 We will continue our discussion on theory of oligopoly, typically the oligopoly form of market structure and if you remember in the last session we discussed, this is the most realistic form of market structure, although when it comes to theory and when we talks about the determination of equilibrium price and output, it is it is not very certain like in case of perfect competitive market structure or monopoly market structure. So, in the previous session we discussed about the features of oligopoly and one of the significant feature of oligopoly is that when one price one firm decides the price and output, generally they keeps in the mind that what will be the rival's action with respect to the change in the their price and output. And second is even if they knows that there is interdependence, but sometimes they ignore or they suggest, assume the plan as such to be before and they never consider the revised plan into their action whenever they are fixing up this price and output. The different kind of models are there on the basis of that how what is the group behavior of the oligopolist. When they collude work for joint profit, generally we call it say collusive oligopoly and when they compete with each other on the basis of price or on the basis of non-price like other factor than price, it is called as non-collusive oligopoly. And in the context of non-collusive oligopoly, in previous class we discussed about the Karnat models. We discussed about the Stackelberg model and we also discussed about the King demand curve model. To sum up, we can say that Karnat model is one where two main outcome emerge from their one is always the individual firm thinks that they are not the rivals is not going to change their plan with the revised period, but practically that does not happen and that leads to a situation where may be one-third of the market is untapped, it is not being produced or supplied by any of this firm if it is a case of a duopoly specifically. And secondly, the second outcome comes from Karnat model is that when linear demand curve and the cost of production is 0, generally the monopoly output is half of corporate competitive output and duopoly output is two-third of competitive output. Then we discuss about the Stackelberg model and to sum up Stackelberg model we can say that it is a leader follower models, one firm gets sophisticated, they knows that what is the revised plan of the or what is the reaction function of the other firms, how they are going to react it and generally they also consider the reaction when they are considering their own price and output plan and in that process they become the leader and the other firm has to follow it. But in the long run, if both the firms try to be leader, they get into the price war and in the last firm it becomes a cartel when they feel that price war is not at all profitable. Here to note that oligopoly is they knows that the price war is not going to benefit the producer or the seller rather it is going to benefit the consumer and that is the reason if you look at they never get into price war and even if they are getting into price war they stop at a point, they stabilize at a point beyond which they feel that even they are not covering the normal profit what is associated to the product. Then we discuss about the king demand curve and king demand curve talks about two different kind of group behavior of the oligopoly one when one firm decrease the price other follows it and that is why we get the demand curve as the inelastic demand curve for specific firm because when others follow it there is no much change in the quantity demanded and they have to even if there is a change in the price the consumer they feel that the other firms also they have change their price say there is no significant increase in the quantity demanded of that particular firm. And the second type of group behavior is that when one firm increases the price other hardly follows it and in that case the firm encounter a elastic demand curve. So taking together this inelastic and elastic demand curve with respect to two situation one increase in the price and second decrease in the price the firm generally get a king demand curve which is king between two different segment of the elastic and inelastic demand curve. Corresponding to the king since there is a king in the demand curve we get two level of marginal revenue curve one with respect to the elastic segment of the demand curve and second with respect to the inelastic segment of the demand curve and since there is a king and we get two kind of MR curve in between there is a gap between two MR curve and generally the marginal cost fast through that segment where there is no MR curve and that is the reason even if there is an increase in the cost still the equilibrium price and output never changes. So this typical model talks about the price rigidity of the as a part of the group behavior of the oligopoly firm and how generally it affects the how generally it does not affect the equilibrium price and output. So this is about the price or the non-price competition in case of the non-collusive oligopoly. Today we will discuss about the collusive oligopoly we will talk about two kind of arrangement one it is a cartel and second it is a price leadership model and in both these cases it is a case of collusive oligopoly model where the firms join together in order to maximize the joint profit. Before getting into the model let understand what does it mean when you talk about collusion. So collusion when rival firms or all firms they enter into an agreement in mutual interest on various accounts such as price, market share. So it is a in a simple language to understand collusion we can say it is an agreement where all the firms they comes together and they jointly decide about the what is the price to be following the market what should be the market share. Two kind of collusion may happen one is explicit collusion and second one is the tacit collusion explicit collusion is one where a number of firms enter into such agreement formally and second is the tacit collusion is collusion which is not ever but still they are into the collusion and why this tacit collusion comes into picture if you look at there is no legalized version of collusion typically after the cartel if you will find out opaque as a cartel after that you will find out there is no legal form of cartel exist whatever the form of collusion exists that is in the form of tacit form. So one where formally they agree into a collusion formally they agree into a group and they work together for the joint profit maximization and output maximization and the other one is the tacit collusion where collusion which is not ever. So most commonly if you will find form of explicit collusion is generally known as cartel. So whatever the commonly found explicit collusion is known and cartel and what is the aim of this kind of cartel the aim of such collusion is to reduce competition and increase profit of the individual member. So obviously when they collude together work together for the profit maximization that reduces the competition and increase the profit of the individual member. So basically the individual firms those who are not able to get profit those who are not able to maximize profit they were now in a position to maximize the profit because the firms work for the joint profit maximization they fix up a price which gives at least some amount of profit to each of this firm. Government do not encourage collusion because it creates like monopoly and kills competition and when if there is no competition that reduces the generation of employment and income and reduces the also the innovation. So explicit form of collusion is generally known as cartel and what is the outcome of cartel if you look at the outcome of the cartel in the positive segment is it reduces the competition and the individual firm generally they get some profit out of it earlier who are not able to generate any amount of profit. Generally government or the authority they never encourage this form of cartel or this form of collusion because ideally when the cartel goes for a long period of time in the long run they act become a monopolist which is not beneficial for the consumer it reduces the competition it reduces the innovation it reduces the also to some extent the income and employment generation and that is why if you find authority they always put a restriction on the creation of the collusion or the creation of a cartel. So cartel as we know it is a direct agreement among the competing oligopolist with the aim of reducing uncertainty. Now what is the optimization problem for the oligopolist over here the optimization problem for the oligopolist stage is to reduce the uncertainty. Aim of cartel is to maximize the joint profit and how do they function they appoint a central agency to whom they delegate the authority to decide not only the total quantity that is the output the price but also the allocation of production among members of the cartel and the distribution of joint profit among them. So, the aim to form the cartel is to reduce uncertainty objective is to maximize joint profit and how do they function they generally appoint a central agency in the consultation with all the firms whom they consider as the central agency and what is the role of central agency. The central agency decide what should be the total market output who should produce how much what should be the total what should be the price charge for the product and also when the industry has a whole market as you will they are getting profit how it has to be distributed among the individual firms. So, the role of central agency is to decide about the price output market share of the different firm and also how the distribution of the joint profit will takes place between the different firms. Now, what is the prerequisite for here to the central agency the prerequisite for here if the central agency is to they have full information about the cost function of the firm and how it helps when we talk about the cost function of the firm how it helps because if they know the cost function accordingly they will allocate that how much amount they have to produce by each of this firm. So, it is assumed that all members and produce the identical product because if they are producing homogeneous product the difficulty again comes here that who should produce which kind of product and since we are assuming here that typically in case of cartel this is assume that all the firms they produce the identical product and the central agency they have the full information about the cost function of the individual firm which one is high cost firm which one is the low cost firm which firm is operating in which stage of the average cost the firm whether they are operating other decreasing portion of the average cost they are operating at the full capacity they are operating at the minimum cost of the average cost or they are operating at the increasing portion of the average cost cost. So, cartel aiming at joint profit the maximization it is one in which cartilization is perfect. So, we call about a perfect kind of cartilization per cartel M8 joint profit maximization. It is an arrangement by all members with an objective to maximize the profit and in such type of arrangement the product is essentially homogeneous centralized body decides the pricing of the product. Price is decided by the association or the central agency on the basis of summation of all firms cost and demand function. And in this case individual firms they are not the price maker, individual firms they are the price taker. And what price they take, they take the price that is decided on the basis by the central agency on the basis of firms cost and demand function. However, when there are large number of firms and size of market is small it is difficult to sustain cartel and there is a every possibility that some firms may deviate the cartel price and thus cheat among other members. So, when the market size is small and there are large number when it comes to the allocation of the production generally it comes very insignificant. And in this case generally the people the firms they get motivated to charge a different price and cheat other firms and in that way generally the cartel never sustain for a longer period of time. Because still the time that agreement is there the trust is among the firm is there that everyone has to everyone is just following the central agency guideline regarding output and the price till that time cartel will sustain otherwise cartel will not sustain. So, we will see that graphically when we talk about the summation of the cost and revenue decides the price or they identify the price or they find the price on the summation of cost function and the revenue function. We will see that how this price is decided how the price is going to followed by both the both the firms or may be the number of firms in the market and what is the allocation how the allocation takes place on that basis and what is the profit. So, we will just have a graphical explanation of this entire cost and output determination or the price and quantity determination in case of a centralized cartel. So, we will just take a case of a geopolitist to make it simple to understand. So, this is the demand curve this is the marginal revenue curve. This demand curve is the demand curve for the entire firm marginal revenue curve is the summation of the marginal revenue curve of all the firms. This is the marginal cost function which is summation of marginal cost 1 and marginal cost 2 and how the price is determined in the market. We take the point where marginal cost is equal to the marginal revenue leads to the of equilibrium price or equilibrium output. So, this is the Q and this is the P same P is going to followed by both the firms. So, this is the price that has to be followed by both the firms. So, we can call this as firm 2 and firm 1. We get the average cost function for firm 1 and we get the average cost function for firm 2. Then we get the marginal cost function for 1. We get the marginal cost function for now corresponding to this we look at this MR how this marginal cost function for the individual firms generally and on that basis we can find out what is the output level. So, output level is Q 2 here output level is 1 here this is the price this is the price. So, price is decided on the basis of marginal revenue and marginal cost and in order to identify the quantity because whatever the price determined that is followed by both the firm. Now, how the output will be allocated? Output will be allocated on the basis of the marginal revenue and marginal cost to 1 that will give the output level for firm 2. This will be the output level for firm 1. So, in that following this we get Q 1 is the level of output for firm 1 and Q 2 is the level of output for firm 2 and Q is Q 1 plus Q 2. So, how it happens in case of a profit maximization or a cartel aiming at profit maximization? The price is decided on the basis of the marginal revenue and marginal cost and that price is followed by all the firms in the market here specifically we have taken the example of Diopoly to make this understand simple and on the basis of the marginal revenue and marginal cost of the specific firm we are finding out the level of output. Now, what happens when this price is followed and this output is being produced by it? Now, in this case this is the price and corresponding to this level of output what is the cost? The cost is this much because this is the average cost this is the price. So, since corresponding to this level of output average revenue or price is greater than average cost the firm gets this much amount of the profit. Similarly, for this level of output this is the average cost this is the price. So, in this case also price is greater than average cost and that is why the firm is getting profit. So, whether it is a case of high cost firm that is a compared to both the firm if you look at firm 1 is the high cost firm and high cost firm still they are getting some amount of the profit and firm 2 they are low cost firm as compared to firm 1 and they are also getting the profit. So, the basic objective of the cartel gets fulfilled here that even if the cost function of the firms in the cartel they are in the different there in the different kind of cost function or there in the different level, but when it comes to the maximization of the joint profit all the firm at least gets some amount of the profit. We will just take a numerical to understand this that how this joint profit maximization happens you are taking a specific demand function and cost function of the firms. So, Q is equal to 160 minus 20 p and C is equal to 10 plus 0.3 Q square. Now, we find out what is the profit maximizing output and what is the total profit. So, we can find out Q is equal to 80 minus 10 p. So, we can get P is equal to 8 minus 0.1 Q total revenue is P Q. So, we get 8 Q minus 0.1 Q square marginal revenue is 8 minus 0.2 Q. So, marginal revenue is nothing, but DTR with respect to DQ and marginal cost is DC with respect to DQ. So, that comes to 0.6 Q. Now, to find out the profit maximizing level of output we need to follow the MRMC rule. So, MR has to be equal to MC. So, 8 minus 0.2 Q is equal to 0.6 Q simplifying this 0.8 Q will be equal to 8 and Q will be equal to 10. So, P is equal to 8 minus 0.1 Q. So, 8 minus 0.1 Q and that comes to 7 and total revenue is P Q. So, it has to be 70 and profit is total revenue minus total cost. So, 70 minus 10 minus 0.3 Q square. So, this is 70 minus 10 minus 0.3 multiplied by 100. So, that comes to 60 minus 0.3 multiplied by 100. So, that comes to rupees 30. So, this is the profit, this is the price and this is the quantity. So now, what are the problems in case of centralized cartel or any form of the cartel? The basic aim is to maximize the joint profit and that they do by finding out a price on the basis of the marginal revenue and marginal cost assessing the total cost function and total revenue function for all the firms. Now, what may be the problem when they are estimating the summation of the total cost or when they are estimating the summation of the total revenue for all the firms? So, there may be a potential problem that there is may be a mistake may arise in the estimation of the market demand. It may also arise in the estimation of marginal cost and whenever there is a existence of high cost firm, sometimes it set an obstacle toward the joint profit maximization. And if the cost curve of the firm lies wholly above the equilibrium marginal cost, profit maximization requires that high cost firm should close down which is not possible. So, a cartel may not also maximize for fear of government of intervention or fear of entry that is one more potential problem and also sometimes the cartel to maintain good image they may not maximize the profit. So, one is fear of government, second one is to maximize the profit and they feel that it is not going to create a good image for them and that is why they do not maximize the profit. Sometimes they feel that when they are maximizing the profit, when they are getting supernormal profit other firms may enter into the market. So, to make this is a entry barrier they generally charge a low price and they do not maximize the profit and also fear of government regulation they generally do not maximize the profit. So, as a whole when the basic objective is to maximize the profit, but there are certain problems or certain inherent problem where the cartel typically the oligopolies they are not maximizing the profit.