One way of achieving cartel stability is for firms to give a threat to punish each other for cheating (by violating the cartel agreement). So it is necessary to determine the exact size of punishments necessary to stabilise a cartel.
Let us consider a simple situation in which the two duopolists are of the same size. If each firm produces half the monopoly output, total profit will be maximised and each firm will make a profit of πm. In such a situation, if firm 1 discovers that firm 2 is producing more than its allotted quota, then firm 1 can punish firm 2 by producing the Cournot level of output for ever. This is known as a punishment strategy. Whether this type of threat is likely to stabilise the cartel or not depends on the profits and costs of two alternative strategies, viz., co-operating and not co-operating (cheating), an issue to which we turn now.
The Benefits and Costs of Co-Operating Vis-a-Vis Cheating:
Let us suppose a firm cheats and the other punishes it. This means that each firm produces the Cournot level of output and makes a profit of πc per year. But the Cournot profit πc is less than the cartel profit πm. If firm 1 deviates from its quota and produces more output it will make a profit of πd which is greater than πm, i.e., the profit it can make by producing its quota of collusive, monopoly level of output.
This is the standard temptation facing a cartel member: if each firm restricts its output and pushes the price up, then each firm has an incentive to take advantage of the high price by increasing its production and thus deviate from the quota.
By producing according to its allotted quota, each firm gets a steady stream of profits of πm.
The present value of this stream is given by the following equation:
Present value of profit from cartel behaviour = πm + πm/r
If the firm produces more than the cartel amount, it makes a one-time profit of πd and nothing thereafter due to the break-up of the cartel and the reversion to Cournot behavior;
Present value of cheating = πd + πc/r
It is quite obvious that the present value of profit from producing cartel output will be greater than the present value of cheating, i.e., deviation from the cartel agreement when the following inequality holds;
Here πm – πc > 0 because πm (monopoly profits) > πc (Cournot profits); πm – π d is also positive because deviation is even more profitable than sticking with the monopoly quota. The above inequality clearly suggests that as long as the interest rate is very low, so that the prospect of future punishment is sufficiently important, it will be in the interest of both the firms to produce according to their allotted quotas.
Criticisms of the Model:
One main drawback of the cartel model is that the threat to revert to Cournot behaviour for- ever is not really strong or very realistic. One firm certainly may believe that the other firm will punish it for deviating, but this is unlikely to happen period after period or forever. A more realistic model would consider shorter periods of retaliation. Some models of game theoretic literature, called models of repeated games, illustrate some of the possible patterns of behaviour.
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