 We will continue our discussion on collusive oligopoly model in this session also. So, if you remember in the last session, we talked about the different kind of collusion and primarily there are two types of collusion, one is explicit collusion, another is tacit collusion. And one of the most common form of explicit collusion is cartel. And cartel is generally joint agreement among the oligopoly firms to maximize the profit and here generally the central agency decide the price and output. There are two major type of cartel, one is cartel maximizing at joint profit, centralized cartel and second type of cartel is market sharing cartel. And again market sharing cartel has comes in two form, one is on the basis of market sharing on the basis of non-price competition and secondly the market share on the basis of quota. And if you look at the cartel is sustainable and there are some prerequisite to form the cartel also and this is going to be sustainable, if the all the firms they are producing homogeneous product and if you look at all the firms they are producing homogeneous product and that gives the scope at least to follow a uniform price whatever is followed by the cartel or whatever is the cartel price that becomes easy to follow by all the firms. So, today we will discuss on the other form of collusive model that is other form of collusive model that is price leadership. Here we will discuss the price leadership model in three context, one is when the price leadership is the price is decided by low cost firm, when price is decided by dominant firm and when the price is decided by the barometric firm. So, to start with we know what is price leadership first. So, it is a firm where one firm sets price, others firms follow it because it is advantageous to them or because they prefer to avoid uncertainty. So, if you look at the collusion the major objective is to avoid the uncertainty, uncertainty in term of getting the profit and uncertainty in term of being in the market or sustain in the market. So, in case of price leadership one firm set the price and other firms just follow it because they feel that by following this price and they are getting some amount of profit and there is no uncertainty associated with what kind of profit they are going to get it. If the product is homogeneous and if there are no transport cost the same price will be charged by all the firms because product is homogeneous no transport cost to assume that that all the cost of production comes within a identical frame on whatever the price follow price decided by the one firm generally that is acceptable to all. But if there is a transport cost or if the product are not homogeneous maybe that time whatever the price decided by the one firm that may not be followed by the others. However, if the product is differentiated prices will differ, but the direction of their change will be same and the same price differential will be more or less maintained. So, how they tackle with the price if the product is differentiated they will initially they will fix up the price of all the products, but they will control their direction of change if it is going to increase if it is going to decrease they will give a range and in that range only the price has to increase or the price has to decrease. If it is homogeneous product they have to charge a constant price same price for all the products, but if it is a differential product or if it is a heterogeneous product in this case they will fix up the price at once and the direction of the change of the price has to be controlled by the firm which decides the price. So, in this case the same price differential is going to maintain more or less for all this category of the product when it is a heterogeneous products in the market. So, we will discuss three types of price leadership, one is price leadership by a low cost firm, second one is the price leadership by a large dominant firm and third one is the barometric price leadership. To start with when we talk about the price leadership of a low cost firm let us know what can be a low cost firm and why we call it low cost firm. Low cost firm is one where the cost of production is less to produce the product. There may be number of possibilities that why firms get into or how come firms reach to a situation where they become the low cost firm. The basic argument for this goes that if it is a large firm and the scale of operation is more in the long run the per unit cost decreases and they emerge as a low cost firm. Second again if it is a mass production again the same reason if it is a mass production large scale in the long run generally they get into a situation where the per unit cost decreases, goes on decreases, they reaches the minimum and then it increases. So, low cost firm is one firm which generally lies in the decreasing portion of the long run average cost curve till the time it is reaching to the minimum cost. So, to produce the same product if there are number of firms in the market if one firm is producing that it will lower cost of production as compared to the other firm generally they are known as the low cost firm and their low cost firm may be because of economies of scale and again if you want to specifically find out a reason may be efficiency of raw material, efficiency of inputs, efficiency of technology, efficiency of the manpower involved in the production process they become they makes the firm become the low cost firm. Now if the low cost firm generally decides the price in a market in one kind of price leadership model find that the low cost firm decides the price. If the low cost firm decides the price let us find out graphically and also numerically that how the outcome is on the other firms in the market or why the low cost firm is being chosen is the price leader particularly in this type of market or in this type of arrangement of collusive model collusive model of oligopoly. So, we will see the price leadership of low cost firm. So, we will take the demand curve we assume there are mainly two firms one is firm one another is firm two. So, we will take the demand curve as average revenue one and also average revenue two and this is shown in the form of the demand curve. We will take the marginal revenue curve that is MR1 equal to MR2 we will take cost function we will take separate cost function for both the firm. So, one we have as marginal cost one and second we have the marginal cost two. So, we have taken the demand curve where this is the average revenue curve of firm one and also equal to the average revenue curve of firm two. We have taken the marginal revenue curve in the form of MR where MR1 is equal to MR2. We have taken two separate cost function because here the leadership comes in the form of the low cost firm. So, MC1 is the cost function for firm one and MC2 is the cost function for firm two. Now, to find out what is the price to be followed we get one point here where marginal revenue one and marginal revenue one intersect the marginal cost of firm one and we get a price which is equal to may be we can this is marginal revenue one. So, here we will get a price which is equal to P1 and correspondingly also we will get a price level taking the point where MR2 is equal to MC2. We get one more price that is P2 let us call it P2 star. Now, what is the thumb rule here since the price leadership is by the low cost firm both the firm they have to accept the price which is given by the low cost firm price given by the low cost firm and what is the price given by the low cost firm that is P1. So, ideally this P1 should be equal to also P2. So, this is the price since firm one is the low cost firm and according to the low cost firm cost function we take the MC1 is equal to MR1 corresponding to that we get the price which is equal to P1 and also we get the quantity which is equal to Q1 and this is the price the firm two they have to also follow it because they have accepted low cost firm as the price leader and they are going to produce Q2 star. Ideally they should produce Q2 star when the price is P2, but since they are following this price given by firm one they are also producing the output that is Q1 is equal to Q2. Now, if you look at the price is given by the low cost firm that is why this is lower corresponding to firm one we have firm two which is having a higher cost function and if higher cost function if their price is being charged on the basis of higher cost function ideally the price should be P2 star, but since they have accepted this firm one as the low cost firm and they have to be the price taker in this case they will take a price which is equal to P1 and they will produce that is Q1, but ideally what is their profit maximizing model profit maximizing model is they will produce less, but they will charge a higher price in order to produce it. So, when the price is given by the low cost firm the high cost firm they have to accept it, but in the long run if the price is going to be continuously lowest as compared to their profit maximizing price they may not accept the firm as the leader and they will they will not into be the collision they will go out of the collision and they will independently charge their price on the basis of their profit maximizing level of output because they will feel that continuously in the long run also if they are charging a price which is much lower to their cost function or much lower to their market price what it would have been on their profit maximizing level then in that case they will go out of the collision and they will charge independently their price. Now, we will just take a numerical to understand this price leadership by the low cost firm. So, we will get two demand function that is Q 1 is equal to 50 minus 0.5 P 1, P 1 is equal to 100 minus 2 Q 1 this is for firm 1 then we look for firm 2. So, for firm 2 Q 2 is equal to 50 minus 0.5 P 2 and from here we can find out this P 2 P 2 is equal to 100 minus 2 Q 2 then we will take the cost function T c 1 is equal to 100 plus 20 Q 1 plus 2 Q 1 square and total cost 2 is equal to 48 plus 36 Q 2 plus 2 Q 2 square. So, Q 2 is equal to 50 minus 0.5 P 2, P 2 is equal to 100 minus 2 Q 2 this is for firm 2 this is for firm 1. So, here firm 1 is the low cost firm and firm 2 is high cost firm. So, ideally the price has to set by the low cost firm and that has to be followed by the high cost firm in order to operate in the market. To find out the price for on the basis of low cost firm what we have to do we need to find out the marginal revenue 1 with respect to firm 1. We need to find out the marginal cost for firm 1 and we will equalize the marginal revenue marginal cost in order to get the profit maximizing level of output and profit maximizing level of price and that price has to accepted by firm 2. Then we will find out the price with respect to firm 2 and we will find that whether that is the same amount of profit what they are getting if they are charging the price on their own. So, to find this marginal revenue and marginal cost we will find out the total revenue 1 total revenue 1 is P 1 Q 1. So, P 1 is equal to 100 minus 2 Q 1 multiplied by Q 1. So, that comes to 100 Q 1 minus 2 Q 1 square marginal revenue will take as dT R 1 with respect to Q 1. So, that will continue or maybe we can find out the profit. Profit is total revenue 1 minus total cost 1. So, 100 Q 1 minus 2 Q 1 square which is our total revenue 1 minus 100 plus 20 Q 1 square plus 2 Q 1 square. So, this is our total cost. So, this is total cost 1. Now, if we simplify this we will get total revenue minus total cost 1 in order to get profit. So, this will be if you multiply this if you will deduct this total revenue 1 from total cost 1 then we get 80 Q 1 minus 4 Q 1 square minus 100. And we will take the first order derivative in order to find out the profit and in order to find out the profit price and output. So, that will become 80 minus 8 Q 1 equal to 0 and Q 1 is equal to 10. So, if Q 1 is equal to 10 P 1 is equal to 100 minus 2 Q 1. So, 100 minus 2 multiplied by 10 that will come to 80. So, P 1 is equal to 80 Q 1 is equal to 10 that is if the price is decided on the basis of the low cost firm P 1 has to be equal to 80. Now, we will find out for firm 2 and we will see whether if they are following their profit maximizing formula whether they are also getting the same amount of price or they are getting a different price. So, to find this we need to get the total revenue 2 and total cost 2 because that will give us the profit. So, total revenue 2 is equal to 100 Q 2 minus 2 Q 2 square and pi 2 will be equal to 100 Q 2 minus 2 Q 2 square minus the total cost 2. So, that is 48 plus 36 Q 2 plus 2 Q 2 square. So, if we simplify this we get 64 Q 2 minus 4 Q 2 square minus 48 and 2 will take the derivative in order to get the price and output. So, that has to be equal to 0 to maximize pi we need to take this first order derivative equal to 0. So, what is the first order derivative that is 60 minus 8 Q 2 has to be equal to 0. So, 8 Q 2 is equal to 0 equal to 64 Q 2 is equal to 8. This is the output for the firm 2. If you put the value of Q 2 is equal to 8 we will get p 2 is equal to 84. So, this is if the profit maximizing level on the basis of the firm 1. So, firm 2. So, this is the price and quantity if firm 2 decides what should be the price and quantity. But since this is a low cost firm we will take price is equal to 80 because this is the collusion that the low cost firm will decide the price and the outcome for this is that p 1 is equal to 80 is going to be followed in the market. If p 1 is going to be 80 followed in the market what is the outcome? Outcome is there is a reduction in the profit by reduction in the profit by firm 2. And what will be the reduction if you calculate the profit by taking the price 80 and 84 the profit will reduce from 26 to 22. So, this is the outcome the reduction in the profit is the outcome for the firm 2 if they are following a low cost firm. But here if you look at what is the arrangement? The arrangement is that low cost firm has to follow the the high cost firm has to follow that whatever the price decided by the low cost firm. Because the when they are getting into an agreement they are colluding to get them maybe the market share to maximize the joint profit the agreement is that the low cost firm has to decide the price. Then we will go to the next kind of price leadership model and the next kind of price leadership leadership model is where the price is set by the dominant firm. So, in this case the price leadership typically in this form of oligopoly here one dominant firm sets price and all the smaller firm in the industry follow its pricing policy. So, one firm is going to typically the dominant firm they are going to decide the price and other firms they are going to follow it. Now, before going into the detail that what is the outcome or how the price output of the other firms get affected will understand what is the meaning of a dominant firm, how the firm become emerge as a dominant leader and what is their trait when they become the dominant firm in the market. So, if you look at the first feature of oligopoly we say that even if there are large number of firms in the oligopoly at least few of them have to lead the market or few of them have to dominate the market light at least two of them should have the having the largest market share in the typical market. So, oligopoly market is dominated by few firms among the one way one may be the larger player at least one or two have to the larger player. So, if you take the example when you talk about a search search engine Google is the largest market share, when you talk about a cheap Intel is the largest market share, when you talk about a mobile phone Nokia is the largest market share, when you talk about the PC segment IBM is the IBM is the largest market player, when you talk about at least before the liberalization when you talk about the car industry Marathi was having the highest market share, when you talk about a steel furniture Godrej is having the larger player. So, in all this segment if you look at there are many firms, but when it comes to the larger player they are the larger player in their own segment and that is why they emerge as a dominant firm, because they are having a largest market share as compared to the other firm those were having a smaller market share. The other firms here what is the basic or what is the success of this dominant firm depends, the other firms acknowledge the leadership of the largest firm for the price determination. So, when it comes to dominant firm even if they are the large they have the largest market share they are the large firm in the market, the other firms should accept them as the large firm or the other firm should acknowledge when they are when they are giving the or when they are fixing up the price the other firm should follow it and in other way we can say that the other firms have to accept this firm as the large market share then only they will follow the price whatever decided by the dominant firm. So, dominant firm is a leader in term of market share or presence in all segment or just being the pioneer in the particular product agency product category. So, dominant firm may be the leader in term of the market share either they are having a maximum market share or they are presence in all the segment or just being a pioneer in the particular product category in all these three when they are having this all these three characteristics or one of these three characteristics they can be the dominant firm. So, this dominant firm is very or if they are getting into a leader they have to very large in size an economies of scale produce optimum output at which he is able to maximize the return. So, this price leaders or the dominant firm has to be very large in size and they have to earn economies of scale then only they can consider as the dominant firm because they are having a large market share and they are getting the profit and they should produce at the optimum output they should not produce at a output level where which leaves some excess capacity for the firm. When it comes to a trade of the dominant firm the dominant firm can be either benevolent or they can be the exploitative firm either they can be benevolent for the other firms in the market or they can be the exploitative in firm in the market. Now, who are the who is a benevolent firm or who are the benevolent firm? The benevolent firm allow other firm to exist by fixing of a price at which small firm may also sell. So, when it if the dominant or the market leader is the benevolent firm their trade says that if they are fixing of a price they fix at that level where even the small firm can also survive. So, they generally fix up with the price which is above the marginal cost of the small firms then only that that will actually leads the small firm to survive in the market or that price leads the firms to get some amount of the profit at specifically the small firms in the market to get some amount of the profit. Now, how the firms they become a benevolent firm? Because all the dominant firm they are not the benevolent firms some firms they are there some some dominance firm are there they generally the exploit other firms taking the cue from their the dominant firm or taking the cue that they are the large firm in the market. Now, what situation leads to this creation of this benevolent firm? It leads other exist. So, it does not have to face allegation of the monopoly creation. So, if someone is having a 90 percent share rather than getting into the allegation that they are trying to monopolize they become nice to the other small firms and they allow them to survive in that way they also avoid the allegation of the monopoly creation and they become emerge as a benevolent trader because they allow the small firm to stay in the market. So, one way to get away from the allegation of the monopolization or the monopoly creation they become the benevolent firm. Second, it earn sufficient margin at the price and still remain market leadership. So, whatever the price they are charging they earn maximum or the sufficient margin at this price and still retain the market leadership and success of this type of leadership depends on the assumption that the other will follow the leader. So, when it comes to this price leadership by a dominant firm obviously, if we look at from the angle of small firm also they cannot compete directly with the large firm. So, in that case the only options available to them that they are following the leader and if they are following the leader may be the out of good will the if the dominant firm is a benevolent firm they will at least think about the small firm and they will fix up a price which is lower than the which is lower than their standard and by with that price at least the small firms getting some amount of the profit. Then the other category of dominant firm is the firm who exploits the small firms in the market. And how they how do they exploit the small firm in the market they fixes a price at which small inefficient player may not survive and thus it gains a large share of the market. So, in this case the firm set up a price to exploit the small firm and what they do they set a price in such a level where the small firm or the firm those who are not doing well in the last period they are going to get out of this market or they will get the they will get the exit out of this market. So, in this case the price whatever given by the firm that will not suit the small inefficient player in the market they will be out of the market and in this case the dominant firm become more dominant because they also get the share of the small firm those who have already exit out of this market. So, we will see the graphical explanation and algebraic explanation of this dominant firm. Generally graphically how we get the demand curve of the dominant firm how the supply curve gets gets extracted from the supply curve for the rest of the firm. And we will see how generally the small firms is whether it is suitable for them till how long the small firm will be there in the market at what stage generally they go out of this market. So, we will get a demand curve this is the market demand curve then we will get a supply curve and correspondingly we will get the price and this is the demand curve of the large firm this is the price. Then we will find out the this is the marginal revenue curve then we will get the marginal cost corresponding to marginal revenue and marginal cost we will get the price that is by the dominant firm that is P 2 this is P 3 this is P 1 this is E this we can call as P 2 dash this is our D D L and here we can call it as B 1 here we can call it as A this is our Q this is our O. So, let us understand this graph now this SS if you look at suppose we understand that there is one large firm and number of small firms. So, this supply curve if you look at this S you can call it SS dash this is the aggregate supply curve of the small firms this is not the aggregate this is here the supply of the dominant firm is not added this is the aggregate supply curve of only the small firms that is there in the market. And how we get this SS dash this is the horizontal summation of the marginal cost curve of all the small firms. This demand curve is the market demand curve where we have also added the demand for the dominant firm product. The difference between the horizontal difference between the demand curve and supply curve if you look at that will give us the demand between that will give us the demand by the dominant firm. So, if you look at in that through that we get the demand function that is D D L that is the demand function for the large firm or the demand function of the dominant firm. So, the horizontal distance between the supply curve and the supply curve of the small firms and the market demand curve that gives us the demand curve of the dominant firm. So, the if you look at the logic is very simple total demand is this much this is the total supply of the small firm. So, whatever the gap between the market demand and the supply of the small firms from there generally the immerse the demand curve for the large firm because the rest of the demand has to be given from the dominant firm. Now, price falls below at any point of time if the price falls below P 1 which is the market price decided on the basis of the supply curve of small one and the market demand. If price falls below P 1 generally the demand curve for the large firm increases because this is the market demand. This is the demand curve for the large firm. If price falls below this the demand curve for this dominant firm increases because once price decreases demand is more than the supply and that leaves the scope for the more demand for the dominant firm. Now, how we get the price P 2? We get the price P 2 following the marginal cost and marginal revenue rule. So, doing this we get this price P 2 and at this price P 2 the total demand is P 2 B and small firm supply only the amount here if you look at this is the P 2 A. So, here we can call it this is the B. So, at this price if the price fixed by marginal cost marginal revenue rule that is by the dominant firm because price has to set by dominant firm. This is the marginal revenue curve of the dominant firm this is the marginal cost function of the dominant firm taking this the price is decided by the dominant firm. If the price is decided by the dominant firm at this price small firm just supply this much because this is the supply curve for the small firm and the large firm they supply what is the large firm they supply large firm they supply AB. So, in this case if you look at this is the this has to be given for the demand for the dominant firm and in this case this is what they are going to this is the demand for the dominant firm and this is what they are going to supply. If the price is P 3 up to this if you look at the supply given by the small firm is 0 and at this point now this is entirely the demand for the large firm because the supply is not going to get by the small firm. So, the entire demand is get satisfied from the small firm from the large firm because small firm is not supplying anything when price is P 3. Any price below this P 3 supply curve for the small firm is not existing because this is the price beyond which the small firm is not going to supply in the market or small firm small firm is not going to sell in the market. So, that is the reason if you look at when the price is given by the dominant firm when the price leadership is by the dominant firm the amount what the supply the getting supplied by the small firm is less and the amount which is getting supplied by the large firm is more. So, that is how the dominant firm if they are deciding the price they are supplying more and the small firm is supplying less. So, now we will see numerically whether the share gets more by the large firm when they set the price and less by the small firm because they are just following the price or it gets a equal share or it gets at least a proportionate share. So, to summarize this how we can say this typically dominant firm the there is a market demand and the demand comes to all the firms in the market and we get the supply curve for the small firms on the where we do not consider the supply curve for the dominant firm. So, the the gap between the supply given by the small firms and the total market demand for the product that generally the demand curve for the dominant firm. So, we identify the demand curve from there we find out the marginal revenue curve we get the marginal cost curve this is the marginal cost curve on that basis we set the price. When the price set by the dominant firm this is the this is the amount of supply that comes from the dominant firm and this is the amount of supply that comes from the small firm and correspondingly if at any point of time if the dominant firm would like to if the dominant firm is going to exploit this number of small firms they will reduce the price and if they are reducing the price from P 2 to P 3 small firm is not supplying any more product in the market or they are not taking care of the demand market demand and that what they will do they will go out of this market and the large market or the dominant market they get all the share of the total market and they become the monopoly leader. So, in this case if you look at the if it is a benevolent firm they will not go beyond P 2 they will give at least small portion of the market to be shared by the small firms, but if they are if the firm if the dominant firm is not benevolent rather they are in the exploit in nature. So, they will prefer to charge the price P 3 which is much below P 2 because at this price the small firm will become inefficient they will not able to survive they will go out of the market and the entire market share will go to the large firm. So, here the trait of this dominant leader comes whether they are in a way to exploit the small firms or they are the benevolent leader because there it will make the difference that in this case this price leadership will lead to the monopoly situation or it will not lead to a monopoly situation. Then we will just take a numerical or algebraic solution to this dominant firm leader in order to understand that how the share gets divided between the dominant firm and the small firms. So, we will assume that there are six firms in the market. So, one is dominant firm and rest five is small firms. So, this is the total market demand that is 100 minus 2 P and Q S is the supply of the small firms, supply function of the small firms excluding the large firm. So, Q S is equal to 10 plus P this is the combined supply function. To find the equilibrium output or equilibrium without the dominant firm demand that is Q M has to be equal to Q S has to be equal to the supply and if you take Q M is equal to 100 minus 2 P and Q S is equal to 10 plus P we get 3 P is equal to 90 P is equal to 30. So, equilibrium price without the supply of the dominant firm we get P is equal to 30 and what will be the supply here? If you put the value of the P here then it is 10 plus P. So, that comes to 10 plus 30 which is equal to 40. How do you interpret this 40 now? This is this 40 is the total supply comes from this five small firms. So, once we know the market demand, once we know the total supply we can find out what is the demand for the dominant firm. So, total supply is 40 units. Now, we will find out what is the market demand and the difference will give us what is the demand for the dominant firm. So, total supply is by the small firm is equal to 40 units and price is equal to 30 units. Now, this is the demand function for the dominant firm. So, this is Q M minus Q S, Q M is the total market demand, Q S is the supply of the small firm. So, Q M minus Q S. So, this is 100 minus 2 P minus 40. So, 60 minus 2 P that is the demand function for the dominant firm. So, total cost for dominant firm is given that is 50 plus 60 Q D plus 0.25 Q D square. This is the total cost function. From here we can find out the marginal cost function for the dominant firm. So, that will come as 60 plus 0.5 Q D. From the demand function, we will try to find out the total revenue function. From total revenue function, we will find out the marginal revenue function. Just now we calculated the marginal cost function. So, we will follow the profit maximizing rule, the marginal cost marginal revenue rule in order to find out the price. So, to find this, we will find out total revenue for demand function. For this, we need the price this demand function for the dominated firm and also the price for the dominated firm. So, how to find out this price of D? This is 30 minus 0.5 Q D and how we got this because our Q D is equal to 60 minus 2 P. Then we will find this total revenue is equal to now 30 minus 0.5 Q D multiplied by Q D. So, that comes to 30 Q D minus 0.5 Q D square. This is the total revenue for dominated firm. Then we will find out the marginal revenue of dominated firm. That is derivative of total revenue with respect to D Q D and that comes to 30 minus Q D. This is the marginal revenue for D. So, we have a marginal cost function what we got previously. Now, we have the marginal revenue function. To find the price and quantity, now we will take the marginal cost and marginal revenue rule. So, at profit maximizing equilibrium, marginal cost of D has to be equal to the marginal revenue of D. So, 6 plus 0.5 Q D has to be equal to marginal revenue for D. That is 30 minus Q D. Then simplifying this, we can get 1.5 Q D is equal to 24 Q D is equal to 16. So, this is the demand that is quantity that has to be produced by dominant firm. This is the price. Price is again 30 minus 0.5 Q D. So, this will give 30 minus 0.5 16. So, this comes to 22. So, price is 22, quantity demanded is 16. Now, this price, this price 22 has to be accepted by the small firm because this is the price leadership model where there is the dominant firm has to be, has to set the price and small firm simply they have to follow this. So, taking this price now what will be the market demand? That is Q M. So, Q M is equal to 100 minus 2 P. So, that comes to 100 minus 44 that is come to 56. This is our total market demand. What is the market demand for the dominant firm? The market demand for the dominant firm is the 16 and this is the total market demand. So, rest this 56 minus 16 40 unit has to be supplied by the smaller firm. So, if you try to analyze the world from here, price is 22 that is followed by small firms and if the total market demand if you look at it is 56 out of this, if not even less than one third is supplied by the dominant firm and rest is supplied by the smaller firm. So, maybe we can say that this is a kind of a price leadership or the dominant leader is such that at least it is benevolent in nature because the firm is setting a price such that at least more than two third is getting supplied by the five smaller firm and the dominant firm itself with supplying only less than one third of the total market demand. So, at least from the result if you want to analyze and if you want to read between the line at least you can say that the price is set by the dominant firm which is benevolent in nature because he is just supplying less than one third of the total market demand and rest all is supplied by the smaller firms. So, in case of low cost firm, generally the low cost firm set the price, other firm follow it. In case of dominant firm, dominant firm set the price others they will follow it and the third category of the price leadership is if you look at it is the kind of more subjective in nature when we will find that there is no clear case of a low cost firm or no clear case of a dominant firm. In that case what model to be followed and in this case the model follow is price leadership by the barometric firm and here why the need comes from the barometric firm because there is no clear cut, clear cut emergence of a dominant firm or clear cut emergence of a low cost firm. So, there is evidence in the some market that there is no single player is so large to emerge as leader, but there may be one firm which has better understanding of the market. So, the firm may not be large in nature they are not operating in the large scale of operations, but when it comes to making a leader whether to make that firm as the leader they are considered to be the leader because at least they have a better understanding of the market. So, this firm acts like a barometer for the firms and why they are known as the barometer firm or the how why they are considered as the barometer of the market because they have the better industry intelligence and can preempt and reinterpret the external environment in an effective manner. So, suppose there is a change in the government policy, suppose there is a crisis, suppose there is an event which has some influence on the price and quantity combination or the demand of the market. So, in this case generally the barometric firm they get into a situation where they are the best judge to they are the best firm to judge the event and lead the price output decision on that manner. So, they are considered as the barometric firm and the the barometric firm should act as the leader they should decide the price and the other firms they have to simply follow this. So, either the so three kind of models or three kind of arrangement in case of a price leadership model either the price has to set by the low cost firm or the price has to set up by the dominant firm or the price has to set up by the barometric firm. So, in the last couple of session we discussed about a oligopoly market structure identifying two different kind of model one is collusive models another is the non-collusive model. Non-collusive model where the oligopoly firm they compete with each other and in case of collusive model they generally collude together to maximize the profit and also reduce uncertainty and in the way if it look at to look at that at least get some amount of the profit from the collusion. Next session we will see that how game theory generally helps or game theory as a tool helps the firms to or game theory as a tool helps the analysis to analyze the firm's behavior or the group behavior in the oligopoly market or typically how the economics of cooperation what comes from the group behavior of the oligopoly firm generally whether it is competition or whether it is collusion both are considered as the group behavior and next next class we will say game theory as a mathematical tool how it helps to identify both the economics of cooperation whether it is competition or whether it is collusion.