 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 a joint agreement among the oligopoly firms to maximize the profit and here generally the central agency decides 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 this will 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 discovered 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 may be 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 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 firm one is firm one and another firm 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 follow, 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 at 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 not into be the collusion they will go out of the collusion 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 collusion 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 Q1 is equal to 50 minus 0.5 P1, P1 is equal to 100 minus 2 Q1 this is for firm 1 then we will look for firm 2. So, for firm 2 Q2 is equal to 50 minus 0.5 P2 and from here we can find out this P2, P2 is equal to 100 minus 2 Q2 then we will take the cost function Tc1 is equal to 100 plus 20 Q1 plus 2 Q1 square and total cost 2 is equal to 48 plus 36 Q2 plus 2 Q2 square. So, Q2 is equal to 50 minus 0.5 P2, P2 is equal to 100 minus 2 Q2 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 P1 Q1. So, P1 is equal to 100 minus 2 Q1 multiplied by Q1. So, that comes to 100 Q1 minus 2 Q1 square. Marginal revenue will take as TTR1 with respect to Q1. So, that will continue or maybe we can find out the profit. Profit is total revenue 1 minus total cost 1. So, 100 Q1 minus 2 Q1 square which is our total revenue 1 minus 100 plus 20 Q1 square plus 2 Q1 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 Q1 minus 4 Q1 square minus 100 and we will take the first order of 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 Q1 equal to 0 and Q1 is equal to 10. So, if Q1 is equal to 10, P1 is equal to 100 minus 2 Q1. So, 100 minus 2 multiplied by 10 that will come to 80. So, P1 is equal to 80, Q1 is equal to 10. That is if the price is decided on the basis of the low cost firm P1 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 Q2 minus 2 Q2 square and pi 2 will be equal to 100 Q2 minus 2 Q2 square minus the total cost 2. So, that is 48. So, if we simplify this we get 64 Q2 minus 4 Q2 square minus 48 and we 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 Q2 has to be equal to 0. So, 8 Q2 is equal to 64 Q2 is equal to 8. This is the output for the firm 2. If you put the value of Q2 is equal to 0. So, Q2 is equal to 8 will get P2 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 get the price and the outcome for this is that the P1 is equal to 80 is going to be followed in the market. If P1 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 high cost firm has to follow that whatever the price decided by the low cost firm because when they are getting into an agreement they are colluding to get the maybe the market share or to maximize the joint profit the agreement is that the low cost firm has to decide the price.